9"""Z3 is a high performance theorem prover developed at Microsoft Research.
11Z3 is used in many applications such as: software/hardware verification and testing,
12constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13and geometrical problems.
16Please send feedback, comments and/or corrections on the Issue tracker for
17https://github.com/Z3prover/z3.git. Your comments are very valuable.
38... x = BitVec('x', 32)
40... # the expression x + y is type incorrect
42... except Z3Exception as ex:
43... print("failed: %s" % ex)
49from .z3consts
import *
50from .z3printer
import *
51from fractions
import Fraction
56if sys.version_info.major >= 3:
57 from typing
import Iterable
67if sys.version_info.major < 3:
69 return isinstance(v, (int, long))
72 return isinstance(v, int)
84 major = ctypes.c_uint(0)
85 minor = ctypes.c_uint(0)
86 build = ctypes.c_uint(0)
87 rev = ctypes.c_uint(0)
89 return "%s.%s.%s" % (major.value, minor.value, build.value)
93 major = ctypes.c_uint(0)
94 minor = ctypes.c_uint(0)
95 build = ctypes.c_uint(0)
96 rev = ctypes.c_uint(0)
98 return (major.value, minor.value, build.value, rev.value)
107 raise Z3Exception(msg)
111 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
115 """Log interaction to a file. This function must be invoked immediately after init(). """
120 """Append user-defined string to interaction log. """
125 """Convert an integer or string into a Z3 symbol."""
133 """Convert a Z3 symbol back into a Python object. """
146 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
148 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
149 return [arg
for arg
in args[0]]
160 if isinstance(args, (set, AstVector, tuple)):
161 return [arg
for arg
in args]
169 if isinstance(val, bool):
170 return "true" if val
else "false"
181 """A Context manages all other Z3 objects, global configuration options, etc.
183 Z3Py uses a default global context. For most applications this is sufficient.
184 An application may use multiple Z3 contexts. Objects created in one context
185 cannot be used in another one. However, several objects may be "translated" from
186 one context to another. It is not safe to access Z3 objects from multiple threads.
187 The only exception is the method `interrupt()` that can be used to interrupt() a long
189 The initialization method receives global configuration options for the new context.
194 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
213 if Z3_del_context
is not None and self.
owner:
219 """Return a reference to the actual C pointer to the Z3 context."""
223 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
225 This method can be invoked from a thread different from the one executing the
226 interruptible procedure.
231 """Return the global parameter description set."""
240 """Return a reference to the global Z3 context.
243 >>> x.ctx == main_ctx()
248 >>> x2 = Real('x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
274 >>> set_param(precision=10)
277 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
281 if not set_pp_option(k, v):
296 """Reset all global (or module) parameters.
302 """Alias for 'set_param' for backward compatibility.
308 """Return the value of a Z3 global (or module) parameter
310 >>> get_param('nlsat.reorder')
313 ptr = (ctypes.c_char_p * 1)()
315 r = z3core._to_pystr(ptr[0])
317 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
329 """Superclass for all Z3 objects that have support for pretty printing."""
335 in_html = in_html_mode()
338 set_html_mode(in_html)
343 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
351 if self.
ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
359 return obj_to_string(self)
362 return obj_to_string(self)
365 return self.
eq(other)
378 elif is_eq(self)
and self.num_args() == 2:
379 return self.arg(0).
eq(self.arg(1))
381 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
384 """Return a string representing the AST node in s-expression notation.
387 >>> ((x + 1)*x).sexpr()
393 """Return a pointer to the corresponding C Z3_ast object."""
397 """Return unique identifier for object. It can be used for hash-tables and maps."""
401 """Return a reference to the C context where this AST node is stored."""
402 return self.
ctx.ref()
405 """Return `True` if `self` and `other` are structurally identical.
412 >>> n1 = simplify(n1)
413 >>> n2 = simplify(n2)
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
428 >>> # Nodes in different contexts can't be mixed.
429 >>> # However, we can translate nodes from one context to another.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
443 >>> n1 = simplify(Int('x') + 1)
444 >>> n2 = simplify(2 + Int('x') - 1)
445 >>> n1.hash() == n2.hash()
451 """Return a Python value that is equivalent to `self`."""
456 """Return `True` if `a` is an AST node.
460 >>> is_ast(IntVal(10))
464 >>> is_ast(BoolSort())
466 >>> is_ast(Function('f', IntSort(), IntSort()))
473 return isinstance(a, AstRef)
477 """Return `True` if `a` and `b` are structurally identical AST nodes.
487 >>> eq(simplify(x + 1), simplify(1 + x))
521 _args = (FuncDecl * sz)()
523 _args[i] = args[i].as_func_decl()
531 _args[i] = args[i].as_ast()
539 _args[i] = args[i].as_ast()
547 elif k == Z3_FUNC_DECL_AST:
564 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
573 """Return the Z3 internal kind of a sort.
574 This method can be used to test if `self` is one of the Z3 builtin sorts.
577 >>> b.kind() == Z3_BOOL_SORT
579 >>> b.kind() == Z3_INT_SORT
581 >>> A = ArraySort(IntSort(), IntSort())
582 >>> A.kind() == Z3_ARRAY_SORT
584 >>> A.kind() == Z3_INT_SORT
590 """Return `True` if `self` is a subsort of `other`.
592 >>> IntSort().subsort(RealSort())
598 """Try to cast `val` as an element of sort `self`.
600 This method is used in Z3Py to convert Python objects such as integers,
601 floats, longs and strings into Z3 expressions.
604 >>> RealSort().cast(x)
613 """Return the name (string) of sort `self`.
615 >>> BoolSort().name()
617 >>> ArraySort(IntSort(), IntSort()).name()
623 """Return `True` if `self` and `other` are the same Z3 sort.
626 >>> p.sort() == BoolSort()
628 >>> p.sort() == IntSort()
636 """Return `True` if `self` and `other` are not the same Z3 sort.
639 >>> p.sort() != BoolSort()
641 >>> p.sort() != IntSort()
648 return AstRef.__hash__(self)
652 """Return `True` if `s` is a Z3 sort.
654 >>> is_sort(IntSort())
656 >>> is_sort(Int('x'))
658 >>> is_expr(Int('x'))
661 return isinstance(s, SortRef)
666 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
668 if k == Z3_BOOL_SORT:
670 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
672 elif k == Z3_BV_SORT:
674 elif k == Z3_ARRAY_SORT:
676 elif k == Z3_DATATYPE_SORT:
678 elif k == Z3_FINITE_DOMAIN_SORT:
680 elif k == Z3_FLOATING_POINT_SORT:
682 elif k == Z3_ROUNDING_MODE_SORT:
684 elif k == Z3_RE_SORT:
686 elif k == Z3_SEQ_SORT:
688 elif k == Z3_CHAR_SORT:
690 elif k == Z3_TYPE_VAR:
700 """Create a new uninterpreted sort named `name`.
702 If `ctx=None`, then the new sort is declared in the global Z3Py context.
704 >>> A = DeclareSort('A')
705 >>> a = Const('a', A)
706 >>> b = Const('b', A)
718 """Type variable reference"""
728 """Create a new type variable named `name`.
730 If `ctx=None`, then the new sort is declared in the global Z3Py context.
745 """Function declaration. Every constant and function have an associated declaration.
747 The declaration assigns a name, a sort (i.e., type), and for function
748 the sort (i.e., type) of each of its arguments. Note that, in Z3,
749 a constant is a function with 0 arguments.
762 """Return the name of the function declaration `self`.
764 >>> f = Function('f', IntSort(), IntSort())
767 >>> isinstance(f.name(), str)
773 """Return the number of arguments of a function declaration.
774 If `self` is a constant, then `self.arity()` is 0.
776 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
783 """Return the sort of the argument `i` of a function declaration.
784 This method assumes that `0 <= i < self.arity()`.
786 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
795 """Return the sort of the range of a function declaration.
796 For constants, this is the sort of the constant.
798 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
805 """Return the internal kind of a function declaration.
806 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
809 >>> d = (x + 1).decl()
810 >>> d.kind() == Z3_OP_ADD
812 >>> d.kind() == Z3_OP_MUL
820 result = [
None for i
in range(n)]
823 if k == Z3_PARAMETER_INT:
825 elif k == Z3_PARAMETER_DOUBLE:
827 elif k == Z3_PARAMETER_RATIONAL:
829 elif k == Z3_PARAMETER_SYMBOL:
831 elif k == Z3_PARAMETER_SORT:
833 elif k == Z3_PARAMETER_AST:
835 elif k == Z3_PARAMETER_FUNC_DECL:
837 elif k == Z3_PARAMETER_INTERNAL:
838 result[i] =
"internal parameter"
839 elif k == Z3_PARAMETER_ZSTRING:
840 result[i] =
"internal string"
846 """Create a Z3 application expression using the function `self`, and the given arguments.
848 The arguments must be Z3 expressions. This method assumes that
849 the sorts of the elements in `args` match the sorts of the
850 domain. Limited coercion is supported. For example, if
851 args[0] is a Python integer, and the function expects a Z3
852 integer, then the argument is automatically converted into a
855 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
865 _args = (Ast * num)()
870 tmp = self.
domain(i).cast(args[i])
872 _args[i] = tmp.as_ast()
877 """Return `True` if `a` is a Z3 function declaration.
879 >>> f = Function('f', IntSort(), IntSort())
886 return isinstance(a, FuncDeclRef)
890 """Create a new Z3 uninterpreted function with the given sorts.
892 >>> f = Function('f', IntSort(), IntSort())
898 _z3_assert(len(sig) > 0,
"At least two arguments expected")
903 dom = (Sort * arity)()
904 for i
in range(arity):
913 """Create a new fresh Z3 uninterpreted function with the given sorts.
917 _z3_assert(len(sig) > 0,
"At least two arguments expected")
922 dom = (z3.Sort * arity)()
923 for i
in range(arity):
936 """Create a new Z3 recursive with the given sorts."""
939 _z3_assert(len(sig) > 0,
"At least two arguments expected")
944 dom = (Sort * arity)()
945 for i
in range(arity):
954 """Set the body of a recursive function.
955 Recursive definitions can be simplified if they are applied to ground
958 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
959 >>> n = Int('n', ctx)
960 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
963 >>> s = Solver(ctx=ctx)
964 >>> s.add(fac(n) < 3)
967 >>> s.model().eval(fac(5))
977 _args[i] = args[i].ast
988 """Constraints, formulas and terms are expressions in Z3.
990 Expressions are ASTs. Every expression has a sort.
991 There are three main kinds of expressions:
992 function applications, quantifiers and bounded variables.
993 A constant is a function application with 0 arguments.
994 For quantifier free problems, all expressions are
995 function applications.
1005 """Return the sort of expression `self`.
1017 """Shorthand for `self.sort().kind()`.
1019 >>> a = Array('a', IntSort(), IntSort())
1020 >>> a.sort_kind() == Z3_ARRAY_SORT
1022 >>> a.sort_kind() == Z3_INT_SORT
1028 """Return a Z3 expression that represents the constraint `self == other`.
1030 If `other` is `None`, then this method simply returns `False`.
1046 return AstRef.__hash__(self)
1049 """Return a Z3 expression that represents the constraint `self != other`.
1051 If `other` is `None`, then this method simply returns `True`.
1070 """Return the Z3 function declaration associated with a Z3 application.
1072 >>> f = Function('f', IntSort(), IntSort())
1085 """Return the Z3 internal kind of a function application."""
1092 """Return the number of arguments of a Z3 application.
1096 >>> (a + b).num_args()
1098 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1108 """Return argument `idx` of the application `self`.
1110 This method assumes that `self` is a function application with at least `idx+1` arguments.
1114 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1129 """Return a list containing the children of the given expression
1133 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1139 return [self.
arg(i)
for i
in range(self.
num_args())]
1153 """inverse function to the serialize method on ExprRef.
1154 It is made available to make it easier for users to serialize expressions back and forth between
1155 strings. Solvers can be serialized using the 'sexpr()' method.
1159 if len(s.assertions()) != 1:
1160 raise Z3Exception(
"single assertion expected")
1161 fml = s.assertions()[0]
1162 if fml.num_args() != 1:
1163 raise Z3Exception(
"dummy function 'F' expected")
1167 if isinstance(a, Pattern):
1171 if k == Z3_QUANTIFIER_AST:
1174 if sk == Z3_BOOL_SORT:
1176 if sk == Z3_INT_SORT:
1177 if k == Z3_NUMERAL_AST:
1180 if sk == Z3_REAL_SORT:
1181 if k == Z3_NUMERAL_AST:
1186 if sk == Z3_BV_SORT:
1187 if k == Z3_NUMERAL_AST:
1191 if sk == Z3_ARRAY_SORT:
1193 if sk == Z3_DATATYPE_SORT:
1195 if sk == Z3_FLOATING_POINT_SORT:
1199 return FPRef(a, ctx)
1200 if sk == Z3_FINITE_DOMAIN_SORT:
1201 if k == Z3_NUMERAL_AST:
1205 if sk == Z3_ROUNDING_MODE_SORT:
1207 if sk == Z3_SEQ_SORT:
1209 if sk == Z3_CHAR_SORT:
1211 if sk == Z3_RE_SORT:
1212 return ReRef(a, ctx)
1229 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1239 if isinstance(a, str)
and isinstance(b, SeqRef):
1241 if isinstance(b, str)
and isinstance(a, SeqRef):
1243 if isinstance(a, float)
and isinstance(b, ArithRef):
1245 if isinstance(b, float)
and isinstance(a, ArithRef):
1258 for element
in sequence:
1259 result = func(result, element)
1270 alist = [
_py2expr(a, ctx)
for a
in alist]
1271 s =
_reduce(_coerce_expr_merge, alist,
None)
1272 return [s.cast(a)
for a
in alist]
1276 """Return `True` if `a` is a Z3 expression.
1283 >>> is_expr(IntSort())
1287 >>> is_expr(IntVal(1))
1290 >>> is_expr(ForAll(x, x >= 0))
1292 >>> is_expr(FPVal(1.0))
1295 return isinstance(a, ExprRef)
1299 """Return `True` if `a` is a Z3 function application.
1301 Note that, constants are function applications with 0 arguments.
1308 >>> is_app(IntSort())
1312 >>> is_app(IntVal(1))
1315 >>> is_app(ForAll(x, x >= 0))
1318 if not isinstance(a, ExprRef):
1321 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1325 """Return `True` if `a` is Z3 constant/variable expression.
1334 >>> is_const(IntVal(1))
1337 >>> is_const(ForAll(x, x >= 0))
1340 return is_app(a)
and a.num_args() == 0
1344 """Return `True` if `a` is variable.
1346 Z3 uses de-Bruijn indices for representing bound variables in
1354 >>> f = Function('f', IntSort(), IntSort())
1355 >>> # Z3 replaces x with bound variables when ForAll is executed.
1356 >>> q = ForAll(x, f(x) == x)
1362 >>> is_var(b.arg(1))
1369 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1377 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1378 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1379 >>> q = ForAll([x, y], f(x, y) == x + y)
1381 f(Var(1), Var(0)) == Var(1) + Var(0)
1385 >>> v1 = b.arg(0).arg(0)
1386 >>> v2 = b.arg(0).arg(1)
1391 >>> get_var_index(v1)
1393 >>> get_var_index(v2)
1402 """Return `True` if `a` is an application of the given kind `k`.
1406 >>> is_app_of(n, Z3_OP_ADD)
1408 >>> is_app_of(n, Z3_OP_MUL)
1411 return is_app(a)
and a.kind() == k
1414def If(a, b, c, ctx=None):
1415 """Create a Z3 if-then-else expression.
1419 >>> max = If(x > y, x, y)
1425 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1426 return Cond(a, b, c, ctx)
1433 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1438 """Create a Z3 distinct expression.
1445 >>> Distinct(x, y, z)
1447 >>> simplify(Distinct(x, y, z))
1449 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1450 And(Not(x == y), Not(x == z), Not(y == z))
1455 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1464 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1465 args[0] = a.as_ast()
1466 args[1] = b.as_ast()
1467 return f(a.ctx.ref(), 2, args)
1471 """Create a constant of the given sort.
1473 >>> Const('x', IntSort())
1477 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1483 """Create several constants of the given sort.
1485 `names` is a string containing the names of all constants to be created.
1486 Blank spaces separate the names of different constants.
1488 >>> x, y, z = Consts('x y z', IntSort())
1492 if isinstance(names, str):
1493 names = names.split(
" ")
1494 return [
Const(name, sort)
for name
in names]
1498 """Create a fresh constant of a specified sort"""
1504 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1505 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1508 >>> Var(0, IntSort())
1510 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1520 Create a real free variable. Free variables are used to create quantified formulas.
1521 They are also used to create polynomials.
1531 Create a list of Real free variables.
1532 The variables have ids: 0, 1, ..., n-1
1534 >>> x0, x1, x2, x3 = RealVarVector(4)
1538 return [
RealVar(i, ctx)
for i
in range(n)]
1551 """Try to cast `val` as a Boolean.
1553 >>> x = BoolSort().cast(True)
1563 if isinstance(val, bool):
1567 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1569 if not self.
eq(val.sort()):
1570 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1574 return isinstance(other, ArithSortRef)
1584 """All Boolean expressions are instances of this class."""
1590 if isinstance(other, BoolRef):
1591 other =
If(other, 1, 0)
1592 return If(self, 1, 0) + other
1601 """Create the Z3 expression `self * other`.
1603 if isinstance(other, int)
and other == 1:
1604 return If(self, 1, 0)
1605 if isinstance(other, int)
and other == 0:
1607 if isinstance(other, BoolRef):
1608 other =
If(other, 1, 0)
1609 return If(self, other, 0)
1612 return And(self, other)
1615 return Or(self, other)
1618 return Xor(self, other)
1634 """Return `True` if `a` is a Z3 Boolean expression.
1640 >>> is_bool(And(p, q))
1648 return isinstance(a, BoolRef)
1652 """Return `True` if `a` is the Z3 true expression.
1657 >>> is_true(simplify(p == p))
1662 >>> # True is a Python Boolean expression
1670 """Return `True` if `a` is the Z3 false expression.
1677 >>> is_false(BoolVal(False))
1684 """Return `True` if `a` is a Z3 and expression.
1686 >>> p, q = Bools('p q')
1687 >>> is_and(And(p, q))
1689 >>> is_and(Or(p, q))
1696 """Return `True` if `a` is a Z3 or expression.
1698 >>> p, q = Bools('p q')
1701 >>> is_or(And(p, q))
1708 """Return `True` if `a` is a Z3 implication expression.
1710 >>> p, q = Bools('p q')
1711 >>> is_implies(Implies(p, q))
1713 >>> is_implies(And(p, q))
1720 """Return `True` if `a` is a Z3 not expression.
1732 """Return `True` if `a` is a Z3 equality expression.
1734 >>> x, y = Ints('x y')
1742 """Return `True` if `a` is a Z3 distinct expression.
1744 >>> x, y, z = Ints('x y z')
1745 >>> is_distinct(x == y)
1747 >>> is_distinct(Distinct(x, y, z))
1754 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1758 >>> p = Const('p', BoolSort())
1761 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1764 >>> is_bool(r(0, 1))
1772 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1776 >>> is_true(BoolVal(True))
1780 >>> is_false(BoolVal(False))
1791 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1803 """Return a tuple of Boolean constants.
1805 `names` is a single string containing all names separated by blank spaces.
1806 If `ctx=None`, then the global context is used.
1808 >>> p, q, r = Bools('p q r')
1809 >>> And(p, Or(q, r))
1813 if isinstance(names, str):
1814 names = names.split(
" ")
1815 return [
Bool(name, ctx)
for name
in names]
1819 """Return a list of Boolean constants of size `sz`.
1821 The constants are named using the given prefix.
1822 If `ctx=None`, then the global context is used.
1824 >>> P = BoolVector('p', 3)
1828 And(p__0, p__1, p__2)
1830 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1834 """Return a fresh Boolean constant in the given context using the given prefix.
1836 If `ctx=None`, then the global context is used.
1838 >>> b1 = FreshBool()
1839 >>> b2 = FreshBool()
1848 """Create a Z3 implies expression.
1850 >>> p, q = Bools('p q')
1862 """Create a Z3 Xor expression.
1864 >>> p, q = Bools('p q')
1867 >>> simplify(Xor(p, q))
1878 """Create a Z3 not expression or probe.
1883 >>> simplify(Not(Not(p)))
1904 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1912 """Create a Z3 and-expression or and-probe.
1914 >>> p, q, r = Bools('p q r')
1917 >>> P = BoolVector('p', 5)
1919 And(p__0, p__1, p__2, p__3, p__4)
1923 last_arg = args[len(args) - 1]
1924 if isinstance(last_arg, Context):
1925 ctx = args[len(args) - 1]
1926 args = args[:len(args) - 1]
1927 elif len(args) == 1
and isinstance(args[0], AstVector):
1929 args = [a
for a
in args[0]]
1935 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1945 """Create a Z3 or-expression or or-probe.
1947 >>> p, q, r = Bools('p q r')
1950 >>> P = BoolVector('p', 5)
1952 Or(p__0, p__1, p__2, p__3, p__4)
1956 last_arg = args[len(args) - 1]
1957 if isinstance(last_arg, Context):
1958 ctx = args[len(args) - 1]
1959 args = args[:len(args) - 1]
1960 elif len(args) == 1
and isinstance(args[0], AstVector):
1962 args = [a
for a
in args[0]]
1968 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1984 """Patterns are hints for quantifier instantiation.
1996 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
1998 >>> f = Function('f', IntSort(), IntSort())
2000 >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
2002 ForAll(x, f(x) == 0)
2003 >>> q.num_patterns()
2005 >>> is_pattern(q.pattern(0))
2010 return isinstance(a, PatternRef)
2014 """Create a Z3 multi-pattern using the given expressions `*args`
2016 >>> f = Function('f', IntSort(), IntSort())
2017 >>> g = Function('g', IntSort(), IntSort())
2019 >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
2021 ForAll(x, f(x) != g(x))
2022 >>> q.num_patterns()
2024 >>> is_pattern(q.pattern(0))
2027 MultiPattern(f(Var(0)), g(Var(0)))
2030 _z3_assert(len(args) > 0,
"At least one argument expected")
2051 """Universally and Existentially quantified formulas."""
2060 """Return the Boolean sort or sort of Lambda."""
2066 """Return `True` if `self` is a universal quantifier.
2068 >>> f = Function('f', IntSort(), IntSort())
2070 >>> q = ForAll(x, f(x) == 0)
2073 >>> q = Exists(x, f(x) != 0)
2080 """Return `True` if `self` is an existential quantifier.
2082 >>> f = Function('f', IntSort(), IntSort())
2084 >>> q = ForAll(x, f(x) == 0)
2087 >>> q = Exists(x, f(x) != 0)
2094 """Return `True` if `self` is a lambda expression.
2096 >>> f = Function('f', IntSort(), IntSort())
2098 >>> q = Lambda(x, f(x))
2101 >>> q = Exists(x, f(x) != 0)
2108 """Return the Z3 expression `self[arg]`.
2115 """Return the weight annotation of `self`.
2117 >>> f = Function('f', IntSort(), IntSort())
2119 >>> q = ForAll(x, f(x) == 0)
2122 >>> q = ForAll(x, f(x) == 0, weight=10)
2129 """Return the skolem id of `self`.
2134 """Return the quantifier id of `self`.
2139 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2141 >>> f = Function('f', IntSort(), IntSort())
2142 >>> g = Function('g', IntSort(), IntSort())
2144 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2145 >>> q.num_patterns()
2151 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2153 >>> f = Function('f', IntSort(), IntSort())
2154 >>> g = Function('g', IntSort(), IntSort())
2156 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2157 >>> q.num_patterns()
2169 """Return the number of no-patterns."""
2173 """Return a no-pattern."""
2179 """Return the expression being quantified.
2181 >>> f = Function('f', IntSort(), IntSort())
2183 >>> q = ForAll(x, f(x) == 0)
2190 """Return the number of variables bounded by this quantifier.
2192 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2195 >>> q = ForAll([x, y], f(x, y) >= x)
2202 """Return a string representing a name used when displaying the quantifier.
2204 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2207 >>> q = ForAll([x, y], f(x, y) >= x)
2218 """Return the sort of a bound variable.
2220 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2223 >>> q = ForAll([x, y], f(x, y) >= x)
2234 """Return a list containing a single element self.body()
2236 >>> f = Function('f', IntSort(), IntSort())
2238 >>> q = ForAll(x, f(x) == 0)
2242 return [self.
body()]
2246 """Return `True` if `a` is a Z3 quantifier.
2248 >>> f = Function('f', IntSort(), IntSort())
2250 >>> q = ForAll(x, f(x) == 0)
2251 >>> is_quantifier(q)
2253 >>> is_quantifier(f(x))
2256 return isinstance(a, QuantifierRef)
2259def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2264 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2275 _vs = (Ast * num_vars)()
2276 for i
in range(num_vars):
2278 _vs[i] = vs[i].as_ast()
2280 num_pats = len(patterns)
2281 _pats = (Pattern * num_pats)()
2282 for i
in range(num_pats):
2283 _pats[i] = patterns[i].ast
2290 num_no_pats, _no_pats,
2291 body.as_ast()), ctx)
2294def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2295 """Create a Z3 forall formula.
2297 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2299 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2302 >>> ForAll([x, y], f(x, y) >= x)
2303 ForAll([x, y], f(x, y) >= x)
2304 >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2305 ForAll([x, y], f(x, y) >= x)
2306 >>> ForAll([x, y], f(x, y) >= x, weight=10)
2307 ForAll([x, y], f(x, y) >= x)
2309 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2312def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2313 """Create a Z3 exists formula.
2315 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2318 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2321 >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
2323 Exists([x, y], f(x, y) >= x)
2324 >>> is_quantifier(q)
2326 >>> r = Tactic('nnf')(q).as_expr()
2327 >>> is_quantifier(r)
2330 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2334 """Create a Z3 lambda expression.
2336 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2337 >>> mem0 = Array('mem0', IntSort(), IntSort())
2338 >>> lo, hi, e, i = Ints('lo hi e i')
2339 >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
2341 Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
2347 _vs = (Ast * num_vars)()
2348 for i
in range(num_vars):
2350 _vs[i] = vs[i].as_ast()
2361 """Real and Integer sorts."""
2364 """Return `True` if `self` is of the sort Real.
2369 >>> (x + 1).is_real()
2375 return self.
kind() == Z3_REAL_SORT
2378 """Return `True` if `self` is of the sort Integer.
2383 >>> (x + 1).is_int()
2389 return self.
kind() == Z3_INT_SORT
2395 """Return `True` if `self` is a subsort of `other`."""
2399 """Try to cast `val` as an Integer or Real.
2401 >>> IntSort().cast(10)
2403 >>> is_int(IntSort().cast(10))
2407 >>> RealSort().cast(10)
2409 >>> is_real(RealSort().cast(10))
2418 if val_s.is_int()
and self.
is_real():
2420 if val_s.is_bool()
and self.
is_int():
2421 return If(val, 1, 0)
2422 if val_s.is_bool()
and self.
is_real():
2425 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2432 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2437 """Return `True` if s is an arithmetical sort (type).
2439 >>> is_arith_sort(IntSort())
2441 >>> is_arith_sort(RealSort())
2443 >>> is_arith_sort(BoolSort())
2445 >>> n = Int('x') + 1
2446 >>> is_arith_sort(n.sort())
2449 return isinstance(s, ArithSortRef)
2453 """Integer and Real expressions."""
2456 """Return the sort (type) of the arithmetical expression `self`.
2460 >>> (Real('x') + 1).sort()
2466 """Return `True` if `self` is an integer expression.
2471 >>> (x + 1).is_int()
2474 >>> (x + y).is_int()
2480 """Return `True` if `self` is an real expression.
2485 >>> (x + 1).is_real()
2491 """Create the Z3 expression `self + other`.
2504 """Create the Z3 expression `other + self`.
2514 """Create the Z3 expression `self * other`.
2523 if isinstance(other, BoolRef):
2524 return If(other, self, 0)
2529 """Create the Z3 expression `other * self`.
2539 """Create the Z3 expression `self - other`.
2552 """Create the Z3 expression `other - self`.
2562 """Create the Z3 expression `self**other` (** is the power operator).
2569 >>> simplify(IntVal(2)**8)
2576 """Create the Z3 expression `other**self` (** is the power operator).
2583 >>> simplify(2**IntVal(8))
2590 """Create the Z3 expression `other/self`.
2613 """Create the Z3 expression `other/self`."""
2617 """Create the Z3 expression `other/self`.
2634 """Create the Z3 expression `other/self`."""
2638 """Create the Z3 expression `other%self`.
2644 >>> simplify(IntVal(10) % IntVal(3))
2649 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2653 """Create the Z3 expression `other%self`.
2661 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2665 """Return an expression representing `-self`.
2685 """Create the Z3 expression `other <= self`.
2687 >>> x, y = Ints('x y')
2698 """Create the Z3 expression `other < self`.
2700 >>> x, y = Ints('x y')
2711 """Create the Z3 expression `other > self`.
2713 >>> x, y = Ints('x y')
2724 """Create the Z3 expression `other >= self`.
2726 >>> x, y = Ints('x y')
2738 """Return `True` if `a` is an arithmetical expression.
2747 >>> is_arith(IntVal(1))
2755 return isinstance(a, ArithRef)
2759 """Return `True` if `a` is an integer expression.
2766 >>> is_int(IntVal(1))
2778 """Return `True` if `a` is a real expression.
2790 >>> is_real(RealVal(1))
2805 """Return `True` if `a` is an integer value of sort Int.
2807 >>> is_int_value(IntVal(1))
2811 >>> is_int_value(Int('x'))
2813 >>> n = Int('x') + 1
2818 >>> is_int_value(n.arg(1))
2820 >>> is_int_value(RealVal("1/3"))
2822 >>> is_int_value(RealVal(1))
2829 """Return `True` if `a` is rational value of sort Real.
2831 >>> is_rational_value(RealVal(1))
2833 >>> is_rational_value(RealVal("3/5"))
2835 >>> is_rational_value(IntVal(1))
2837 >>> is_rational_value(1)
2839 >>> n = Real('x') + 1
2842 >>> is_rational_value(n.arg(1))
2844 >>> is_rational_value(Real('x'))
2851 """Return `True` if `a` is an algebraic value of sort Real.
2853 >>> is_algebraic_value(RealVal("3/5"))
2855 >>> n = simplify(Sqrt(2))
2858 >>> is_algebraic_value(n)
2865 """Return `True` if `a` is an expression of the form b + c.
2867 >>> x, y = Ints('x y')
2877 """Return `True` if `a` is an expression of the form b * c.
2879 >>> x, y = Ints('x y')
2889 """Return `True` if `a` is an expression of the form b - c.
2891 >>> x, y = Ints('x y')
2901 """Return `True` if `a` is an expression of the form b / c.
2903 >>> x, y = Reals('x y')
2908 >>> x, y = Ints('x y')
2918 """Return `True` if `a` is an expression of the form b div c.
2920 >>> x, y = Ints('x y')
2930 """Return `True` if `a` is an expression of the form b % c.
2932 >>> x, y = Ints('x y')
2942 """Return `True` if `a` is an expression of the form b <= c.
2944 >>> x, y = Ints('x y')
2954 """Return `True` if `a` is an expression of the form b < c.
2956 >>> x, y = Ints('x y')
2966 """Return `True` if `a` is an expression of the form b >= c.
2968 >>> x, y = Ints('x y')
2978 """Return `True` if `a` is an expression of the form b > c.
2980 >>> x, y = Ints('x y')
2990 """Return `True` if `a` is an expression of the form IsInt(b).
2993 >>> is_is_int(IsInt(x))
3002 """Return `True` if `a` is an expression of the form ToReal(b).
3017 """Return `True` if `a` is an expression of the form ToInt(b).
3032 """Integer values."""
3035 """Return a Z3 integer numeral as a Python long (bignum) numeral.
3048 """Return a Z3 integer numeral as a Python string.
3056 """Return a Z3 integer numeral as a Python binary string.
3058 >>> v.as_binary_string()
3068 """Rational values."""
3071 """ Return the numerator of a Z3 rational numeral.
3073 >>> is_rational_value(RealVal("3/5"))
3075 >>> n = RealVal("3/5")
3078 >>> is_rational_value(Q(3,5))
3080 >>> Q(3,5).numerator()
3086 """ Return the denominator of a Z3 rational numeral.
3088 >>> is_rational_value(Q(3,5))
3097 """ Return the numerator as a Python long.
3099 >>> v = RealVal(10000000000)
3104 >>> v.numerator_as_long() + 1 == 10000000001
3110 """ Return the denominator as a Python long.
3112 >>> v = RealVal("1/3")
3115 >>> v.denominator_as_long()
3134 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3136 >>> v = RealVal("1/5")
3139 >>> v = RealVal("1/3")
3146 """Return a Z3 rational numeral as a Python string.
3155 """Return a Z3 rational as a Python Fraction object.
3157 >>> v = RealVal("1/5")
3168 """Algebraic irrational values."""
3171 """Return a Z3 rational number that approximates the algebraic number `self`.
3172 The result `r` is such that |r - self| <= 1/10^precision
3174 >>> x = simplify(Sqrt(2))
3176 6838717160008073720548335/4835703278458516698824704
3183 """Return a string representation of the algebraic number `self` in decimal notation
3184 using `prec` decimal places.
3186 >>> x = simplify(Sqrt(2))
3187 >>> x.as_decimal(10)
3189 >>> x.as_decimal(20)
3190 '1.41421356237309504880?'
3202 if isinstance(a, bool):
3206 if isinstance(a, float):
3208 if isinstance(a, str):
3213 _z3_assert(
False,
"Python bool, int, long or float expected")
3217 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3221 >>> x = Const('x', IntSort())
3224 >>> x.sort() == IntSort()
3226 >>> x.sort() == BoolSort()
3234 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3238 >>> x = Const('x', RealSort())
3243 >>> x.sort() == RealSort()
3251 if isinstance(val, float):
3252 return str(int(val))
3253 elif isinstance(val, bool):
3263 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3275 """Return a Z3 real value.
3277 `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
3278 If `ctx=None`, then the global context is used.
3282 >>> RealVal(1).sort()
3294 """Return a Z3 rational a/b.
3296 If `ctx=None`, then the global context is used.
3300 >>> RatVal(3,5).sort()
3304 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3305 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3309def Q(a, b, ctx=None):
3310 """Return a Z3 rational a/b.
3312 If `ctx=None`, then the global context is used.
3323 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3336 """Return a tuple of Integer constants.
3338 >>> x, y, z = Ints('x y z')
3343 if isinstance(names, str):
3344 names = names.split(
" ")
3345 return [
Int(name, ctx)
for name
in names]
3349 """Return a list of integer constants of size `sz`.
3351 >>> X = IntVector('x', 3)
3358 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3362 """Return a fresh integer constant in the given context using the given prefix.
3376 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3389 """Return a tuple of real constants.
3391 >>> x, y, z = Reals('x y z')
3394 >>> Sum(x, y, z).sort()
3398 if isinstance(names, str):
3399 names = names.split(
" ")
3400 return [
Real(name, ctx)
for name
in names]
3404 """Return a list of real constants of size `sz`.
3406 >>> X = RealVector('x', 3)
3415 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3419 """Return a fresh real constant in the given context using the given prefix.
3433 """ Return the Z3 expression ToReal(a).
3445 if isinstance(a, BoolRef):
3448 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3453 """ Return the Z3 expression ToInt(a).
3465 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3471 """ Return the Z3 predicate IsInt(a).
3474 >>> IsInt(x + "1/2")
3476 >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
3478 >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
3482 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3488 """ Return a Z3 expression which represents the square root of a.
3501 """ Return a Z3 expression which represents the cubic root of a.
3520 """Bit-vector sort."""
3523 """Return the size (number of bits) of the bit-vector sort `self`.
3525 >>> b = BitVecSort(32)
3535 """Try to cast `val` as a Bit-Vector.
3537 >>> b = BitVecSort(32)
3540 >>> b.cast(10).sexpr()
3553 """Return True if `s` is a Z3 bit-vector sort.
3555 >>> is_bv_sort(BitVecSort(32))
3557 >>> is_bv_sort(IntSort())
3560 return isinstance(s, BitVecSortRef)
3564 """Bit-vector expressions."""
3567 """Return the sort of the bit-vector expression `self`.
3569 >>> x = BitVec('x', 32)
3572 >>> x.sort() == BitVecSort(32)
3578 """Return the number of bits of the bit-vector expression `self`.
3580 >>> x = BitVec('x', 32)
3583 >>> Concat(x, x).size()
3589 """Create the Z3 expression `self + other`.
3591 >>> x = BitVec('x', 32)
3592 >>> y = BitVec('y', 32)
3602 """Create the Z3 expression `other + self`.
3604 >>> x = BitVec('x', 32)
3612 """Create the Z3 expression `self * other`.
3614 >>> x = BitVec('x', 32)
3615 >>> y = BitVec('y', 32)
3625 """Create the Z3 expression `other * self`.
3627 >>> x = BitVec('x', 32)
3635 """Create the Z3 expression `self - other`.
3637 >>> x = BitVec('x', 32)
3638 >>> y = BitVec('y', 32)
3648 """Create the Z3 expression `other - self`.
3650 >>> x = BitVec('x', 32)
3658 """Create the Z3 expression bitwise-or `self | other`.
3660 >>> x = BitVec('x', 32)
3661 >>> y = BitVec('y', 32)
3671 """Create the Z3 expression bitwise-or `other | self`.
3673 >>> x = BitVec('x', 32)
3681 """Create the Z3 expression bitwise-and `self & other`.
3683 >>> x = BitVec('x', 32)
3684 >>> y = BitVec('y', 32)
3694 """Create the Z3 expression bitwise-or `other & self`.
3696 >>> x = BitVec('x', 32)
3704 """Create the Z3 expression bitwise-xor `self ^ other`.
3706 >>> x = BitVec('x', 32)
3707 >>> y = BitVec('y', 32)
3717 """Create the Z3 expression bitwise-xor `other ^ self`.
3719 >>> x = BitVec('x', 32)
3729 >>> x = BitVec('x', 32)
3736 """Return an expression representing `-self`.
3738 >>> x = BitVec('x', 32)
3747 """Create the Z3 expression bitwise-not `~self`.
3749 >>> x = BitVec('x', 32)
3758 """Create the Z3 expression (signed) division `self / other`.
3760 Use the function UDiv() for unsigned division.
3762 >>> x = BitVec('x', 32)
3763 >>> y = BitVec('y', 32)
3770 >>> UDiv(x, y).sexpr()
3777 """Create the Z3 expression (signed) division `self / other`."""
3781 """Create the Z3 expression (signed) division `other / self`.
3783 Use the function UDiv() for unsigned division.
3785 >>> x = BitVec('x', 32)
3788 >>> (10 / x).sexpr()
3789 '(bvsdiv #x0000000a x)'
3790 >>> UDiv(10, x).sexpr()
3791 '(bvudiv #x0000000a x)'
3797 """Create the Z3 expression (signed) division `other / self`."""
3801 """Create the Z3 expression (signed) mod `self % other`.
3803 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3805 >>> x = BitVec('x', 32)
3806 >>> y = BitVec('y', 32)
3813 >>> URem(x, y).sexpr()
3815 >>> SRem(x, y).sexpr()
3822 """Create the Z3 expression (signed) mod `other % self`.
3824 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3826 >>> x = BitVec('x', 32)
3829 >>> (10 % x).sexpr()
3830 '(bvsmod #x0000000a x)'
3831 >>> URem(10, x).sexpr()
3832 '(bvurem #x0000000a x)'
3833 >>> SRem(10, x).sexpr()
3834 '(bvsrem #x0000000a x)'
3840 """Create the Z3 expression (signed) `other <= self`.
3842 Use the function ULE() for unsigned less than or equal to.
3844 >>> x, y = BitVecs('x y', 32)
3847 >>> (x <= y).sexpr()
3849 >>> ULE(x, y).sexpr()
3856 """Create the Z3 expression (signed) `other < self`.
3858 Use the function ULT() for unsigned less than.
3860 >>> x, y = BitVecs('x y', 32)
3865 >>> ULT(x, y).sexpr()
3872 """Create the Z3 expression (signed) `other > self`.
3874 Use the function UGT() for unsigned greater than.
3876 >>> x, y = BitVecs('x y', 32)
3881 >>> UGT(x, y).sexpr()
3888 """Create the Z3 expression (signed) `other >= self`.
3890 Use the function UGE() for unsigned greater than or equal to.
3892 >>> x, y = BitVecs('x y', 32)
3895 >>> (x >= y).sexpr()
3897 >>> UGE(x, y).sexpr()
3904 """Create the Z3 expression (arithmetical) right shift `self >> other`
3906 Use the function LShR() for the right logical shift
3908 >>> x, y = BitVecs('x y', 32)
3911 >>> (x >> y).sexpr()
3913 >>> LShR(x, y).sexpr()
3917 >>> BitVecVal(4, 3).as_signed_long()
3919 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
3921 >>> simplify(BitVecVal(4, 3) >> 1)
3923 >>> simplify(LShR(BitVecVal(4, 3), 1))
3925 >>> simplify(BitVecVal(2, 3) >> 1)
3927 >>> simplify(LShR(BitVecVal(2, 3), 1))
3934 """Create the Z3 expression left shift `self << other`
3936 >>> x, y = BitVecs('x y', 32)
3939 >>> (x << y).sexpr()
3941 >>> simplify(BitVecVal(2, 3) << 1)
3948 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3950 Use the function LShR() for the right logical shift
3952 >>> x = BitVec('x', 32)
3955 >>> (10 >> x).sexpr()
3956 '(bvashr #x0000000a x)'
3962 """Create the Z3 expression left shift `other << self`.
3964 Use the function LShR() for the right logical shift
3966 >>> x = BitVec('x', 32)
3969 >>> (10 << x).sexpr()
3970 '(bvshl #x0000000a x)'
3977 """Bit-vector values."""
3980 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3982 >>> v = BitVecVal(0xbadc0de, 32)
3985 >>> print("0x%.8x" % v.as_long())
3991 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3992 The most significant bit is assumed to be the sign.
3994 >>> BitVecVal(4, 3).as_signed_long()
3996 >>> BitVecVal(7, 3).as_signed_long()
3998 >>> BitVecVal(3, 3).as_signed_long()
4000 >>> BitVecVal(2**32 - 1, 32).as_signed_long()
4002 >>> BitVecVal(2**64 - 1, 64).as_signed_long()
4007 if val >= 2**(sz - 1):
4009 if val < -2**(sz - 1):
4020 """Return the Python value of a Z3 bit-vector numeral."""
4026 """Return `True` if `a` is a Z3 bit-vector expression.
4028 >>> b = BitVec('b', 32)
4036 return isinstance(a, BitVecRef)
4040 """Return `True` if `a` is a Z3 bit-vector numeral value.
4042 >>> b = BitVec('b', 32)
4045 >>> b = BitVecVal(10, 32)
4055 """Return the Z3 expression BV2Int(a).
4057 >>> b = BitVec('b', 3)
4058 >>> BV2Int(b).sort()
4063 >>> x > BV2Int(b, is_signed=False)
4065 >>> x > BV2Int(b, is_signed=True)
4066 x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
4067 >>> solve(x > BV2Int(b), b == 1, x < 3)
4071 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4078 """Return the z3 expression Int2BV(a, num_bits).
4079 It is a bit-vector of width num_bits and represents the
4080 modulo of a by 2^num_bits
4087 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4089 >>> Byte = BitVecSort(8)
4090 >>> Word = BitVecSort(16)
4093 >>> x = Const('x', Byte)
4094 >>> eq(x, BitVec('x', 8))
4102 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4104 >>> v = BitVecVal(10, 32)
4107 >>> print("0x%.8x" % v.as_long())
4119 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4120 If `ctx=None`, then the global context is used.
4122 >>> x = BitVec('x', 16)
4129 >>> word = BitVecSort(16)
4130 >>> x2 = BitVec('x', word)
4134 if isinstance(bv, BitVecSortRef):
4143 """Return a tuple of bit-vector constants of size bv.
4145 >>> x, y, z = BitVecs('x y z', 16)
4152 >>> Product(x, y, z)
4154 >>> simplify(Product(x, y, z))
4158 if isinstance(names, str):
4159 names = names.split(
" ")
4160 return [
BitVec(name, bv, ctx)
for name
in names]
4164 """Create a Z3 bit-vector concatenation expression.
4166 >>> v = BitVecVal(1, 4)
4167 >>> Concat(v, v+1, v)
4168 Concat(Concat(1, 1 + 1), 1)
4169 >>> simplify(Concat(v, v+1, v))
4171 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
4177 _z3_assert(sz >= 2,
"At least two arguments expected.")
4184 if is_seq(args[0])
or isinstance(args[0], str):
4187 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4190 v[i] = args[i].as_ast()
4195 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4198 v[i] = args[i].as_ast()
4202 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4204 for i
in range(sz - 1):
4210 """Create a Z3 bit-vector extraction expression.
4211 Extract is overloaded to also work on sequence extraction.
4212 The functions SubString and SubSeq are redirected to Extract.
4213 For this case, the arguments are reinterpreted as:
4214 high - is a sequence (string)
4216 a - is the length to be extracted
4218 >>> x = BitVec('x', 8)
4219 >>> Extract(6, 2, x)
4221 >>> Extract(6, 2, x).sort()
4223 >>> simplify(Extract(StringVal("abcd"),2,1))
4226 if isinstance(high, str):
4233 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4235 "First and second arguments must be non negative integers")
4236 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4242 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4246 """Create the Z3 expression (unsigned) `other <= self`.
4248 Use the operator <= for signed less than or equal to.
4250 >>> x, y = BitVecs('x y', 32)
4253 >>> (x <= y).sexpr()
4255 >>> ULE(x, y).sexpr()
4264 """Create the Z3 expression (unsigned) `other < self`.
4266 Use the operator < for signed less than.
4268 >>> x, y = BitVecs('x y', 32)
4273 >>> ULT(x, y).sexpr()
4282 """Create the Z3 expression (unsigned) `other >= self`.
4284 Use the operator >= for signed greater than or equal to.
4286 >>> x, y = BitVecs('x y', 32)
4289 >>> (x >= y).sexpr()
4291 >>> UGE(x, y).sexpr()
4300 """Create the Z3 expression (unsigned) `other > self`.
4302 Use the operator > for signed greater than.
4304 >>> x, y = BitVecs('x y', 32)
4309 >>> UGT(x, y).sexpr()
4318 """Create the Z3 expression (unsigned) division `self / other`.
4320 Use the operator / for signed division.
4322 >>> x = BitVec('x', 32)
4323 >>> y = BitVec('y', 32)
4326 >>> UDiv(x, y).sort()
4330 >>> UDiv(x, y).sexpr()
4339 """Create the Z3 expression (unsigned) remainder `self % other`.
4341 Use the operator % for signed modulus, and SRem() for signed remainder.
4343 >>> x = BitVec('x', 32)
4344 >>> y = BitVec('y', 32)
4347 >>> URem(x, y).sort()
4351 >>> URem(x, y).sexpr()
4360 """Create the Z3 expression signed remainder.
4362 Use the operator % for signed modulus, and URem() for unsigned remainder.
4364 >>> x = BitVec('x', 32)
4365 >>> y = BitVec('y', 32)
4368 >>> SRem(x, y).sort()
4372 >>> SRem(x, y).sexpr()
4381 """Create the Z3 expression logical right shift.
4383 Use the operator >> for the arithmetical right shift.
4385 >>> x, y = BitVecs('x y', 32)
4388 >>> (x >> y).sexpr()
4390 >>> LShR(x, y).sexpr()
4394 >>> BitVecVal(4, 3).as_signed_long()
4396 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
4398 >>> simplify(BitVecVal(4, 3) >> 1)
4400 >>> simplify(LShR(BitVecVal(4, 3), 1))
4402 >>> simplify(BitVecVal(2, 3) >> 1)
4404 >>> simplify(LShR(BitVecVal(2, 3), 1))
4413 """Return an expression representing `a` rotated to the left `b` times.
4415 >>> a, b = BitVecs('a b', 16)
4416 >>> RotateLeft(a, b)
4418 >>> simplify(RotateLeft(a, 0))
4420 >>> simplify(RotateLeft(a, 16))
4429 """Return an expression representing `a` rotated to the right `b` times.
4431 >>> a, b = BitVecs('a b', 16)
4432 >>> RotateRight(a, b)
4434 >>> simplify(RotateRight(a, 0))
4436 >>> simplify(RotateRight(a, 16))
4445 """Return a bit-vector expression with `n` extra sign-bits.
4447 >>> x = BitVec('x', 16)
4448 >>> n = SignExt(8, x)
4455 >>> v0 = BitVecVal(2, 2)
4460 >>> v = simplify(SignExt(6, v0))
4465 >>> print("%.x" % v.as_long())
4470 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4475 """Return a bit-vector expression with `n` extra zero-bits.
4477 >>> x = BitVec('x', 16)
4478 >>> n = ZeroExt(8, x)
4485 >>> v0 = BitVecVal(2, 2)
4490 >>> v = simplify(ZeroExt(6, v0))
4498 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4503 """Return an expression representing `n` copies of `a`.
4505 >>> x = BitVec('x', 8)
4506 >>> n = RepeatBitVec(4, x)
4511 >>> v0 = BitVecVal(10, 4)
4512 >>> print("%.x" % v0.as_long())
4514 >>> v = simplify(RepeatBitVec(4, v0))
4517 >>> print("%.x" % v.as_long())
4522 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4527 """Return the reduction-and expression of `a`."""
4529 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4534 """Return the reduction-or expression of `a`."""
4536 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4541 """A predicate the determines that bit-vector addition does not overflow"""
4548 """A predicate the determines that signed bit-vector addition does not underflow"""
4555 """A predicate the determines that bit-vector subtraction does not overflow"""
4562 """A predicate the determines that bit-vector subtraction does not underflow"""
4569 """A predicate the determines that bit-vector signed division does not overflow"""
4576 """A predicate the determines that bit-vector unary negation does not overflow"""
4578 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4583 """A predicate the determines that bit-vector multiplication does not overflow"""
4590 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4606 """Return the domain of the array sort `self`.
4608 >>> A = ArraySort(IntSort(), BoolSort())
4615 """Return the domain of the array sort `self`.
4620 """Return the range of the array sort `self`.
4622 >>> A = ArraySort(IntSort(), BoolSort())
4630 """Array expressions. """
4633 """Return the array sort of the array expression `self`.
4635 >>> a = Array('a', IntSort(), BoolSort())
4642 """Shorthand for `self.sort().domain()`.
4644 >>> a = Array('a', IntSort(), BoolSort())
4651 """Shorthand for self.sort().domain_n(i)`."""
4655 """Shorthand for `self.sort().range()`.
4657 >>> a = Array('a', IntSort(), BoolSort())
4664 """Return the Z3 expression `self[arg]`.
4666 >>> a = Array('a', IntSort(), BoolSort())
4680 if isinstance(arg, tuple):
4681 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4684 arg = ar.sort().domain().cast(arg)
4693 """Return `True` if `a` is a Z3 array expression.
4695 >>> a = Array('a', IntSort(), IntSort())
4698 >>> is_array(Store(a, 0, 1))
4703 return isinstance(a, ArrayRef)
4707 """Return `True` if `a` is a Z3 constant array.
4709 >>> a = K(IntSort(), 10)
4710 >>> is_const_array(a)
4712 >>> a = Array('a', IntSort(), IntSort())
4713 >>> is_const_array(a)
4720 """Return `True` if `a` is a Z3 constant array.
4722 >>> a = K(IntSort(), 10)
4725 >>> a = Array('a', IntSort(), IntSort())
4733 """Return `True` if `a` is a Z3 map array expression.
4735 >>> f = Function('f', IntSort(), IntSort())
4736 >>> b = Array('b', IntSort(), IntSort())
4749 """Return `True` if `a` is a Z3 default array expression.
4750 >>> d = Default(K(IntSort(), 10))
4754 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4758 """Return the function declaration associated with a Z3 map array expression.
4760 >>> f = Function('f', IntSort(), IntSort())
4761 >>> b = Array('b', IntSort(), IntSort())
4763 >>> eq(f, get_map_func(a))
4767 >>> get_map_func(a)(0)
4782 """Return the Z3 array sort with the given domain and range sorts.
4784 >>> A = ArraySort(IntSort(), BoolSort())
4791 >>> AA = ArraySort(IntSort(), A)
4793 Array(Int, Array(Int, Bool))
4797 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4798 arity = len(sig) - 1
4804 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4808 dom = (Sort * arity)()
4809 for i
in range(arity):
4815 """Return an array constant named `name` with the given domain and range sorts.
4817 >>> a = Array('a', IntSort(), IntSort())
4829 """Return a Z3 store array expression.
4831 >>> a = Array('a', IntSort(), IntSort())
4832 >>> i, v = Ints('i v')
4833 >>> s = Update(a, i, v)
4836 >>> prove(s[i] == v)
4839 >>> prove(Implies(i != j, s[j] == a[j]))
4847 raise Z3Exception(
"array update requires index and value arguments")
4851 i = a.sort().domain().cast(i)
4852 v = a.sort().range().cast(v)
4854 v = a.sort().range().cast(args[-1])
4855 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4861 """ Return a default value for array expression.
4862 >>> b = K(IntSort(), 1)
4863 >>> prove(Default(b) == 1)
4872 """Return a Z3 store array expression.
4874 >>> a = Array('a', IntSort(), IntSort())
4875 >>> i, v = Ints('i v')
4876 >>> s = Store(a, i, v)
4879 >>> prove(s[i] == v)
4882 >>> prove(Implies(i != j, s[j] == a[j]))
4889 """Return a Z3 select array expression.
4891 >>> a = Array('a', IntSort(), IntSort())
4895 >>> eq(Select(a, i), a[i])
4905 """Return a Z3 map array expression.
4907 >>> f = Function('f', IntSort(), IntSort(), IntSort())
4908 >>> a1 = Array('a1', IntSort(), IntSort())
4909 >>> a2 = Array('a2', IntSort(), IntSort())
4910 >>> b = Map(f, a1, a2)
4913 >>> prove(b[0] == f(a1[0], a2[0]))
4918 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4921 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4928 """Return a Z3 constant array expression.
4930 >>> a = K(IntSort(), 10)
4950 """Return extensionality index for one-dimensional arrays.
4951 >> a, b = Consts('a b', SetSort(IntSort()))
4968 """Return `True` if `a` is a Z3 array select application.
4970 >>> a = Array('a', IntSort(), IntSort())
4981 """Return `True` if `a` is a Z3 array store application.
4983 >>> a = Array('a', IntSort(), IntSort())
4986 >>> is_store(Store(a, 0, 1))
4999 """ Create a set sort over element sort s"""
5004 """Create the empty set
5005 >>> EmptySet(IntSort())
5013 """Create the full set
5014 >>> FullSet(IntSort())
5022 """ Take the union of sets
5023 >>> a = Const('a', SetSort(IntSort()))
5024 >>> b = Const('b', SetSort(IntSort()))
5035 """ Take the union of sets
5036 >>> a = Const('a', SetSort(IntSort()))
5037 >>> b = Const('b', SetSort(IntSort()))
5038 >>> SetIntersect(a, b)
5048 """ Add element e to set s
5049 >>> a = Const('a', SetSort(IntSort()))
5059 """ Remove element e to set s
5060 >>> a = Const('a', SetSort(IntSort()))
5070 """ The complement of set s
5071 >>> a = Const('a', SetSort(IntSort()))
5072 >>> SetComplement(a)
5080 """ The set difference of a and b
5081 >>> a = Const('a', SetSort(IntSort()))
5082 >>> b = Const('b', SetSort(IntSort()))
5083 >>> SetDifference(a, b)
5091 """ Check if e is a member of set s
5092 >>> a = Const('a', SetSort(IntSort()))
5102 """ Check if a is a subset of b
5103 >>> a = Const('a', SetSort(IntSort()))
5104 >>> b = Const('b', SetSort(IntSort()))
5119 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5120 if not isinstance(acc, tuple):
5124 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5128 """Helper class for declaring Z3 datatypes.
5130 >>> List = Datatype('List')
5131 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5132 >>> List.declare('nil')
5133 >>> List = List.create()
5134 >>> # List is now a Z3 declaration
5137 >>> List.cons(10, List.nil)
5139 >>> List.cons(10, List.nil).sort()
5141 >>> cons = List.cons
5145 >>> n = cons(1, cons(0, nil))
5147 cons(1, cons(0, nil))
5148 >>> simplify(cdr(n))
5150 >>> simplify(car(n))
5166 _z3_assert(isinstance(name, str),
"String expected")
5167 _z3_assert(isinstance(rec_name, str),
"String expected")
5170 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5175 """Declare constructor named `name` with the given accessors `args`.
5176 Each accessor is a pair `(name, sort)`, where `name` is a string and `sort` a Z3 sort
5177 or a reference to the datatypes being declared.
5179 In the following example `List.declare('cons', ('car', IntSort()), ('cdr', List))`
5180 declares the constructor named `cons` that builds a new List using an integer and a List.
5181 It also declares the accessors `car` and `cdr`. The accessor `car` extracts the integer
5182 of a `cons` cell, and `cdr` the list of a `cons` cell. After all constructors were declared,
5183 we use the method create() to create the actual datatype in Z3.
5185 >>> List = Datatype('List')
5186 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5187 >>> List.declare('nil')
5188 >>> List = List.create()
5191 _z3_assert(isinstance(name, str),
"String expected")
5192 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5199 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5201 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5203 >>> List = Datatype('List')
5204 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5205 >>> List.declare('nil')
5206 >>> List = List.create()
5209 >>> List.cons(10, List.nil)
5216 """Auxiliary object used to create Z3 datatypes."""
5223 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5228 """Auxiliary object used to create Z3 datatypes."""
5235 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5240 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5242 In the following example we define a Tree-List using two mutually recursive datatypes.
5244 >>> TreeList = Datatype('TreeList')
5245 >>> Tree = Datatype('Tree')
5246 >>> # Tree has two constructors: leaf and node
5247 >>> Tree.declare('leaf', ('val', IntSort()))
5248 >>> # a node contains a list of trees
5249 >>> Tree.declare('node', ('children', TreeList))
5250 >>> TreeList.declare('nil')
5251 >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
5252 >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
5253 >>> Tree.val(Tree.leaf(10))
5255 >>> simplify(Tree.val(Tree.leaf(10)))
5257 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5259 node(cons(leaf(10), cons(leaf(20), nil)))
5260 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5261 >>> simplify(n2 == n1)
5263 >>> simplify(TreeList.car(Tree.children(n2)) == n1)
5268 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5269 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5270 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5271 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5274 names = (Symbol * num)()
5275 out = (Sort * num)()
5276 clists = (ConstructorList * num)()
5278 for i
in range(num):
5281 num_cs = len(d.constructors)
5282 cs = (Constructor * num_cs)()
5283 for j
in range(num_cs):
5284 c = d.constructors[j]
5289 fnames = (Symbol * num_fs)()
5290 sorts = (Sort * num_fs)()
5291 refs = (ctypes.c_uint * num_fs)()
5292 for k
in range(num_fs):
5296 if isinstance(ftype, Datatype):
5299 ds.count(ftype) == 1,
5300 "One and only one occurrence of each datatype is expected",
5303 refs[k] = ds.index(ftype)
5307 sorts[k] = ftype.ast
5316 for i
in range(num):
5318 num_cs = dref.num_constructors()
5319 for j
in range(num_cs):
5320 cref = dref.constructor(j)
5321 cref_name = cref.name()
5322 cref_arity = cref.arity()
5323 if cref.arity() == 0:
5325 setattr(dref, cref_name, cref)
5326 rref = dref.recognizer(j)
5327 setattr(dref,
"is_" + cref_name, rref)
5328 for k
in range(cref_arity):
5329 aref = dref.accessor(j, k)
5330 setattr(dref, aref.name(), aref)
5332 return tuple(result)
5336 """Datatype sorts."""
5339 """Return the number of constructors in the given Z3 datatype.
5341 >>> List = Datatype('List')
5342 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5343 >>> List.declare('nil')
5344 >>> List = List.create()
5345 >>> # List is now a Z3 declaration
5346 >>> List.num_constructors()
5352 """Return a constructor of the datatype `self`.
5354 >>> List = Datatype('List')
5355 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5356 >>> List.declare('nil')
5357 >>> List = List.create()
5358 >>> # List is now a Z3 declaration
5359 >>> List.num_constructors()
5361 >>> List.constructor(0)
5363 >>> List.constructor(1)
5371 """In Z3, each constructor has an associated recognizer predicate.
5373 If the constructor is named `name`, then the recognizer `is_name`.
5375 >>> List = Datatype('List')
5376 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5377 >>> List.declare('nil')
5378 >>> List = List.create()
5379 >>> # List is now a Z3 declaration
5380 >>> List.num_constructors()
5382 >>> List.recognizer(0)
5384 >>> List.recognizer(1)
5386 >>> simplify(List.is_nil(List.cons(10, List.nil)))
5388 >>> simplify(List.is_cons(List.cons(10, List.nil)))
5390 >>> l = Const('l', List)
5391 >>> simplify(List.is_cons(l))
5399 """In Z3, each constructor has 0 or more accessor.
5400 The number of accessors is equal to the arity of the constructor.
5402 >>> List = Datatype('List')
5403 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5404 >>> List.declare('nil')
5405 >>> List = List.create()
5406 >>> List.num_constructors()
5408 >>> List.constructor(0)
5410 >>> num_accs = List.constructor(0).arity()
5413 >>> List.accessor(0, 0)
5415 >>> List.accessor(0, 1)
5417 >>> List.constructor(1)
5419 >>> num_accs = List.constructor(1).arity()
5433 """Datatype expressions."""
5436 """Return the datatype sort of the datatype expression `self`."""
5440 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5445 """Create a named tuple sort base on a set of underlying sorts
5447 >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
5450 projects = [(
"project%d" % i, sorts[i])
for i
in range(len(sorts))]
5451 tuple.declare(name, *projects)
5452 tuple = tuple.create()
5453 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5457 """Create a named tagged union sort base on a set of underlying sorts
5459 >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
5462 for i
in range(len(sorts)):
5463 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5465 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5469 """Return a new enumeration sort named `name` containing the given values.
5471 The result is a pair (sort, list of constants).
5473 >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
5476 _z3_assert(isinstance(name, str),
"Name must be a string")
5477 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Enumeration sort values must be strings")
5478 _z3_assert(len(values) > 0,
"At least one value expected")
5481 _val_names = (Symbol * num)()
5482 for i
in range(num):
5483 _val_names[i] =
to_symbol(values[i], ctx)
5484 _values = (FuncDecl * num)()
5485 _testers = (FuncDecl * num)()
5489 for i
in range(num):
5491 V = [a()
for a
in V]
5502 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5504 Consider using the function `args2params` to create instances of this object.
5519 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5523 """Set parameter name with value val."""
5525 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5527 if isinstance(val, bool):
5531 elif isinstance(val, float):
5533 elif isinstance(val, str):
5543 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5548 """Convert python arguments into a Z3_params object.
5549 A ':' is added to the keywords, and '_' is replaced with '-'
5551 >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
5552 (params model true relevancy 2 elim_and true)
5555 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5571 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5575 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5581 return ParamsDescrsRef(self.
descr, self.
ctx)
5584 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5588 """Return the size of in the parameter description `self`.
5593 """Return the size of in the parameter description `self`.
5598 """Return the i-th parameter name in the parameter description `self`.
5603 """Return the kind of the parameter named `n`.
5608 """Return the documentation string of the parameter named `n`.
5629 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5631 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5632 A goal has a solution if one of its subgoals has a solution.
5633 A goal is unsatisfiable if all subgoals are unsatisfiable.
5636 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5639 "If goal is different from None, then ctx must be also different from None")
5642 if self.
goal is None:
5647 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5651 """Return the depth of the goal `self`.
5652 The depth corresponds to the number of tactics applied to `self`.
5654 >>> x, y = Ints('x y')
5656 >>> g.add(x == 0, y >= x + 1)
5659 >>> r = Then('simplify', 'solve-eqs')(g)
5660 >>> # r has 1 subgoal
5669 """Return `True` if `self` contains the `False` constraints.
5671 >>> x, y = Ints('x y')
5673 >>> g.inconsistent()
5675 >>> g.add(x == 0, x == 1)
5678 >>> g.inconsistent()
5680 >>> g2 = Tactic('propagate-values')(g)[0]
5681 >>> g2.inconsistent()
5687 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5690 >>> g.prec() == Z3_GOAL_PRECISE
5692 >>> x, y = Ints('x y')
5693 >>> g.add(x == y + 1)
5694 >>> g.prec() == Z3_GOAL_PRECISE
5696 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5699 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5700 >>> g2.prec() == Z3_GOAL_PRECISE
5702 >>> g2.prec() == Z3_GOAL_UNDER
5708 """Alias for `prec()`.
5711 >>> g.precision() == Z3_GOAL_PRECISE
5717 """Return the number of constraints in the goal `self`.
5722 >>> x, y = Ints('x y')
5723 >>> g.add(x == 0, y > x)
5730 """Return the number of constraints in the goal `self`.
5735 >>> x, y = Ints('x y')
5736 >>> g.add(x == 0, y > x)
5743 """Return a constraint in the goal `self`.
5746 >>> x, y = Ints('x y')
5747 >>> g.add(x == 0, y > x)
5756 """Return a constraint in the goal `self`.
5759 >>> x, y = Ints('x y')
5760 >>> g.add(x == 0, y > x)
5766 if arg >= len(self):
5768 return self.
get(arg)
5771 """Assert constraints into the goal.
5775 >>> g.assert_exprs(x > 0, x < 2)
5790 >>> g.append(x > 0, x < 2)
5801 >>> g.insert(x > 0, x < 2)
5812 >>> g.add(x > 0, x < 2)
5819 """Retrieve model from a satisfiable goal
5820 >>> a, b = Ints('a b')
5822 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5823 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5826 [Or(b == 0, b == 1), Not(0 <= b)]
5828 [Or(b == 0, b == 1), Not(1 <= b)]
5829 >>> # Remark: the subgoal r[0] is unsatisfiable
5830 >>> # Creating a solver for solving the second subgoal
5837 >>> # Model s.model() does not assign a value to `a`
5838 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5839 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5840 >>> r[1].convert_model(s.model())
5844 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5848 return obj_to_string(self)
5851 """Return a textual representation of the s-expression representing the goal."""
5855 """Return a textual representation of the goal in DIMACS format."""
5859 """Copy goal `self` to context `target`.
5867 >>> g2 = g.translate(c2)
5870 >>> g.ctx == main_ctx()
5874 >>> g2.ctx == main_ctx()
5878 _z3_assert(isinstance(target, Context),
"target must be a context")
5888 """Return a new simplified goal.
5890 This method is essentially invoking the simplify tactic.
5894 >>> g.add(x + 1 >= 2)
5897 >>> g2 = g.simplify()
5900 >>> # g was not modified
5905 return t.apply(self, *arguments, **keywords)[0]
5908 """Return goal `self` as a single Z3 expression.
5927 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5937 """A collection (vector) of ASTs."""
5946 assert ctx
is not None
5951 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5955 """Return the size of the vector `self`.
5960 >>> A.push(Int('x'))
5961 >>> A.push(Int('x'))
5968 """Return the AST at position `i`.
5971 >>> A.push(Int('x') + 1)
5972 >>> A.push(Int('y'))
5979 if isinstance(i, int):
5987 elif isinstance(i, slice):
5989 for ii
in range(*i.indices(self.
__len__())):
5997 """Update AST at position `i`.
6000 >>> A.push(Int('x') + 1)
6001 >>> A.push(Int('y'))
6013 """Add `v` in the end of the vector.
6018 >>> A.push(Int('x'))
6025 """Resize the vector to `sz` elements.
6031 >>> for i in range(10): A[i] = Int('x')
6038 """Return `True` if the vector contains `item`.
6061 """Copy vector `self` to context `other_ctx`.
6067 >>> B = A.translate(c2)
6083 return obj_to_string(self)
6086 """Return a textual representation of the s-expression representing the vector."""
6097 """A mapping from ASTs to ASTs."""
6106 assert ctx
is not None
6114 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6118 """Return the size of the map.
6124 >>> M[x] = IntVal(1)
6131 """Return `True` if the map contains key `key`.
6144 """Retrieve the value associated with key `key`.
6155 """Add/Update key `k` with value `v`.
6164 >>> M[x] = IntVal(1)
6174 """Remove the entry associated with key `k`.
6188 """Remove all entries from the map.
6193 >>> M[x+x] = IntVal(1)
6203 """Return an AstVector containing all keys in the map.
6208 >>> M[x+x] = IntVal(1)
6222 """Store the value of the interpretation of a function in a particular point."""
6233 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6237 """Return the number of arguments in the given entry.
6239 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6241 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6246 >>> f_i.num_entries()
6248 >>> e = f_i.entry(0)
6255 """Return the value of argument `idx`.
6257 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6259 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6264 >>> f_i.num_entries()
6266 >>> e = f_i.entry(0)
6277 ... except IndexError:
6278 ... print("index error")
6286 """Return the value of the function at point `self`.
6288 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6290 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6295 >>> f_i.num_entries()
6297 >>> e = f_i.entry(0)
6308 """Return entry `self` as a Python list.
6309 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6311 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6316 >>> f_i.num_entries()
6318 >>> e = f_i.entry(0)
6323 args.append(self.
value())
6331 """Stores the interpretation of a function in a Z3 model."""
6336 if self.
f is not None:
6340 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6345 Return the `else` value for a function interpretation.
6346 Return None if Z3 did not specify the `else` value for
6349 >>> f = Function('f', IntSort(), IntSort())
6351 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6357 >>> m[f].else_value()
6367 """Return the number of entries/points in the function interpretation `self`.
6369 >>> f = Function('f', IntSort(), IntSort())
6371 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6377 >>> m[f].num_entries()
6383 """Return the number of arguments for each entry in the function interpretation `self`.
6385 >>> f = Function('f', IntSort(), IntSort())
6387 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6397 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6399 >>> f = Function('f', IntSort(), IntSort())
6401 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6407 >>> m[f].num_entries()
6417 """Copy model 'self' to context 'other_ctx'.
6428 """Return the function interpretation as a Python list.
6429 >>> f = Function('f', IntSort(), IntSort())
6431 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6445 return obj_to_string(self)
6449 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6452 assert ctx
is not None
6458 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6462 return obj_to_string(self)
6465 """Return a textual representation of the s-expression representing the model."""
6468 def eval(self, t, model_completion=False):
6469 """Evaluate the expression `t` in the model `self`.
6470 If `model_completion` is enabled, then a default interpretation is automatically added
6471 for symbols that do not have an interpretation in the model `self`.
6475 >>> s.add(x > 0, x < 2)
6488 >>> m.eval(y, model_completion=True)
6490 >>> # Now, m contains an interpretation for y
6497 raise Z3Exception(
"failed to evaluate expression in the model")
6500 """Alias for `eval`.
6504 >>> s.add(x > 0, x < 2)
6508 >>> m.evaluate(x + 1)
6510 >>> m.evaluate(x == 1)
6513 >>> m.evaluate(y + x)
6517 >>> m.evaluate(y, model_completion=True)
6519 >>> # Now, m contains an interpretation for y
6520 >>> m.evaluate(y + x)
6523 return self.
eval(t, model_completion)
6526 """Return the number of constant and function declarations in the model `self`.
6528 >>> f = Function('f', IntSort(), IntSort())
6531 >>> s.add(x > 0, f(x) != x)
6540 return num_consts + num_funcs
6543 """Return the interpretation for a given declaration or constant.
6545 >>> f = Function('f', IntSort(), IntSort())
6548 >>> s.add(x > 0, x < 2, f(x) == 0)
6558 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6562 if decl.arity() == 0:
6564 if _r.value
is None:
6580 sz = fi.num_entries()
6584 e =
Store(e, fe.arg_value(0), fe.value())
6595 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6597 >>> A = DeclareSort('A')
6598 >>> a, b = Consts('a b', A)
6610 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6612 >>> A = DeclareSort('A')
6613 >>> B = DeclareSort('B')
6614 >>> a1, a2 = Consts('a1 a2', A)
6615 >>> b1, b2 = Consts('b1 b2', B)
6617 >>> s.add(a1 != a2, b1 != b2)
6633 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6635 >>> A = DeclareSort('A')
6636 >>> B = DeclareSort('B')
6637 >>> a1, a2 = Consts('a1 a2', A)
6638 >>> b1, b2 = Consts('b1 b2', B)
6640 >>> s.add(a1 != a2, b1 != b2)
6650 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6652 >>> A = DeclareSort('A')
6653 >>> a, b = Consts('a b', A)
6659 >>> m.get_universe(A)
6663 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6670 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6671 If `idx` is a declaration, then the actual interpretation is returned.
6673 The elements can be retrieved using position or the actual declaration.
6675 >>> f = Function('f', IntSort(), IntSort())
6678 >>> s.add(x > 0, x < 2, f(x) == 0)
6692 >>> for d in m: print("%s -> %s" % (d, m[d]))
6697 if idx >= len(self):
6700 if (idx < num_consts):
6704 if isinstance(idx, FuncDeclRef):
6708 if isinstance(idx, SortRef):
6711 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6715 """Return a list with all symbols that have an interpretation in the model `self`.
6716 >>> f = Function('f', IntSort(), IntSort())
6719 >>> s.add(x > 0, x < 2, f(x) == 0)
6734 """Update the interpretation of a constant"""
6737 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6741 for i
in range(value.num_entries()):
6746 v.push(e.arg_value(j))
6751 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6756 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6759 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6764 """Perform model-based projection on fml with respect to vars.
6765 Assume that the model satisfies fml. Then compute a projection fml_p, such
6766 that vars do not occur free in fml_p, fml_p is true in the model and
6767 fml_p => exists vars . fml
6769 ctx = self.
ctx.ref()
6770 _vars = (Ast * len(vars))()
6771 for i
in range(len(vars)):
6772 _vars[i] = vars[i].as_ast()
6776 """Perform model-based projection, but also include realizer terms for the projected variables"""
6777 ctx = self.
ctx.ref()
6778 _vars = (Ast * len(vars))()
6779 for i
in range(len(vars)):
6780 _vars[i] = vars[i].as_ast()
6782 result = Z3_qe_model_project_with_witness(ctx, self.
model, len(vars), _vars, fml.ast, defs.map)
6797 for k, v
in eval.items():
6798 mdl.update_value(k, v)
6803 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6804 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6808 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6821 """Statistics for `Solver.check()`."""
6832 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6839 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6842 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6845 out.write(u(
"<tr>"))
6847 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6848 out.write(u(
"</table>"))
6849 return out.getvalue()
6854 """Return the number of statistical counters.
6857 >>> s = Then('simplify', 'nlsat').solver()
6861 >>> st = s.statistics()
6868 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6871 >>> s = Then('simplify', 'nlsat').solver()
6875 >>> st = s.statistics()
6879 ('nlsat propagations', 2)
6881 ('nlsat restarts', 1)
6883 if idx >= len(self):
6892 """Return the list of statistical counters.
6895 >>> s = Then('simplify', 'nlsat').solver()
6899 >>> st = s.statistics()
6904 """Return the value of a particular statistical counter.
6907 >>> s = Then('simplify', 'nlsat').solver()
6911 >>> st = s.statistics()
6912 >>> st.get_key_value('nlsat propagations')
6915 for idx
in range(len(self)):
6921 raise Z3Exception(
"unknown key")
6924 """Access the value of statistical using attributes.
6926 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6927 we should use '_' (e.g., 'nlsat_propagations').
6930 >>> s = Then('simplify', 'nlsat').solver()
6934 >>> st = s.statistics()
6935 >>> st.nlsat_propagations
6940 key = name.replace(
"_",
" ")
6944 raise AttributeError
6954 """Represents the result of a satisfiability check: sat, unsat, unknown.
6960 >>> isinstance(r, CheckSatResult)
6971 return isinstance(other, CheckSatResult)
and self.
r == other.r
6974 return not self.
__eq__(other)
6978 if self.
r == Z3_L_TRUE:
6980 elif self.
r == Z3_L_FALSE:
6981 return "<b>unsat</b>"
6983 return "<b>unknown</b>"
6985 if self.
r == Z3_L_TRUE:
6987 elif self.
r == Z3_L_FALSE:
6993 in_html = in_html_mode()
6996 set_html_mode(in_html)
7007 Solver API provides methods for implementing the main SMT 2.0 commands:
7008 push, pop, check, get-model, etc.
7011 def __init__(self, solver=None, ctx=None, logFile=None):
7012 assert solver
is None or ctx
is not None
7021 if logFile
is not None:
7022 self.
set(
"smtlib2_log", logFile)
7025 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
7036 """Set a configuration option.
7037 The method `help()` return a string containing all available options.
7040 >>> # The option MBQI can be set using three different approaches.
7041 >>> s.set(mbqi=True)
7042 >>> s.set('MBQI', True)
7043 >>> s.set(':mbqi', True)
7049 """Create a backtracking point.
7071 """Backtrack \\c num backtracking points.
7093 """Return the current number of backtracking points.
7111 """Remove all asserted constraints and backtracking points created using `push()`.
7125 """Assert constraints into the solver.
7129 >>> s.assert_exprs(x > 0, x < 2)
7136 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7144 """Assert constraints into the solver.
7148 >>> s.add(x > 0, x < 2)
7159 """Assert constraints into the solver.
7163 >>> s.append(x > 0, x < 2)
7170 """Assert constraints into the solver.
7174 >>> s.insert(x > 0, x < 2)
7181 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7183 If `p` is a string, it will be automatically converted into a Boolean constant.
7188 >>> s.set(unsat_core=True)
7189 >>> s.assert_and_track(x > 0, 'p1')
7190 >>> s.assert_and_track(x != 1, 'p2')
7191 >>> s.assert_and_track(x < 0, p3)
7192 >>> print(s.check())
7194 >>> c = s.unsat_core()
7204 if isinstance(p, str):
7206 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7211 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7217 >>> s.add(x > 0, x < 2)
7220 >>> s.model().eval(x)
7226 >>> s.add(2**x == 4)
7232 num = len(assumptions)
7233 _assumptions = (Ast * num)()
7234 for i
in range(num):
7235 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7240 """Return a model for the last `check()`.
7242 This function raises an exception if
7243 a model is not available (e.g., last `check()` returned unsat).
7247 >>> s.add(a + 2 == 0)
7256 raise Z3Exception(
"model is not available")
7259 """Import model converter from other into the current solver"""
7260 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7262 def interrupt(self):
7263 """Interrupt the execution of the solver object.
7264 Remarks: This ensures that the interrupt applies only
7265 to the given solver object and it applies only if it is running.
7267 Z3_solver_interrupt(self.ctx.ref(), self.solver)
7269 def unsat_core(self):
7270 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7272 These are the assumptions Z3 used in the unsatisfiability proof.
7273 Assumptions are available in Z3. They are used to extract unsatisfiable cores.
7274 They may be also used to "retract" assumptions. Note that, assumptions are not really
7275 "soft constraints", but they can be used to implement them.
7277 >>> p1, p2, p3 = Bools('p1 p2 p3')
7278 >>> x, y = Ints('x y')
7280 >>> s.add(Implies(p1, x > 0))
7281 >>> s.add(Implies(p2, y > x))
7282 >>> s.add(Implies(p2, y < 1))
7283 >>> s.add(Implies(p3, y > -3))
7284 >>> s.check(p1, p2, p3)
7286 >>> core = s.unsat_core()
7295 >>> # "Retracting" p2
7299 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7301 def consequences(self, assumptions, variables):
7302 """Determine fixed values for the variables based on the solver state and assumptions.
7304 >>> a, b, c, d = Bools('a b c d')
7305 >>> s.add(Implies(a,b), Implies(b, c))
7306 >>> s.consequences([a],[b,c,d])
7307 (sat, [Implies(a, b), Implies(a, c)])
7308 >>> s.consequences([Not(c),d],[a,b,c,d])
7309 (sat, [Implies(d, d), Implies(Not(c), Not(c)), Implies(Not(c), Not(b)), Implies(Not(c), Not(a))])
7311 if isinstance(assumptions, list):
7312 _asms = AstVector(None, self.ctx)
7313 for a in assumptions:
7316 if isinstance(variables, list):
7317 _vars = AstVector(None, self.ctx)
7321 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7322 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7323 consequences = AstVector(None, self.ctx)
7324 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7325 variables.vector, consequences.vector)
7326 sz = len(consequences)
7327 consequences = [consequences[i] for i in range(sz)]
7328 return CheckSatResult(r), consequences
7330 def from_file(self, filename):
7331 """Parse assertions from a file"""
7332 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7334 def from_string(self, s):
7335 """Parse assertions from a string"""
7336 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7338 def cube(self, vars=None):
7340 The method takes an optional set of variables that restrict which
7341 variables may be used as a starting point for cubing.
7342 If vars is not None, then the first case split is based on a variable in
7345 self.cube_vs = AstVector(None, self.ctx)
7346 if vars is not None:
7348 self.cube_vs.push(v)
7350 lvl = self.backtrack_level
7351 self.backtrack_level = 4000000000
7352 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7353 if (len(r) == 1 and is_false(r[0])):
7359 def cube_vars(self):
7360 """Access the set of variables that were touched by the most recently generated cube.
7361 This set of variables can be used as a starting point for additional cubes.
7362 The idea is that variables that appear in clauses that are reduced by the most recent
7363 cube are likely more useful to cube on."""
7367 """Retrieve congruence closure root of the term t relative to the current search state
7368 The function primarily works for SimpleSolver. Terms and variables that are
7369 eliminated during pre-processing are not visible to the congruence closure.
7371 t = _py2expr(t, self.ctx)
7372 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7375 """Retrieve congruence closure sibling of the term t relative to the current search state
7376 The function primarily works for SimpleSolver. Terms and variables that are
7377 eliminated during pre-processing are not visible to the congruence closure.
7379 t = _py2expr(t, self.ctx)
7380 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7382 def explain_congruent(self, a, b):
7383 """Explain congruence of a and b relative to the current search state"""
7384 a = _py2expr(a, self.ctx)
7385 b = _py2expr(b, self.ctx)
7386 return _to_expr_ref(Z3_solver_congruence_explain(self.ctx.ref(), self.solver, a.ast, b.ast), self.ctx)
7388 def solve_for1(self, t):
7389 """Retrieve a solution for t relative to linear equations maintained in the current state.
7390 The function primarily works for SimpleSolver and when there is a solution using linear arithmetic."""
7391 t = _py2expr(t, self.ctx)
7392 return _to_expr_ref(Z3_solver_solve_for1(self.ctx.ref(), self.solver, t.ast), self.ctx)
7394 def solve_for(self, ts):
7395 """Retrieve a solution for t relative to linear equations maintained in the current state."""
7396 vars = AstVector(ctx=self.ctx);
7397 terms = AstVector(ctx=self.ctx);
7398 guards = AstVector(ctx=self.ctx);
7400 t = _py2expr(t, self.ctx)
7402 Z3_solver_solve_for(self.ctx.ref(), self.solver, vars.vector, terms.vector, guards.vector)
7403 return [(vars[i], terms[i], guards[i]) for i in range(len(vars))]
7407 """Return a proof for the last `check()`. Proof construction must be enabled."""
7408 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7410 def assertions(self):
7411 """Return an AST vector containing all added constraints.
7422 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7425 """Return an AST vector containing all currently inferred units.
7427 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7429 def non_units(self):
7430 """Return an AST vector containing all atomic formulas in solver state that are not units.
7432 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7434 def trail_levels(self):
7435 """Return trail and decision levels of the solver state after a check() call.
7437 trail = self.trail()
7438 levels = (ctypes.c_uint * len(trail))()
7439 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7440 return trail, levels
7442 def set_initial_value(self, var, value):
7443 """initialize the solver's state by setting the initial value of var to value
7446 value = s.cast(value)
7447 Z3_solver_set_initial_value(self.ctx.ref(), self.solver, var.ast, value.ast)
7450 """Return trail of the solver state after a check() call.
7452 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7454 def statistics(self):
7455 """Return statistics for the last `check()`.
7457 >>> s = SimpleSolver()
7462 >>> st = s.statistics()
7463 >>> st.get_key_value('final checks')
7470 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7472 def reason_unknown(self):
7473 """Return a string describing why the last `check()` returned `unknown`.
7476 >>> s = SimpleSolver()
7477 >>> s.add(2**x == 4)
7480 >>> s.reason_unknown()
7481 '(incomplete (theory arithmetic))'
7483 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7486 """Display a string describing all available options."""
7487 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7489 def param_descrs(self):
7490 """Return the parameter description set."""
7491 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7494 """Return a formatted string with all added constraints."""
7495 return obj_to_string(self)
7497 def translate(self, target):
7498 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7502 >>> s1 = Solver(ctx=c1)
7503 >>> s2 = s1.translate(c2)
7506 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7507 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7508 return Solver(solver, target)
7511 return self.translate(self.ctx)
7513 def __deepcopy__(self, memo={}):
7514 return self.translate(self.ctx)
7517 """Return a formatted string (in Lisp-like format) with all added constraints.
7518 We say the string is in s-expression format.
7526 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7528 def dimacs(self, include_names=True):
7529 """Return a textual representation of the solver in DIMACS format."""
7530 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7533 """return SMTLIB2 formatted benchmark for solver's assertions"""
7534 es = self.assertions()
7540 for i in range(sz1):
7541 v[i] = es[i].as_ast()
7543 e = es[sz1].as_ast()
7545 e = BoolVal(True, self.ctx).as_ast()
7546 return Z3_benchmark_to_smtlib_string(
7547 self.ctx.ref(), "benchmark generated from python API", "", "unknown", "", sz1, v, e,
7551def SolverFor(logic, ctx=None, logFile=None):
7552 """Create a solver customized for the given logic.
7554 The parameter `logic` is a string. It should be contains
7555 the name of a SMT-LIB logic.
7556 See http://www.smtlib.org/ for the name of all available logics.
7558 >>> s = SolverFor("QF_LIA")
7568 logic = to_symbol(logic)
7569 return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
7572def SimpleSolver(ctx=None, logFile=None):
7573 """Return a simple general purpose solver with limited amount of preprocessing.
7575 >>> s = SimpleSolver()
7582 return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
7584#########################################
7588#########################################
7591class Fixedpoint(Z3PPObject):
7592 """Fixedpoint API provides methods for solving with recursive predicates"""
7594 def __init__(self, fixedpoint=None, ctx=None):
7595 assert fixedpoint is None or ctx is not None
7596 self.ctx = _get_ctx(ctx)
7597 self.fixedpoint = None
7598 if fixedpoint is None:
7599 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7601 self.fixedpoint = fixedpoint
7602 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7605 def __deepcopy__(self, memo={}):
7606 return FixedPoint(self.fixedpoint, self.ctx)
7609 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7610 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7612 def set(self, *args, **keys):
7613 """Set a configuration option. The method `help()` return a string containing all available options.
7615 p = args2params(args, keys, self.ctx)
7616 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7619 """Display a string describing all available options."""
7620 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7622 def param_descrs(self):
7623 """Return the parameter description set."""
7624 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7626 def assert_exprs(self, *args):
7627 """Assert constraints as background axioms for the fixedpoint solver."""
7628 args = _get_args(args)
7629 s = BoolSort(self.ctx)
7631 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7633 f = self.abstract(f)
7634 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7637 arg = self.abstract(arg)
7638 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7640 def add(self, *args):
7641 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7642 self.assert_exprs(*args)
7644 def __iadd__(self, fml):
7648 def append(self, *args):
7649 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7650 self.assert_exprs(*args)
7652 def insert(self, *args):
7653 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7654 self.assert_exprs(*args)
7656 def add_rule(self, head, body=None, name=None):
7657 """Assert rules defining recursive predicates to the fixedpoint solver.
7660 >>> s = Fixedpoint()
7661 >>> s.register_relation(a.decl())
7662 >>> s.register_relation(b.decl())
7670 name = to_symbol(name, self.ctx)
7672 head = self.abstract(head)
7673 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7675 body = _get_args(body)
7676 f = self.abstract(Implies(And(body, self.ctx), head))
7677 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7679 def rule(self, head, body=None, name=None):
7680 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7681 self.add_rule(head, body, name)
7683 def fact(self, head, name=None):
7684 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7685 self.add_rule(head, None, name)
7687 def query(self, *query):
7688 """Query the fixedpoint engine whether formula is derivable.
7689 You can also pass an tuple or list of recursive predicates.
7691 query = _get_args(query)
7693 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7694 _decls = (FuncDecl * sz)()
7699 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7704 query = And(query, self.ctx)
7705 query = self.abstract(query, False)
7706 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7707 return CheckSatResult(r)
7709 def query_from_lvl(self, lvl, *query):
7710 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7712 query = _get_args(query)
7714 if sz >= 1 and isinstance(query[0], FuncDecl):
7715 _z3_assert(False, "unsupported")
7721 query = self.abstract(query, False)
7722 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7723 return CheckSatResult(r)
7725 def update_rule(self, head, body, name):
7729 name = to_symbol(name, self.ctx)
7730 body = _get_args(body)
7731 f = self.abstract(Implies(And(body, self.ctx), head))
7732 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7734 def get_answer(self):
7735 """Retrieve answer from last query call."""
7736 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7737 return _to_expr_ref(r, self.ctx)
7739 def get_ground_sat_answer(self):
7740 """Retrieve a ground cex from last query call."""
7741 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7742 return _to_expr_ref(r, self.ctx)
7744 def get_rules_along_trace(self):
7745 """retrieve rules along the counterexample trace"""
7746 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7748 def get_rule_names_along_trace(self):
7749 """retrieve rule names along the counterexample trace"""
7750 # this is a hack as I don't know how to return a list of symbols from C++;
7751 # obtain names as a single string separated by semicolons
7752 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7753 # split into individual names
7754 return names.split(";")
7756 def get_num_levels(self, predicate):
7757 """Retrieve number of levels used for predicate in PDR engine"""
7758 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7760 def get_cover_delta(self, level, predicate):
7761 """Retrieve properties known about predicate for the level'th unfolding.
7762 -1 is treated as the limit (infinity)
7764 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7765 return _to_expr_ref(r, self.ctx)
7767 def add_cover(self, level, predicate, property):
7768 """Add property to predicate for the level'th unfolding.
7769 -1 is treated as infinity (infinity)
7771 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7773 def register_relation(self, *relations):
7774 """Register relation as recursive"""
7775 relations = _get_args(relations)
7777 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7779 def set_predicate_representation(self, f, *representations):
7780 """Control how relation is represented"""
7781 representations = _get_args(representations)
7782 representations = [to_symbol(s) for s in representations]
7783 sz = len(representations)
7784 args = (Symbol * sz)()
7786 args[i] = representations[i]
7787 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7789 def parse_string(self, s):
7790 """Parse rules and queries from a string"""
7791 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7793 def parse_file(self, f):
7794 """Parse rules and queries from a file"""
7795 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7797 def get_rules(self):
7798 """retrieve rules that have been added to fixedpoint context"""
7799 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7801 def get_assertions(self):
7802 """retrieve assertions that have been added to fixedpoint context"""
7803 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7806 """Return a formatted string with all added rules and constraints."""
7810 """Return a formatted string (in Lisp-like format) with all added constraints.
7811 We say the string is in s-expression format.
7813 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7815 def to_string(self, queries):
7816 """Return a formatted string (in Lisp-like format) with all added constraints.
7817 We say the string is in s-expression format.
7818 Include also queries.
7820 args, len = _to_ast_array(queries)
7821 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7823 def statistics(self):
7824 """Return statistics for the last `query()`.
7826 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7828 def reason_unknown(self):
7829 """Return a string describing why the last `query()` returned `unknown`.
7831 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7833 def declare_var(self, *vars):
7834 """Add variable or several variables.
7835 The added variable or variables will be bound in the rules
7838 vars = _get_args(vars)
7842 def abstract(self, fml, is_forall=True):
7846 return ForAll(self.vars, fml)
7848 return Exists(self.vars, fml)
7851#########################################
7855#########################################
7857class FiniteDomainSortRef(SortRef):
7858 """Finite domain sort."""
7861 """Return the size of the finite domain sort"""
7862 r = (ctypes.c_ulonglong * 1)()
7863 if Z3_get_finite_domain_sort_size(self.ctx_ref(), self.ast, r):
7866 raise Z3Exception("Failed to retrieve finite domain sort size")
7869def FiniteDomainSort(name, sz, ctx=None):
7870 """Create a named finite domain sort of a given size sz"""
7871 if not isinstance(name, Symbol):
7872 name = to_symbol(name)
7874 return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
7877def is_finite_domain_sort(s):
7878 """Return True if `s` is a Z3 finite-domain sort.
7880 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7882 >>> is_finite_domain_sort(IntSort())
7885 return isinstance(s, FiniteDomainSortRef)
7888class FiniteDomainRef(ExprRef):
7889 """Finite-domain expressions."""
7892 """Return the sort of the finite-domain expression `self`."""
7893 return FiniteDomainSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
7895 def as_string(self):
7896 """Return a Z3 floating point expression as a Python string."""
7897 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
7900def is_finite_domain(a):
7901 """Return `True` if `a` is a Z3 finite-domain expression.
7903 >>> s = FiniteDomainSort('S', 100)
7904 >>> b = Const('b', s)
7905 >>> is_finite_domain(b)
7907 >>> is_finite_domain(Int('x'))
7910 return isinstance(a, FiniteDomainRef)
7913class FiniteDomainNumRef(FiniteDomainRef):
7914 """Integer values."""
7917 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7919 >>> s = FiniteDomainSort('S', 100)
7920 >>> v = FiniteDomainVal(3, s)
7926 return int(self.as_string())
7928 def as_string(self):
7929 """Return a Z3 finite-domain numeral as a Python string.
7931 >>> s = FiniteDomainSort('S', 100)
7932 >>> v = FiniteDomainVal(42, s)
7936 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
7939def FiniteDomainVal(val, sort, ctx=None):
7940 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7942 >>> s = FiniteDomainSort('S', 256)
7943 >>> FiniteDomainVal(255, s)
7945 >>> FiniteDomainVal('100', s)
7949 _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
7951 return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
7954def is_finite_domain_value(a):
7955 """Return `True` if `a` is a Z3 finite-domain value.
7957 >>> s = FiniteDomainSort('S', 100)
7958 >>> b = Const('b', s)
7959 >>> is_finite_domain_value(b)
7961 >>> b = FiniteDomainVal(10, s)
7964 >>> is_finite_domain_value(b)
7967 return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
7970#########################################
7974#########################################
7976class OptimizeObjective:
7977 def __init__(self, opt, value, is_max):
7980 self._is_max = is_max
7984 return _to_expr_ref(Z3_optimize_get_lower(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7988 return _to_expr_ref(Z3_optimize_get_upper(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7990 def lower_values(self):
7992 return AstVector(Z3_optimize_get_lower_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7994 def upper_values(self):
7996 return AstVector(Z3_optimize_get_upper_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
8005 return "%s:%s" % (self._value, self._is_max)
8011def _global_on_model(ctx):
8012 (fn, mdl) = _on_models[ctx]
8016_on_model_eh = on_model_eh_type(_global_on_model)
8019class Optimize(Z3PPObject):
8020 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
8022 def __init__(self, optimize=None, ctx=None):
8023 self.ctx = _get_ctx(ctx)
8024 if optimize is None:
8025 self.optimize = Z3_mk_optimize(self.ctx.ref())
8027 self.optimize = optimize
8028 self._on_models_id = None
8029 Z3_optimize_inc_ref(self.ctx.ref(), self.optimize)
8031 def __deepcopy__(self, memo={}):
8032 return Optimize(self.optimize, self.ctx)
8035 if self.optimize is not None and self.ctx.ref() is not None and Z3_optimize_dec_ref is not None:
8036 Z3_optimize_dec_ref(self.ctx.ref(), self.optimize)
8037 if self._on_models_id is not None:
8038 del _on_models[self._on_models_id]
8040 def __enter__(self):
8044 def __exit__(self, *exc_info):
8047 def set(self, *args, **keys):
8048 """Set a configuration option.
8049 The method `help()` return a string containing all available options.
8051 p = args2params(args, keys, self.ctx)
8052 Z3_optimize_set_params(self.ctx.ref(), self.optimize, p.params)
8055 """Display a string describing all available options."""
8056 print(Z3_optimize_get_help(self.ctx.ref(), self.optimize))
8058 def param_descrs(self):
8059 """Return the parameter description set."""
8060 return ParamDescrsRef(Z3_optimize_get_param_descrs(self.ctx.ref(), self.optimize), self.ctx)
8062 def assert_exprs(self, *args):
8063 """Assert constraints as background axioms for the optimize solver."""
8064 args = _get_args(args)
8065 s = BoolSort(self.ctx)
8067 if isinstance(arg, Goal) or isinstance(arg, AstVector):
8069 Z3_optimize_assert(self.ctx.ref(), self.optimize, f.as_ast())
8072 Z3_optimize_assert(self.ctx.ref(), self.optimize, arg.as_ast())
8074 def add(self, *args):
8075 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
8076 self.assert_exprs(*args)
8078 def __iadd__(self, fml):
8082 def assert_and_track(self, a, p):
8083 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
8085 If `p` is a string, it will be automatically converted into a Boolean constant.
8090 >>> s.assert_and_track(x > 0, 'p1')
8091 >>> s.assert_and_track(x != 1, 'p2')
8092 >>> s.assert_and_track(x < 0, p3)
8093 >>> print(s.check())
8095 >>> c = s.unsat_core()
8105 if isinstance(p, str):
8106 p = Bool(p, self.ctx)
8107 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
8108 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
8109 Z3_optimize_assert_and_track(self.ctx.ref(), self.optimize, a.as_ast(), p.as_ast())
8111 def add_soft(self, arg, weight="1", id=None):
8112 """Add soft constraint with optional weight and optional identifier.
8113 If no weight is supplied, then the penalty for violating the soft constraint
8115 Soft constraints are grouped by identifiers. Soft constraints that are
8116 added without identifiers are grouped by default.
8119 weight = "%d" % weight
8120 elif isinstance(weight, float):
8121 weight = "%f" % weight
8122 if not isinstance(weight, str):
8123 raise Z3Exception("weight should be a string or an integer")
8126 id = to_symbol(id, self.ctx)
8129 v = Z3_optimize_assert_soft(self.ctx.ref(), self.optimize, a.as_ast(), weight, id)
8130 return OptimizeObjective(self, v, False)
8131 if sys.version_info.major >= 3 and isinstance(arg, Iterable):
8132 return [asoft(a) for a in arg]
8135 def set_initial_value(self, var, value):
8136 """initialize the solver's state by setting the initial value of var to value
8139 value = s.cast(value)
8140 Z3_optimize_set_initial_value(self.ctx.ref(), self.optimize, var.ast, value.ast)
8142 def maximize(self, arg):
8143 """Add objective function to maximize."""
8144 return OptimizeObjective(
8146 Z3_optimize_maximize(self.ctx.ref(), self.optimize, arg.as_ast()),
8150 def minimize(self, arg):
8151 """Add objective function to minimize."""
8152 return OptimizeObjective(
8154 Z3_optimize_minimize(self.ctx.ref(), self.optimize, arg.as_ast()),
8159 """create a backtracking point for added rules, facts and assertions"""
8160 Z3_optimize_push(self.ctx.ref(), self.optimize)
8163 """restore to previously created backtracking point"""
8164 Z3_optimize_pop(self.ctx.ref(), self.optimize)
8166 def check(self, *assumptions):
8167 """Check consistency and produce optimal values."""
8168 assumptions = _get_args(assumptions)
8169 num = len(assumptions)
8170 _assumptions = (Ast * num)()
8171 for i in range(num):
8172 _assumptions[i] = assumptions[i].as_ast()
8173 return CheckSatResult(Z3_optimize_check(self.ctx.ref(), self.optimize, num, _assumptions))
8175 def reason_unknown(self):
8176 """Return a string that describes why the last `check()` returned `unknown`."""
8177 return Z3_optimize_get_reason_unknown(self.ctx.ref(), self.optimize)
8180 """Return a model for the last check()."""
8182 return ModelRef(Z3_optimize_get_model(self.ctx.ref(), self.optimize), self.ctx)
8184 raise Z3Exception("model is not available")
8186 def unsat_core(self):
8187 return AstVector(Z3_optimize_get_unsat_core(self.ctx.ref(), self.optimize), self.ctx)
8189 def lower(self, obj):
8190 if not isinstance(obj, OptimizeObjective):
8191 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8194 def upper(self, obj):
8195 if not isinstance(obj, OptimizeObjective):
8196 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8199 def lower_values(self, obj):
8200 if not isinstance(obj, OptimizeObjective):
8201 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8202 return obj.lower_values()
8204 def upper_values(self, obj):
8205 if not isinstance(obj, OptimizeObjective):
8206 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8207 return obj.upper_values()
8209 def from_file(self, filename):
8210 """Parse assertions and objectives from a file"""
8211 Z3_optimize_from_file(self.ctx.ref(), self.optimize, filename)
8213 def from_string(self, s):
8214 """Parse assertions and objectives from a string"""
8215 Z3_optimize_from_string(self.ctx.ref(), self.optimize, s)
8217 def assertions(self):
8218 """Return an AST vector containing all added constraints."""
8219 return AstVector(Z3_optimize_get_assertions(self.ctx.ref(), self.optimize), self.ctx)
8221 def objectives(self):
8222 """returns set of objective functions"""
8223 return AstVector(Z3_optimize_get_objectives(self.ctx.ref(), self.optimize), self.ctx)
8226 """Return a formatted string with all added rules and constraints."""
8230 """Return a formatted string (in Lisp-like format) with all added constraints.
8231 We say the string is in s-expression format.
8233 return Z3_optimize_to_string(self.ctx.ref(), self.optimize)
8235 def statistics(self):
8236 """Return statistics for the last check`.
8238 return Statistics(Z3_optimize_get_statistics(self.ctx.ref(), self.optimize), self.ctx)
8240 def set_on_model(self, on_model):
8241 """Register a callback that is invoked with every incremental improvement to
8242 objective values. The callback takes a model as argument.
8243 The life-time of the model is limited to the callback so the
8244 model has to be (deep) copied if it is to be used after the callback
8246 id = len(_on_models) + 41
8247 mdl = Model(self.ctx)
8248 _on_models[id] = (on_model, mdl)
8249 self._on_models_id = id
8250 Z3_optimize_register_model_eh(
8251 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8255#########################################
8259#########################################
8260class ApplyResult(Z3PPObject):
8261 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8262 It also contains model and proof converters.
8265 def __init__(self, result, ctx):
8266 self.result = result
8268 Z3_apply_result_inc_ref(self.ctx.ref(), self.result)
8270 def __deepcopy__(self, memo={}):
8271 return ApplyResult(self.result, self.ctx)
8274 if self.ctx.ref() is not None and Z3_apply_result_dec_ref is not None:
8275 Z3_apply_result_dec_ref(self.ctx.ref(), self.result)
8278 """Return the number of subgoals in `self`.
8280 >>> a, b = Ints('a b')
8282 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8283 >>> t = Tactic('split-clause')
8287 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8290 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8294 return int(Z3_apply_result_get_num_subgoals(self.ctx.ref(), self.result))
8296 def __getitem__(self, idx):
8297 """Return one of the subgoals stored in ApplyResult object `self`.
8299 >>> a, b = Ints('a b')
8301 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8302 >>> t = Tactic('split-clause')
8305 [a == 0, Or(b == 0, b == 1), a > b]
8307 [a == 1, Or(b == 0, b == 1), a > b]
8309 if idx >= len(self):
8311 return Goal(goal=Z3_apply_result_get_subgoal(self.ctx.ref(), self.result, idx), ctx=self.ctx)
8314 return obj_to_string(self)
8317 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8318 return Z3_apply_result_to_string(self.ctx.ref(), self.result)
8321 """Return a Z3 expression consisting of all subgoals.
8326 >>> g.add(Or(x == 2, x == 3))
8327 >>> r = Tactic('simplify')(g)
8329 [[Not(x <= 1), Or(x == 2, x == 3)]]
8331 And(Not(x <= 1), Or(x == 2, x == 3))
8332 >>> r = Tactic('split-clause')(g)
8334 [[x > 1, x == 2], [x > 1, x == 3]]
8336 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8340 return BoolVal(False, self.ctx)
8342 return self[0].as_expr()
8344 return Or([self[i].as_expr() for i in range(len(self))])
8346#########################################
8350#########################################
8353 """Simplifiers act as pre-processing utilities for solvers.
8354 Build a custom simplifier and add it to a solve
r"""
8356 def __init__(self, simplifier, ctx=None):
8357 self.ctx = _get_ctx(ctx)
8358 self.simplifier = None
8359 if isinstance(simplifier, SimplifierObj):
8360 self.simplifier = simplifier
8361 elif isinstance(simplifier, list):
8362 simps = [Simplifier(s, ctx) for s in simplifier]
8363 self.simplifier = simps[0].simplifier
8364 for i in range(1, len(simps)):
8365 self.simplifier = Z3_simplifier_and_then(self.ctx.ref(), self.simplifier, simps[i].simplifier)
8366 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8370 _z3_assert(isinstance(simplifier, str), "simplifier name expected")
8372 self.simplifier = Z3_mk_simplifier(self.ctx.ref(), str(simplifier))
8374 raise Z3Exception("unknown simplifier '%s'" % simplifier)
8375 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8377 def __deepcopy__(self, memo={}):
8378 return Simplifier(self.simplifier, self.ctx)
8381 if self.simplifier is not None and self.ctx.ref() is not None and Z3_simplifier_dec_ref is not None:
8382 Z3_simplifier_dec_ref(self.ctx.ref(), self.simplifier)
8384 def using_params(self, *args, **keys):
8385 """Return a simplifier that uses the given configuration options"""
8386 p = args2params(args, keys, self.ctx)
8387 return Simplifier(Z3_simplifier_using_params(self.ctx.ref(), self.simplifier, p.params), self.ctx)
8389 def add(self, solver):
8390 """Return a solver that applies the simplification pre-processing specified by the simplifie
r"""
8391 return Solver(Z3_solver_add_simplifier(self.ctx.ref(), solver.solver, self.simplifier), self.ctx)
8394 """Display a string containing a description of the available options for the `self` simplifier."""
8395 print(Z3_simplifier_get_help(self.ctx.ref(), self.simplifier))
8397 def param_descrs(self):
8398 """Return the parameter description set."""
8399 return ParamDescrsRef(Z3_simplifier_get_param_descrs(self.ctx.ref(), self.simplifier), self.ctx)
8402#########################################
8406#########################################
8410 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8411 A Tactic can be converted into a Solver using the method solver().
8413 Several combinators are available for creating new tactics using the built-in ones:
8414 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8417 def __init__(self, tactic, ctx=None):
8418 self.ctx = _get_ctx(ctx)
8420 if isinstance(tactic, TacticObj):
8421 self.tactic = tactic
8424 _z3_assert(isinstance(tactic, str), "tactic name expected")
8426 self.tactic = Z3_mk_tactic(self.ctx.ref(), str(tactic))
8428 raise Z3Exception("unknown tactic '%s'" % tactic)
8429 Z3_tactic_inc_ref(self.ctx.ref(), self.tactic)
8431 def __deepcopy__(self, memo={}):
8432 return Tactic(self.tactic, self.ctx)
8435 if self.tactic is not None and self.ctx.ref() is not None and Z3_tactic_dec_ref is not None:
8436 Z3_tactic_dec_ref(self.ctx.ref(), self.tactic)
8438 def solver(self, logFile=None):
8439 """Create a solver using the tactic `self`.
8441 The solver supports the methods `push()` and `pop()`, but it
8442 will always solve each `check()` from scratch.
8444 >>> t = Then('simplify', 'nlsat')
8447 >>> s.add(x**2 == 2, x > 0)
8453 return Solver(Z3_mk_solver_from_tactic(self.ctx.ref(), self.tactic), self.ctx, logFile)
8455 def apply(self, goal, *arguments, **keywords):
8456 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8458 >>> x, y = Ints('x y')
8459 >>> t = Tactic('solve-eqs')
8460 >>> t.apply(And(x == 0, y >= x + 1))
8464 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expressions expected")
8465 goal = _to_goal(goal)
8466 if len(arguments) > 0 or len(keywords) > 0:
8467 p = args2params(arguments, keywords, self.ctx)
8468 return ApplyResult(Z3_tactic_apply_ex(self.ctx.ref(), self.tactic, goal.goal, p.params), self.ctx)
8470 return ApplyResult(Z3_tactic_apply(self.ctx.ref(), self.tactic, goal.goal), self.ctx)
8472 def __call__(self, goal, *arguments, **keywords):
8473 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8475 >>> x, y = Ints('x y')
8476 >>> t = Tactic('solve-eqs')
8477 >>> t(And(x == 0, y >= x + 1))
8480 return self.apply(goal, *arguments, **keywords)
8483 """Display a string containing a description of the available options for the `self` tactic."""
8484 print(Z3_tactic_get_help(self.ctx.ref(), self.tactic))
8486 def param_descrs(self):
8487 """Return the parameter description set."""
8488 return ParamDescrsRef(Z3_tactic_get_param_descrs(self.ctx.ref(), self.tactic), self.ctx)
8492 if isinstance(a, BoolRef):
8493 goal = Goal(ctx=a.ctx)
8500def _to_tactic(t, ctx=None):
8501 if isinstance(t, Tactic):
8504 return Tactic(t, ctx)
8507def _and_then(t1, t2, ctx=None):
8508 t1 = _to_tactic(t1, ctx)
8509 t2 = _to_tactic(t2, ctx)
8511 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8512 return Tactic(Z3_tactic_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8515def _or_else(t1, t2, ctx=None):
8516 t1 = _to_tactic(t1, ctx)
8517 t2 = _to_tactic(t2, ctx)
8519 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8520 return Tactic(Z3_tactic_or_else(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8523def AndThen(*ts, **ks):
8524 """Return a tactic that applies the tactics in `*ts` in sequence.
8526 >>> x, y = Ints('x y')
8527 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8528 >>> t(And(x == 0, y > x + 1))
8530 >>> t(And(x == 0, y > x + 1)).as_expr()
8534 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8535 ctx = ks.get("ctx", None)
8538 for i in range(num - 1):
8539 r = _and_then(r, ts[i + 1], ctx)
8544 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8546 >>> x, y = Ints('x y')
8547 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8548 >>> t(And(x == 0, y > x + 1))
8550 >>> t(And(x == 0, y > x + 1)).as_expr()
8553 return AndThen(*ts, **ks)
8556def OrElse(*ts, **ks):
8557 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8560 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8561 >>> # Tactic split-clause fails if there is no clause in the given goal.
8564 >>> t(Or(x == 0, x == 1))
8565 [[x == 0], [x == 1]]
8568 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8569 ctx = ks.get("ctx", None)
8572 for i in range(num - 1):
8573 r = _or_else(r, ts[i + 1], ctx)
8577def ParOr(*ts, **ks):
8578 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8581 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8586 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8587 ctx = _get_ctx(ks.get("ctx", None))
8588 ts = [_to_tactic(t, ctx) for t in ts]
8590 _args = (TacticObj * sz)()
8592 _args[i] = ts[i].tactic
8593 return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
8596def ParThen(t1, t2, ctx=None):
8597 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8598 The subgoals are processed in parallel.
8600 >>> x, y = Ints('x y')
8601 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8602 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8603 [[x == 1, y == 2], [x == 2, y == 3]]
8605 t1 = _to_tactic(t1, ctx)
8606 t2 = _to_tactic(t2, ctx)
8608 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8609 return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8612def ParAndThen(t1, t2, ctx=None):
8613 """Alias for ParThen(t1, t2, ctx)."""
8614 return ParThen(t1, t2, ctx)
8617def With(t, *args, **keys):
8618 """Return a tactic that applies tactic `t` using the given configuration options.
8620 >>> x, y = Ints('x y')
8621 >>> t = With(Tactic('simplify'), som=True)
8622 >>> t((x + 1)*(y + 2) == 0)
8623 [[2*x + y + x*y == -2]]
8625 ctx = keys.pop("ctx", None)
8626 t = _to_tactic(t, ctx)
8627 p = args2params(args, keys, t.ctx)
8628 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8631def WithParams(t, p):
8632 """Return a tactic that applies tactic `t` using the given configuration options.
8634 >>> x, y = Ints('x y')
8636 >>> p.set("som", True)
8637 >>> t = WithParams(Tactic('simplify'), p)
8638 >>> t((x + 1)*(y + 2) == 0)
8639 [[2*x + y + x*y == -2]]
8641 t = _to_tactic(t, None)
8642 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8645def Repeat(t, max=4294967295, ctx=None):
8646 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8647 or the maximum number of iterations `max` is reached.
8649 >>> x, y = Ints('x y')
8650 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8651 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8653 >>> for subgoal in r: print(subgoal)
8654 [x == 0, y == 0, x > y]
8655 [x == 0, y == 1, x > y]
8656 [x == 1, y == 0, x > y]
8657 [x == 1, y == 1, x > y]
8658 >>> t = Then(t, Tactic('propagate-values'))
8662 t = _to_tactic(t, ctx)
8663 return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
8666def TryFor(t, ms, ctx=None):
8667 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8669 If `t` does not terminate in `ms` milliseconds, then it fails.
8671 t = _to_tactic(t, ctx)
8672 return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
8675def tactics(ctx=None):
8676 """Return a list of all available tactics in Z3.
8679 >>> l.count('simplify') == 1
8683 return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
8686def tactic_description(name, ctx=None):
8687 """Return a short description for the tactic named `name`.
8689 >>> d = tactic_description('simplify')
8692 return Z3_tactic_get_descr(ctx.ref(), name)
8695def describe_tactics():
8696 """Display a (tabular) description of all available tactics in Z3."""
8699 print('<table border="1" cellpadding="2" cellspacing="0">')
8702 print('<tr style="background-color:#CFCFCF">')
8707 print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
8711 print("%s : %s" % (t, tactic_description(t)))
8715 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8716 to decide which solver and/or preprocessing step will be used.
8719 def __init__(self, probe, ctx=None):
8720 self.ctx = _get_ctx(ctx)
8722 if isinstance(probe, ProbeObj):
8724 elif isinstance(probe, float):
8725 self.probe = Z3_probe_const(self.ctx.ref(), probe)
8726 elif _is_int(probe):
8727 self.probe = Z3_probe_const(self.ctx.ref(), float(probe))
8728 elif isinstance(probe, bool):
8730 self.probe = Z3_probe_const(self.ctx.ref(), 1.0)
8732 self.probe = Z3_probe_const(self.ctx.ref(), 0.0)
8735 _z3_assert(isinstance(probe, str), "probe name expected")
8737 self.probe = Z3_mk_probe(self.ctx.ref(), probe)
8739 raise Z3Exception("unknown probe '%s'" % probe)
8740 Z3_probe_inc_ref(self.ctx.ref(), self.probe)
8742 def __deepcopy__(self, memo={}):
8743 return Probe(self.probe, self.ctx)
8746 if self.probe is not None and self.ctx.ref() is not None and Z3_probe_dec_ref is not None:
8747 Z3_probe_dec_ref(self.ctx.ref(), self.probe)
8749 def __lt__(self, other):
8750 """Return a probe that evaluates to "true" when the value returned by `self`
8751 is less than the value returned by `other`.
8753 >>> p = Probe('size') < 10
8761 return Probe(Z3_probe_lt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8763 def __gt__(self, other):
8764 """Return a probe that evaluates to "true" when the value returned by `self`
8765 is greater than the value returned by `other`.
8767 >>> p = Probe('size') > 10
8775 return Probe(Z3_probe_gt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8777 def __le__(self, other):
8778 """Return a probe that evaluates to "true" when the value returned by `self`
8779 is less than or equal to the value returned by `other`.
8781 >>> p = Probe('size') <= 2
8789 return Probe(Z3_probe_le(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8791 def __ge__(self, other):
8792 """Return a probe that evaluates to "true" when the value returned by `self`
8793 is greater than or equal to the value returned by `other`.
8795 >>> p = Probe('size') >= 2
8803 return Probe(Z3_probe_ge(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8805 def __eq__(self, other):
8806 """Return a probe that evaluates to "true" when the value returned by `self`
8807 is equal to the value returned by `other`.
8809 >>> p = Probe('size') == 2
8817 return Probe(Z3_probe_eq(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8819 def __ne__(self, other):
8820 """Return a probe that evaluates to "true" when the value returned by `self`
8821 is not equal to the value returned by `other`.
8823 >>> p = Probe('size') != 2
8831 p = self.__eq__(other)
8832 return Probe(Z3_probe_not(self.ctx.ref(), p.probe), self.ctx)
8834 def __call__(self, goal):
8835 """Evaluate the probe `self` in the given goal.
8837 >>> p = Probe('size')
8847 >>> p = Probe('num-consts')
8850 >>> p = Probe('is-propositional')
8853 >>> p = Probe('is-qflia')
8858 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expression expected")
8859 goal = _to_goal(goal)
8860 return Z3_probe_apply(self.ctx.ref(), self.probe, goal.goal)
8864 """Return `True` if `p` is a Z3 probe.
8866 >>> is_probe(Int('x'))
8868 >>> is_probe(Probe('memory'))
8871 return isinstance(p, Probe)
8874def _to_probe(p, ctx=None):
8878 return Probe(p, ctx)
8881def probes(ctx=None):
8882 """Return a list of all available probes in Z3.
8885 >>> l.count('memory') == 1
8889 return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
8892def probe_description(name, ctx=None):
8893 """Return a short description for the probe named `name`.
8895 >>> d = probe_description('memory')
8898 return Z3_probe_get_descr(ctx.ref(), name)
8901def describe_probes():
8902 """Display a (tabular) description of all available probes in Z3."""
8905 print('<table border="1" cellpadding="2" cellspacing="0">')
8908 print('<tr style="background-color:#CFCFCF">')
8913 print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
8917 print("%s : %s" % (p, probe_description(p)))
8920def _probe_nary(f, args, ctx):
8922 _z3_assert(len(args) > 0, "At least one argument expected")
8924 r = _to_probe(args[0], ctx)
8925 for i in range(num - 1):
8926 r = Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8930def _probe_and(args, ctx):
8931 return _probe_nary(Z3_probe_and, args, ctx)
8934def _probe_or(args, ctx):
8935 return _probe_nary(Z3_probe_or, args, ctx)
8938def FailIf(p, ctx=None):
8939 """Return a tactic that fails if the probe `p` evaluates to true.
8940 Otherwise, it returns the input goal unmodified.
8942 In the following example, the tactic applies 'simplify' if and only if there are
8943 more than 2 constraints in the goal.
8945 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8946 >>> x, y = Ints('x y')
8952 >>> g.add(x == y + 1)
8954 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8956 p = _to_probe(p, ctx)
8957 return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
8960def When(p, t, ctx=None):
8961 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8962 Otherwise, it returns the input goal unmodified.
8964 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8965 >>> x, y = Ints('x y')
8971 >>> g.add(x == y + 1)
8973 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8975 p = _to_probe(p, ctx)
8976 t = _to_tactic(t, ctx)
8977 return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
8980def Cond(p, t1, t2, ctx=None):
8981 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8983 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8985 p = _to_probe(p, ctx)
8986 t1 = _to_tactic(t1, ctx)
8987 t2 = _to_tactic(t2, ctx)
8988 return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
8990#########################################
8994#########################################
8997def simplify(a, *arguments, **keywords):
8998 """Simplify the expression `a` using the given options.
9000 This function has many options. Use `help_simplify` to obtain the complete list.
9004 >>> simplify(x + 1 + y + x + 1)
9006 >>> simplify((x + 1)*(y + 1), som=True)
9008 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
9009 And(Not(x == y), Not(x == 1), Not(y == 1))
9010 >>> simplify(And(x == 0, y == 1), elim_and=True)
9011 Not(Or(Not(x == 0), Not(y == 1)))
9014 _z3_assert(is_expr(a), "Z3 expression expected")
9015 if len(arguments) > 0 or len(keywords) > 0:
9016 p = args2params(arguments, keywords, a.ctx)
9017 return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
9019 return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
9023 """Return a string describing all options available for Z3 `simplify` procedure."""
9024 print(Z3_simplify_get_help(main_ctx().ref()))
9027def simplify_param_descrs():
9028 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
9029 return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
9032def substitute(t, *m):
9033 """Apply substitution m on t, m is a list of pairs of the form (from, to).
9034 Every occurrence in t of from is replaced with to.
9038 >>> substitute(x + 1, (x, y + 1))
9040 >>> f = Function('f', IntSort(), IntSort())
9041 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
9044 if isinstance(m, tuple):
9046 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9049 _z3_assert(is_expr(t), "Z3 expression expected")
9051 all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
9052 "Z3 invalid substitution, expression pairs expected.")
9054 all([p[0].sort().eq(p[1].sort()) for p in m]),
9055 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
9057 _from = (Ast * num)()
9059 for i in range(num):
9060 _from[i] = m[i][0].as_ast()
9061 _to[i] = m[i][1].as_ast()
9062 return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9065def substitute_vars(t, *m):
9066 """Substitute the free variables in t with the expression in m.
9068 >>> v0 = Var(0, IntSort())
9069 >>> v1 = Var(1, IntSort())
9071 >>> f = Function('f', IntSort(), IntSort(), IntSort())
9072 >>> # replace v0 with x+1 and v1 with x
9073 >>> substitute_vars(f(v0, v1), x + 1, x)
9077 _z3_assert(is_expr(t), "Z3 expression expected")
9078 _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
9081 for i in range(num):
9082 _to[i] = m[i].as_ast()
9083 return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
9085def substitute_funs(t, *m):
9086 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
9087 Every occurrence in to of the function from is replaced with the expression to.
9088 The expression to can have free variables, that refer to the arguments of from.
9091 if isinstance(m, tuple):
9093 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9096 _z3_assert(is_expr(t), "Z3 expression expected")
9097 _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, function pairs expected.")
9099 _from = (FuncDecl * num)()
9101 for i in range(num):
9102 _from[i] = m[i][0].as_func_decl()
9103 _to[i] = m[i][1].as_ast()
9104 return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9108 """Create the sum of the Z3 expressions.
9110 >>> a, b, c = Ints('a b c')
9115 >>> A = IntVector('a', 5)
9117 a__0 + a__1 + a__2 + a__3 + a__4
9119 args = _get_args(args)
9122 ctx = _ctx_from_ast_arg_list(args)
9124 return _reduce(lambda a, b: a + b, args, 0)
9125 args = _coerce_expr_list(args, ctx)
9127 return _reduce(lambda a, b: a + b, args, 0)
9129 _args, sz = _to_ast_array(args)
9130 return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
9134 """Create the product of the Z3 expressions.
9136 >>> a, b, c = Ints('a b c')
9137 >>> Product(a, b, c)
9139 >>> Product([a, b, c])
9141 >>> A = IntVector('a', 5)
9143 a__0*a__1*a__2*a__3*a__4
9145 args = _get_args(args)
9148 ctx = _ctx_from_ast_arg_list(args)
9150 return _reduce(lambda a, b: a * b, args, 1)
9151 args = _coerce_expr_list(args, ctx)
9153 return _reduce(lambda a, b: a * b, args, 1)
9155 _args, sz = _to_ast_array(args)
9156 return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
9159 """Create the absolute value of an arithmetic expression"""
9160 return If(arg > 0, arg, -arg)
9164 """Create an at-most Pseudo-Boolean k constraint.
9166 >>> a, b, c = Bools('a b c')
9167 >>> f = AtMost(a, b, c, 2)
9169 args = _get_args(args)
9171 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9172 ctx = _ctx_from_ast_arg_list(args)
9174 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9175 args1 = _coerce_expr_list(args[:-1], ctx)
9177 _args, sz = _to_ast_array(args1)
9178 return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
9182 """Create an at-least Pseudo-Boolean k constraint.
9184 >>> a, b, c = Bools('a b c')
9185 >>> f = AtLeast(a, b, c, 2)
9187 args = _get_args(args)
9189 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9190 ctx = _ctx_from_ast_arg_list(args)
9192 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9193 args1 = _coerce_expr_list(args[:-1], ctx)
9195 _args, sz = _to_ast_array(args1)
9196 return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
9199def _reorder_pb_arg(arg):
9201 if not _is_int(b) and _is_int(a):
9206def _pb_args_coeffs(args, default_ctx=None):
9207 args = _get_args_ast_list(args)
9209 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9210 args = [_reorder_pb_arg(arg) for arg in args]
9211 args, coeffs = zip(*args)
9213 _z3_assert(len(args) > 0, "Non empty list of arguments expected")
9214 ctx = _ctx_from_ast_arg_list(args)
9216 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9217 args = _coerce_expr_list(args, ctx)
9218 _args, sz = _to_ast_array(args)
9219 _coeffs = (ctypes.c_int * len(coeffs))()
9220 for i in range(len(coeffs)):
9221 _z3_check_cint_overflow(coeffs[i], "coefficient")
9222 _coeffs[i] = coeffs[i]
9223 return ctx, sz, _args, _coeffs, args
9227 """Create a Pseudo-Boolean inequality k constraint.
9229 >>> a, b, c = Bools('a b c')
9230 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9232 _z3_check_cint_overflow(k, "k")
9233 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9234 return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
9238 """Create a Pseudo-Boolean inequality k constraint.
9240 >>> a, b, c = Bools('a b c')
9241 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9243 _z3_check_cint_overflow(k, "k")
9244 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9245 return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
9248def PbEq(args, k, ctx=None):
9249 """Create a Pseudo-Boolean equality k constraint.
9251 >>> a, b, c = Bools('a b c')
9252 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9254 _z3_check_cint_overflow(k, "k")
9255 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9256 return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
9259def solve(*args, **keywords):
9260 """Solve the constraints `*args`.
9262 This is a simple function for creating demonstrations. It creates a solver,
9263 configure it using the options in `keywords`, adds the constraints
9264 in `args`, and invokes check.
9267 >>> solve(a > 0, a < 2)
9270 show = keywords.pop("show", False)
9278 print("no solution")
9280 print("failed to solve")
9289def solve_using(s, *args, **keywords):
9290 """Solve the constraints `*args` using solver `s`.
9292 This is a simple function for creating demonstrations. It is similar to `solve`,
9293 but it uses the given solver `s`.
9294 It configures solver `s` using the options in `keywords`, adds the constraints
9295 in `args`, and invokes check.
9297 show = keywords.pop("show", False)
9299 _z3_assert(isinstance(s, Solver), "Solver object expected")
9307 print("no solution")
9309 print("failed to solve")
9320def prove(claim, show=False, **keywords):
9321 """Try to prove the given claim.
9323 This is a simple function for creating demonstrations. It tries to prove
9324 `claim` by showing the negation is unsatisfiable.
9326 >>> p, q = Bools('p q')
9327 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9331 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9341 print("failed to prove")
9344 print("counterexample")
9348def _solve_html(*args, **keywords):
9349 """Version of function `solve` that renders HTML output."""
9350 show = keywords.pop("show", False)
9355 print("<b>Problem:</b>")
9359 print("<b>no solution</b>")
9361 print("<b>failed to solve</b>")
9368 print("<b>Solution:</b>")
9372def _solve_using_html(s, *args, **keywords):
9373 """Version of function `solve_using` that renders HTML."""
9374 show = keywords.pop("show", False)
9376 _z3_assert(isinstance(s, Solver), "Solver object expected")
9380 print("<b>Problem:</b>")
9384 print("<b>no solution</b>")
9386 print("<b>failed to solve</b>")
9393 print("<b>Solution:</b>")
9397def _prove_html(claim, show=False, **keywords):
9398 """Version of function `prove` that renders HTML."""
9400 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9408 print("<b>proved</b>")
9410 print("<b>failed to prove</b>")
9413 print("<b>counterexample</b>")
9417def _dict2sarray(sorts, ctx):
9419 _names = (Symbol * sz)()
9420 _sorts = (Sort * sz)()
9425 _z3_assert(isinstance(k, str), "String expected")
9426 _z3_assert(is_sort(v), "Z3 sort expected")
9427 _names[i] = to_symbol(k, ctx)
9430 return sz, _names, _sorts
9433def _dict2darray(decls, ctx):
9435 _names = (Symbol * sz)()
9436 _decls = (FuncDecl * sz)()
9441 _z3_assert(isinstance(k, str), "String expected")
9442 _z3_assert(is_func_decl(v) or is_const(v), "Z3 declaration or constant expected")
9443 _names[i] = to_symbol(k, ctx)
9445 _decls[i] = v.decl().ast
9449 return sz, _names, _decls
9452 def __init__(self, ctx= None):
9453 self.ctx = _get_ctx(ctx)
9454 self.pctx = Z3_mk_parser_context(self.ctx.ref())
9455 Z3_parser_context_inc_ref(self.ctx.ref(), self.pctx)
9458 if self.ctx.ref() is not None and self.pctx is not None and Z3_parser_context_dec_ref is not None:
9459 Z3_parser_context_dec_ref(self.ctx.ref(), self.pctx)
9462 def add_sort(self, sort):
9463 Z3_parser_context_add_sort(self.ctx.ref(), self.pctx, sort.as_ast())
9465 def add_decl(self, decl):
9466 Z3_parser_context_add_decl(self.ctx.ref(), self.pctx, decl.as_ast())
9468 def from_string(self, s):
9469 return AstVector(Z3_parser_context_from_string(self.ctx.ref(), self.pctx, s), self.ctx)
9471def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
9472 """Parse a string in SMT 2.0 format using the given sorts and decls.
9474 The arguments sorts and decls are Python dictionaries used to initialize
9475 the symbol table used for the SMT 2.0 parser.
9477 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9479 >>> x, y = Ints('x y')
9480 >>> f = Function('f', IntSort(), IntSort())
9481 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9483 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9487 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9488 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9489 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9492def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9493 """Parse a file in SMT 2.0 format using the given sorts and decls.
9495 This function is similar to parse_smt2_string().
9498 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9499 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9500 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9503#########################################
9505# Floating-Point Arithmetic
9507#########################################
9510# Global default rounding mode
9511_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9512_dflt_fpsort_ebits = 11
9513_dflt_fpsort_sbits = 53
9516def get_default_rounding_mode(ctx=None):
9517 """Retrieves the global default rounding mode."""
9518 global _dflt_rounding_mode
9519 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9521 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9523 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9525 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9527 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9531_ROUNDING_MODES = frozenset({
9532 Z3_OP_FPA_RM_TOWARD_ZERO,
9533 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9534 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9535 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9536 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9540def set_default_rounding_mode(rm, ctx=None):
9541 global _dflt_rounding_mode
9542 if is_fprm_value(rm):
9543 _dflt_rounding_mode = rm.kind()
9545 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9546 _dflt_rounding_mode = rm
9549def get_default_fp_sort(ctx=None):
9550 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9553def set_default_fp_sort(ebits, sbits, ctx=None):
9554 global _dflt_fpsort_ebits
9555 global _dflt_fpsort_sbits
9556 _dflt_fpsort_ebits = ebits
9557 _dflt_fpsort_sbits = sbits
9560def _dflt_rm(ctx=None):
9561 return get_default_rounding_mode(ctx)
9564def _dflt_fps(ctx=None):
9565 return get_default_fp_sort(ctx)
9568def _coerce_fp_expr_list(alist, ctx):
9569 first_fp_sort = None
9572 if first_fp_sort is None:
9573 first_fp_sort = a.sort()
9574 elif first_fp_sort == a.sort():
9575 pass # OK, same as before
9577 # we saw at least 2 different float sorts; something will
9578 # throw a sort mismatch later, for now assume None.
9579 first_fp_sort = None
9583 for i in range(len(alist)):
9585 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9586 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9587 r.append(FPVal(a, None, first_fp_sort, ctx))
9590 return _coerce_expr_list(r, ctx)
9595class FPSortRef(SortRef):
9596 """Floating-point sort."""
9599 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9600 >>> b = FPSort(8, 24)
9604 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9607 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9608 >>> b = FPSort(8, 24)
9612 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9614 def cast(self, val):
9615 """Try to cast `val` as a floating-point expression.
9616 >>> b = FPSort(8, 24)
9619 >>> b.cast(1.0).sexpr()
9620 '(fp #b0 #x7f #b00000000000000000000000)'
9624 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9627 return FPVal(val, None, self, self.ctx)
9630def Float16(ctx=None):
9631 """Floating-point 16-bit (half) sort."""
9633 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9636def FloatHalf(ctx=None):
9637 """Floating-point 16-bit (half) sort."""
9639 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9642def Float32(ctx=None):
9643 """Floating-point 32-bit (single) sort."""
9645 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9648def FloatSingle(ctx=None):
9649 """Floating-point 32-bit (single) sort."""
9651 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9654def Float64(ctx=None):
9655 """Floating-point 64-bit (double) sort."""
9657 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9660def FloatDouble(ctx=None):
9661 """Floating-point 64-bit (double) sort."""
9663 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9666def Float128(ctx=None):
9667 """Floating-point 128-bit (quadruple) sort."""
9669 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9672def FloatQuadruple(ctx=None):
9673 """Floating-point 128-bit (quadruple) sort."""
9675 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9678class FPRMSortRef(SortRef):
9679 """"Floating-point rounding mode sort."""
9683 """Return True if `s` is a Z3 floating-point sort.
9685 >>> is_fp_sort(FPSort(8, 24))
9687 >>> is_fp_sort(IntSort())
9690 return isinstance(s, FPSortRef)
9694 """Return True if `s` is a Z3 floating-point rounding mode sort.
9696 >>> is_fprm_sort(FPSort(8, 24))
9698 >>> is_fprm_sort(RNE().sort())
9701 return isinstance(s, FPRMSortRef)
9706class FPRef(ExprRef):
9707 """Floating-point expressions."""
9710 """Return the sort of the floating-point expression `self`.
9712 >>> x = FP('1.0', FPSort(8, 24))
9715 >>> x.sort() == FPSort(8, 24)
9718 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9721 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9722 >>> b = FPSort(8, 24)
9726 return self.sort().ebits()
9729 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9730 >>> b = FPSort(8, 24)
9734 return self.sort().sbits()
9736 def as_string(self):
9737 """Return a Z3 floating point expression as a Python string."""
9738 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9740 def __le__(self, other):
9741 return fpLEQ(self, other, self.ctx)
9743 def __lt__(self, other):
9744 return fpLT(self, other, self.ctx)
9746 def __ge__(self, other):
9747 return fpGEQ(self, other, self.ctx)
9749 def __gt__(self, other):
9750 return fpGT(self, other, self.ctx)
9752 def __add__(self, other):
9753 """Create the Z3 expression `self + other`.
9755 >>> x = FP('x', FPSort(8, 24))
9756 >>> y = FP('y', FPSort(8, 24))
9762 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9763 return fpAdd(_dflt_rm(), a, b, self.ctx)
9765 def __radd__(self, other):
9766 """Create the Z3 expression `other + self`.
9768 >>> x = FP('x', FPSort(8, 24))
9772 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9773 return fpAdd(_dflt_rm(), a, b, self.ctx)
9775 def __sub__(self, other):
9776 """Create the Z3 expression `self - other`.
9778 >>> x = FP('x', FPSort(8, 24))
9779 >>> y = FP('y', FPSort(8, 24))
9785 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9786 return fpSub(_dflt_rm(), a, b, self.ctx)
9788 def __rsub__(self, other):
9789 """Create the Z3 expression `other - self`.
9791 >>> x = FP('x', FPSort(8, 24))
9795 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9796 return fpSub(_dflt_rm(), a, b, self.ctx)
9798 def __mul__(self, other):
9799 """Create the Z3 expression `self * other`.
9801 >>> x = FP('x', FPSort(8, 24))
9802 >>> y = FP('y', FPSort(8, 24))
9810 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9811 return fpMul(_dflt_rm(), a, b, self.ctx)
9813 def __rmul__(self, other):
9814 """Create the Z3 expression `other * self`.
9816 >>> x = FP('x', FPSort(8, 24))
9817 >>> y = FP('y', FPSort(8, 24))
9823 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9824 return fpMul(_dflt_rm(), a, b, self.ctx)
9827 """Create the Z3 expression `+self`."""
9831 """Create the Z3 expression `-self`.
9833 >>> x = FP('x', Float32())
9839 def __div__(self, other):
9840 """Create the Z3 expression `self / other`.
9842 >>> x = FP('x', FPSort(8, 24))
9843 >>> y = FP('y', FPSort(8, 24))
9851 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9852 return fpDiv(_dflt_rm(), a, b, self.ctx)
9854 def __rdiv__(self, other):
9855 """Create the Z3 expression `other / self`.
9857 >>> x = FP('x', FPSort(8, 24))
9858 >>> y = FP('y', FPSort(8, 24))
9864 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9865 return fpDiv(_dflt_rm(), a, b, self.ctx)
9867 def __truediv__(self, other):
9868 """Create the Z3 expression division `self / other`."""
9869 return self.__div__(other)
9871 def __rtruediv__(self, other):
9872 """Create the Z3 expression division `other / self`."""
9873 return self.__rdiv__(other)
9875 def __mod__(self, other):
9876 """Create the Z3 expression mod `self % other`."""
9877 return fpRem(self, other)
9879 def __rmod__(self, other):
9880 """Create the Z3 expression mod `other % self`."""
9881 return fpRem(other, self)
9884class FPRMRef(ExprRef):
9885 """Floating-point rounding mode expressions"""
9887 def as_string(self):
9888 """Return a Z3 floating point expression as a Python string."""
9889 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9892def RoundNearestTiesToEven(ctx=None):
9894 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9899 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9902def RoundNearestTiesToAway(ctx=None):
9904 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9909 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9912def RoundTowardPositive(ctx=None):
9914 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9919 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9922def RoundTowardNegative(ctx=None):
9924 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9929 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9932def RoundTowardZero(ctx=None):
9934 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9939 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9943 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9952 return isinstance(a, FPRMRef)
9955def is_fprm_value(a):
9956 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9957 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9962class FPNumRef(FPRef):
9963 """The sign of the numeral.
9965 >>> x = FPVal(+1.0, FPSort(8, 24))
9968 >>> x = FPVal(-1.0, FPSort(8, 24))
9974 num = (ctypes.c_int)()
9975 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9977 raise Z3Exception("error retrieving the sign of a numeral.")
9978 return num.value != 0
9980 """The sign of a floating-point numeral as a bit-vector expression.
9982 Remark: NaN's are invalid arguments.
9985 def sign_as_bv(self):
9986 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9988 """The significand of the numeral.
9990 >>> x = FPVal(2.5, FPSort(8, 24))
9995 def significand(self):
9996 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
9998 """The significand of the numeral as a long.
10000 >>> x = FPVal(2.5, FPSort(8, 24))
10001 >>> x.significand_as_long()
10005 def significand_as_long(self):
10006 ptr = (ctypes.c_ulonglong * 1)()
10007 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
10008 raise Z3Exception("error retrieving the significand of a numeral.")
10011 """The significand of the numeral as a bit-vector expression.
10013 Remark: NaN are invalid arguments.
10016 def significand_as_bv(self):
10017 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
10019 """The exponent of the numeral.
10021 >>> x = FPVal(2.5, FPSort(8, 24))
10026 def exponent(self, biased=True):
10027 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
10029 """The exponent of the numeral as a long.
10031 >>> x = FPVal(2.5, FPSort(8, 24))
10032 >>> x.exponent_as_long()
10036 def exponent_as_long(self, biased=True):
10037 ptr = (ctypes.c_longlong * 1)()
10038 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
10039 raise Z3Exception("error retrieving the exponent of a numeral.")
10042 """The exponent of the numeral as a bit-vector expression.
10044 Remark: NaNs are invalid arguments.
10047 def exponent_as_bv(self, biased=True):
10048 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
10050 """Indicates whether the numeral is a NaN."""
10053 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
10055 """Indicates whether the numeral is +oo or -oo."""
10058 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
10060 """Indicates whether the numeral is +zero or -zero."""
10063 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
10065 """Indicates whether the numeral is normal."""
10067 def isNormal(self):
10068 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
10070 """Indicates whether the numeral is subnormal."""
10072 def isSubnormal(self):
10073 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
10075 """Indicates whether the numeral is positive."""
10077 def isPositive(self):
10078 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
10080 """Indicates whether the numeral is negative."""
10082 def isNegative(self):
10083 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
10086 The string representation of the numeral.
10088 >>> x = FPVal(20, FPSort(8, 24))
10093 def as_string(self):
10094 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
10095 return ("FPVal(%s, %s)" % (s, self.sort()))
10097 def py_value(self):
10098 bv = simplify(fpToIEEEBV(self))
10099 binary = bv.py_value()
10100 if not isinstance(binary, int):
10102 # Decode the IEEE 754 binary representation
10104 bytes_rep = binary.to_bytes(8, byteorder='big')
10105 return struct.unpack('>d', bytes_rep)[0]
10109 """Return `True` if `a` is a Z3 floating-point expression.
10111 >>> b = FP('b', FPSort(8, 24))
10116 >>> is_fp(Int('x'))
10119 return isinstance(a, FPRef)
10123 """Return `True` if `a` is a Z3 floating-point numeral value.
10125 >>> b = FP('b', FPSort(8, 24))
10128 >>> b = FPVal(1.0, FPSort(8, 24))
10134 return is_fp(a) and _is_numeral(a.ctx, a.ast)
10137def FPSort(ebits, sbits, ctx=None):
10138 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
10140 >>> Single = FPSort(8, 24)
10141 >>> Double = FPSort(11, 53)
10144 >>> x = Const('x', Single)
10145 >>> eq(x, FP('x', FPSort(8, 24)))
10148 ctx = _get_ctx(ctx)
10149 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
10152def _to_float_str(val, exp=0):
10153 if isinstance(val, float):
10154 if math.isnan(val):
10157 sone = math.copysign(1.0, val)
10162 elif val == float("+inf"):
10164 elif val == float("-inf"):
10167 v = val.as_integer_ratio()
10170 rvs = str(num) + "/" + str(den)
10171 res = rvs + "p" + _to_int_str(exp)
10172 elif isinstance(val, bool):
10179 elif isinstance(val, str):
10180 inx = val.find("*(2**")
10183 elif val[-1] == ")":
10185 exp = str(int(val[inx + 5:-1]) + int(exp))
10187 _z3_assert(False, "String does not have floating-point numeral form.")
10189 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10193 return res + "p" + exp
10197 """Create a Z3 floating-point NaN term.
10199 >>> s = FPSort(8, 24)
10200 >>> set_fpa_pretty(True)
10203 >>> pb = get_fpa_pretty()
10204 >>> set_fpa_pretty(False)
10206 fpNaN(FPSort(8, 24))
10207 >>> set_fpa_pretty(pb)
10209 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10210 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10213def fpPlusInfinity(s):
10214 """Create a Z3 floating-point +oo term.
10216 >>> s = FPSort(8, 24)
10217 >>> pb = get_fpa_pretty()
10218 >>> set_fpa_pretty(True)
10219 >>> fpPlusInfinity(s)
10221 >>> set_fpa_pretty(False)
10222 >>> fpPlusInfinity(s)
10223 fpPlusInfinity(FPSort(8, 24))
10224 >>> set_fpa_pretty(pb)
10226 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10227 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10230def fpMinusInfinity(s):
10231 """Create a Z3 floating-point -oo term."""
10232 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10233 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10236def fpInfinity(s, negative):
10237 """Create a Z3 floating-point +oo or -oo term."""
10238 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10239 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10240 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10244 """Create a Z3 floating-point +0.0 term."""
10245 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10246 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10250 """Create a Z3 floating-point -0.0 term."""
10251 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10252 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10255def fpZero(s, negative):
10256 """Create a Z3 floating-point +0.0 or -0.0 term."""
10257 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10258 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10259 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10262def FPVal(sig, exp=None, fps=None, ctx=None):
10263 """Return a floating-point value of value `val` and sort `fps`.
10264 If `ctx=None`, then the global context is used.
10266 >>> v = FPVal(20.0, FPSort(8, 24))
10269 >>> print("0x%.8x" % v.exponent_as_long(False))
10271 >>> v = FPVal(2.25, FPSort(8, 24))
10274 >>> v = FPVal(-2.25, FPSort(8, 24))
10277 >>> FPVal(-0.0, FPSort(8, 24))
10279 >>> FPVal(0.0, FPSort(8, 24))
10281 >>> FPVal(+0.0, FPSort(8, 24))
10284 ctx = _get_ctx(ctx)
10285 if is_fp_sort(exp):
10289 fps = _dflt_fps(ctx)
10290 _z3_assert(is_fp_sort(fps), "sort mismatch")
10293 val = _to_float_str(sig)
10294 if val == "NaN" or val == "nan":
10296 elif val == "-0.0":
10297 return fpMinusZero(fps)
10298 elif val == "0.0" or val == "+0.0":
10299 return fpPlusZero(fps)
10300 elif val == "+oo" or val == "+inf" or val == "+Inf":
10301 return fpPlusInfinity(fps)
10302 elif val == "-oo" or val == "-inf" or val == "-Inf":
10303 return fpMinusInfinity(fps)
10305 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10308def FP(name, fpsort, ctx=None):
10309 """Return a floating-point constant named `name`.
10310 `fpsort` is the floating-point sort.
10311 If `ctx=None`, then the global context is used.
10313 >>> x = FP('x', FPSort(8, 24))
10320 >>> word = FPSort(8, 24)
10321 >>> x2 = FP('x', word)
10325 if isinstance(fpsort, FPSortRef) and ctx is None:
10328 ctx = _get_ctx(ctx)
10329 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10332def FPs(names, fpsort, ctx=None):
10333 """Return an array of floating-point constants.
10335 >>> x, y, z = FPs('x y z', FPSort(8, 24))
10342 >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
10345 ctx = _get_ctx(ctx)
10346 if isinstance(names, str):
10347 names = names.split(" ")
10348 return [FP(name, fpsort, ctx) for name in names]
10351def fpAbs(a, ctx=None):
10352 """Create a Z3 floating-point absolute value expression.
10354 >>> s = FPSort(8, 24)
10356 >>> x = FPVal(1.0, s)
10359 >>> y = FPVal(-20.0, s)
10363 fpAbs(-1.25*(2**4))
10364 >>> fpAbs(-1.25*(2**4))
10365 fpAbs(-1.25*(2**4))
10366 >>> fpAbs(x).sort()
10369 ctx = _get_ctx(ctx)
10370 [a] = _coerce_fp_expr_list([a], ctx)
10371 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10374def fpNeg(a, ctx=None):
10375 """Create a Z3 floating-point addition expression.
10377 >>> s = FPSort(8, 24)
10382 >>> fpNeg(x).sort()
10385 ctx = _get_ctx(ctx)
10386 [a] = _coerce_fp_expr_list([a], ctx)
10387 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10390def _mk_fp_unary(f, rm, a, ctx):
10391 ctx = _get_ctx(ctx)
10392 [a] = _coerce_fp_expr_list([a], ctx)
10394 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10395 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10396 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10399def _mk_fp_unary_pred(f, a, ctx):
10400 ctx = _get_ctx(ctx)
10401 [a] = _coerce_fp_expr_list([a], ctx)
10403 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10404 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10407def _mk_fp_bin(f, rm, a, b, ctx):
10408 ctx = _get_ctx(ctx)
10409 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10411 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10412 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10413 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10416def _mk_fp_bin_norm(f, a, b, ctx):
10417 ctx = _get_ctx(ctx)
10418 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10420 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10421 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10424def _mk_fp_bin_pred(f, a, b, ctx):
10425 ctx = _get_ctx(ctx)
10426 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10428 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10429 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10432def _mk_fp_tern(f, rm, a, b, c, ctx):
10433 ctx = _get_ctx(ctx)
10434 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10436 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10437 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10438 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10439 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10442def fpAdd(rm, a, b, ctx=None):
10443 """Create a Z3 floating-point addition expression.
10445 >>> s = FPSort(8, 24)
10449 >>> fpAdd(rm, x, y)
10451 >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
10453 >>> fpAdd(rm, x, y).sort()
10456 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10459def fpSub(rm, a, b, ctx=None):
10460 """Create a Z3 floating-point subtraction expression.
10462 >>> s = FPSort(8, 24)
10466 >>> fpSub(rm, x, y)
10468 >>> fpSub(rm, x, y).sort()
10471 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10474def fpMul(rm, a, b, ctx=None):
10475 """Create a Z3 floating-point multiplication expression.
10477 >>> s = FPSort(8, 24)
10481 >>> fpMul(rm, x, y)
10483 >>> fpMul(rm, x, y).sort()
10486 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10489def fpDiv(rm, a, b, ctx=None):
10490 """Create a Z3 floating-point division expression.
10492 >>> s = FPSort(8, 24)
10496 >>> fpDiv(rm, x, y)
10498 >>> fpDiv(rm, x, y).sort()
10501 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10504def fpRem(a, b, ctx=None):
10505 """Create a Z3 floating-point remainder expression.
10507 >>> s = FPSort(8, 24)
10512 >>> fpRem(x, y).sort()
10515 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10518def fpMin(a, b, ctx=None):
10519 """Create a Z3 floating-point minimum expression.
10521 >>> s = FPSort(8, 24)
10527 >>> fpMin(x, y).sort()
10530 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10533def fpMax(a, b, ctx=None):
10534 """Create a Z3 floating-point maximum expression.
10536 >>> s = FPSort(8, 24)
10542 >>> fpMax(x, y).sort()
10545 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10548def fpFMA(rm, a, b, c, ctx=None):
10549 """Create a Z3 floating-point fused multiply-add expression.
10551 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10554def fpSqrt(rm, a, ctx=None):
10555 """Create a Z3 floating-point square root expression.
10557 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10560def fpRoundToIntegral(rm, a, ctx=None):
10561 """Create a Z3 floating-point roundToIntegral expression.
10563 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10566def fpIsNaN(a, ctx=None):
10567 """Create a Z3 floating-point isNaN expression.
10569 >>> s = FPSort(8, 24)
10575 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10578def fpIsInf(a, ctx=None):
10579 """Create a Z3 floating-point isInfinite expression.
10581 >>> s = FPSort(8, 24)
10586 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10589def fpIsZero(a, ctx=None):
10590 """Create a Z3 floating-point isZero expression.
10592 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10595def fpIsNormal(a, ctx=None):
10596 """Create a Z3 floating-point isNormal expression.
10598 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10601def fpIsSubnormal(a, ctx=None):
10602 """Create a Z3 floating-point isSubnormal expression.
10604 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10607def fpIsNegative(a, ctx=None):
10608 """Create a Z3 floating-point isNegative expression.
10610 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10613def fpIsPositive(a, ctx=None):
10614 """Create a Z3 floating-point isPositive expression.
10616 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10619def _check_fp_args(a, b):
10621 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10624def fpLT(a, b, ctx=None):
10625 """Create the Z3 floating-point expression `other < self`.
10627 >>> x, y = FPs('x y', FPSort(8, 24))
10630 >>> (x < y).sexpr()
10633 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10636def fpLEQ(a, b, ctx=None):
10637 """Create the Z3 floating-point expression `other <= self`.
10639 >>> x, y = FPs('x y', FPSort(8, 24))
10642 >>> (x <= y).sexpr()
10645 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10648def fpGT(a, b, ctx=None):
10649 """Create the Z3 floating-point expression `other > self`.
10651 >>> x, y = FPs('x y', FPSort(8, 24))
10654 >>> (x > y).sexpr()
10657 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10660def fpGEQ(a, b, ctx=None):
10661 """Create the Z3 floating-point expression `other >= self`.
10663 >>> x, y = FPs('x y', FPSort(8, 24))
10666 >>> (x >= y).sexpr()
10669 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10672def fpEQ(a, b, ctx=None):
10673 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10675 >>> x, y = FPs('x y', FPSort(8, 24))
10678 >>> fpEQ(x, y).sexpr()
10681 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10684def fpNEQ(a, b, ctx=None):
10685 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10687 >>> x, y = FPs('x y', FPSort(8, 24))
10690 >>> (x != y).sexpr()
10693 return Not(fpEQ(a, b, ctx))
10696def fpFP(sgn, exp, sig, ctx=None):
10697 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10699 >>> s = FPSort(8, 24)
10700 >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
10702 fpFP(1, 127, 4194304)
10703 >>> xv = FPVal(-1.5, s)
10706 >>> slvr = Solver()
10707 >>> slvr.add(fpEQ(x, xv))
10710 >>> xv = FPVal(+1.5, s)
10713 >>> slvr = Solver()
10714 >>> slvr.add(fpEQ(x, xv))
10718 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10719 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10720 ctx = _get_ctx(ctx)
10721 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10722 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10725def fpToFP(a1, a2=None, a3=None, ctx=None):
10726 """Create a Z3 floating-point conversion expression from other term sorts
10729 From a bit-vector term in IEEE 754-2008 format:
10730 >>> x = FPVal(1.0, Float32())
10731 >>> x_bv = fpToIEEEBV(x)
10732 >>> simplify(fpToFP(x_bv, Float32()))
10735 From a floating-point term with different precision:
10736 >>> x = FPVal(1.0, Float32())
10737 >>> x_db = fpToFP(RNE(), x, Float64())
10742 >>> x_r = RealVal(1.5)
10743 >>> simplify(fpToFP(RNE(), x_r, Float32()))
10746 From a signed bit-vector term:
10747 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10748 >>> simplify(fpToFP(RNE(), x_signed, Float32()))
10751 ctx = _get_ctx(ctx)
10752 if is_bv(a1) and is_fp_sort(a2):
10753 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10754 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10755 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10756 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10757 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10758 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10759 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10761 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10764def fpBVToFP(v, sort, ctx=None):
10765 """Create a Z3 floating-point conversion expression that represents the
10766 conversion from a bit-vector term to a floating-point term.
10768 >>> x_bv = BitVecVal(0x3F800000, 32)
10769 >>> x_fp = fpBVToFP(x_bv, Float32())
10775 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10776 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10777 ctx = _get_ctx(ctx)
10778 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10781def fpFPToFP(rm, v, sort, ctx=None):
10782 """Create a Z3 floating-point conversion expression that represents the
10783 conversion from a floating-point term to a floating-point term of different precision.
10785 >>> x_sgl = FPVal(1.0, Float32())
10786 >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
10789 >>> simplify(x_dbl)
10794 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10795 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10796 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10797 ctx = _get_ctx(ctx)
10798 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10801def fpRealToFP(rm, v, sort, ctx=None):
10802 """Create a Z3 floating-point conversion expression that represents the
10803 conversion from a real term to a floating-point term.
10805 >>> x_r = RealVal(1.5)
10806 >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
10812 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10813 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10814 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10815 ctx = _get_ctx(ctx)
10816 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10819def fpSignedToFP(rm, v, sort, ctx=None):
10820 """Create a Z3 floating-point conversion expression that represents the
10821 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10823 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10824 >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
10826 fpToFP(RNE(), 4294967291)
10830 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10831 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10832 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10833 ctx = _get_ctx(ctx)
10834 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10837def fpUnsignedToFP(rm, v, sort, ctx=None):
10838 """Create a Z3 floating-point conversion expression that represents the
10839 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10841 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10842 >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
10844 fpToFPUnsigned(RNE(), 4294967291)
10848 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10849 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10850 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10851 ctx = _get_ctx(ctx)
10852 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10855def fpToFPUnsigned(rm, x, s, ctx=None):
10856 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10858 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10859 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10860 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10861 ctx = _get_ctx(ctx)
10862 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10865def fpToSBV(rm, x, s, ctx=None):
10866 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10868 >>> x = FP('x', FPSort(8, 24))
10869 >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
10870 >>> print(is_fp(x))
10872 >>> print(is_bv(y))
10874 >>> print(is_fp(y))
10876 >>> print(is_bv(x))
10880 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10881 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10882 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10883 ctx = _get_ctx(ctx)
10884 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10887def fpToUBV(rm, x, s, ctx=None):
10888 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10890 >>> x = FP('x', FPSort(8, 24))
10891 >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
10892 >>> print(is_fp(x))
10894 >>> print(is_bv(y))
10896 >>> print(is_fp(y))
10898 >>> print(is_bv(x))
10902 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10903 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10904 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10905 ctx = _get_ctx(ctx)
10906 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10909def fpToReal(x, ctx=None):
10910 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10912 >>> x = FP('x', FPSort(8, 24))
10913 >>> y = fpToReal(x)
10914 >>> print(is_fp(x))
10916 >>> print(is_real(y))
10918 >>> print(is_fp(y))
10920 >>> print(is_real(x))
10924 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10925 ctx = _get_ctx(ctx)
10926 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10929def fpToIEEEBV(x, ctx=None):
10930 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10932 The size of the resulting bit-vector is automatically determined.
10934 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10935 knows only one NaN and it will always produce the same bit-vector representation of
10938 >>> x = FP('x', FPSort(8, 24))
10939 >>> y = fpToIEEEBV(x)
10940 >>> print(is_fp(x))
10942 >>> print(is_bv(y))
10944 >>> print(is_fp(y))
10946 >>> print(is_bv(x))
10950 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10951 ctx = _get_ctx(ctx)
10952 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10955#########################################
10957# Strings, Sequences and Regular expressions
10959#########################################
10961class SeqSortRef(SortRef):
10962 """Sequence sort."""
10964 def is_string(self):
10965 """Determine if sort is a string
10966 >>> s = StringSort()
10969 >>> s = SeqSort(IntSort())
10973 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10976 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10978class CharSortRef(SortRef):
10979 """Character sort."""
10982def StringSort(ctx=None):
10983 """Create a string sort
10984 >>> s = StringSort()
10988 ctx = _get_ctx(ctx)
10989 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10991def CharSort(ctx=None):
10992 """Create a character sort
10993 >>> ch = CharSort()
10997 ctx = _get_ctx(ctx)
10998 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
11002 """Create a sequence sort over elements provided in the argument
11003 >>> s = SeqSort(IntSort())
11004 >>> s == Unit(IntVal(1)).sort()
11007 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
11010class SeqRef(ExprRef):
11011 """Sequence expression."""
11014 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
11016 def __add__(self, other):
11017 return Concat(self, other)
11019 def __radd__(self, other):
11020 return Concat(other, self)
11022 def __getitem__(self, i):
11024 i = IntVal(i, self.ctx)
11025 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11029 i = IntVal(i, self.ctx)
11030 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11032 def is_string(self):
11033 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
11035 def is_string_value(self):
11036 return Z3_is_string(self.ctx_ref(), self.as_ast())
11038 def as_string(self):
11039 """Return a string representation of sequence expression."""
11040 if self.is_string_value():
11041 string_length = ctypes.c_uint()
11042 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
11043 return string_at(chars, size=string_length.value).decode("latin-1")
11044 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
11046 def py_value(self):
11047 return self.as_string()
11049 def __le__(self, other):
11050 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11052 def __lt__(self, other):
11053 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11055 def __ge__(self, other):
11056 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11058 def __gt__(self, other):
11059 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11062def _coerce_char(ch, ctx=None):
11063 if isinstance(ch, str):
11064 ctx = _get_ctx(ctx)
11065 ch = CharVal(ch, ctx)
11066 if not is_expr(ch):
11067 raise Z3Exception("Character expression expected")
11070class CharRef(ExprRef):
11071 """Character expression."""
11073 def __le__(self, other):
11074 other = _coerce_char(other, self.ctx)
11075 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11078 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
11081 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
11083 def is_digit(self):
11084 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
11087def CharVal(ch, ctx=None):
11088 ctx = _get_ctx(ctx)
11089 if isinstance(ch, str):
11091 if not isinstance(ch, int):
11092 raise Z3Exception("character value should be an ordinal")
11093 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
11096 if not is_expr(bv):
11097 raise Z3Exception("Bit-vector expression needed")
11098 return _to_expr_ref(Z3_mk_char_from_bv(bv.ctx_ref(), bv.as_ast()), bv.ctx)
11100def CharToBv(ch, ctx=None):
11101 ch = _coerce_char(ch, ctx)
11104def CharToInt(ch, ctx=None):
11105 ch = _coerce_char(ch, ctx)
11108def CharIsDigit(ch, ctx=None):
11109 ch = _coerce_char(ch, ctx)
11110 return ch.is_digit()
11112def _coerce_seq(s, ctx=None):
11113 if isinstance(s, str):
11114 ctx = _get_ctx(ctx)
11115 s = StringVal(s, ctx)
11117 raise Z3Exception("Non-expression passed as a sequence")
11119 raise Z3Exception("Non-sequence passed as a sequence")
11123def _get_ctx2(a, b, ctx=None):
11134 """Return `True` if `a` is a Z3 sequence expression.
11135 >>> print (is_seq(Unit(IntVal(0))))
11137 >>> print (is_seq(StringVal("abc")))
11140 return isinstance(a, SeqRef)
11144 """Return `True` if `a` is a Z3 string expression.
11145 >>> print (is_string(StringVal("ab")))
11148 return isinstance(a, SeqRef) and a.is_string()
11151def is_string_value(a):
11152 """return 'True' if 'a' is a Z3 string constant expression.
11153 >>> print (is_string_value(StringVal("a")))
11155 >>> print (is_string_value(StringVal("a") + StringVal("b")))
11158 return isinstance(a, SeqRef) and a.is_string_value()
11160def StringVal(s, ctx=None):
11161 """create a string expression"""
11162 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
11163 ctx = _get_ctx(ctx)
11164 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
11167def String(name, ctx=None):
11168 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
11170 >>> x = String('x')
11172 ctx = _get_ctx(ctx)
11173 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
11176def Strings(names, ctx=None):
11177 """Return a tuple of String constants. """
11178 ctx = _get_ctx(ctx)
11179 if isinstance(names, str):
11180 names = names.split(" ")
11181 return [String(name, ctx) for name in names]
11184def SubString(s, offset, length):
11185 """Extract substring or subsequence starting at offset"""
11186 return Extract(s, offset, length)
11189def SubSeq(s, offset, length):
11190 """Extract substring or subsequence starting at offset"""
11191 return Extract(s, offset, length)
11195 """Create the empty sequence of the given sort
11196 >>> e = Empty(StringSort())
11197 >>> e2 = StringVal("")
11198 >>> print(e.eq(e2))
11200 >>> e3 = Empty(SeqSort(IntSort()))
11203 >>> e4 = Empty(ReSort(SeqSort(IntSort())))
11205 Empty(ReSort(Seq(Int)))
11207 if isinstance(s, SeqSortRef):
11208 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11209 if isinstance(s, ReSortRef):
11210 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11211 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11215 """Create the regular expression that accepts the universal language
11216 >>> e = Full(ReSort(SeqSort(IntSort())))
11218 Full(ReSort(Seq(Int)))
11219 >>> e1 = Full(ReSort(StringSort()))
11221 Full(ReSort(String))
11223 if isinstance(s, ReSortRef):
11224 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11225 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11230 """Create a singleton sequence"""
11231 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11235 """Check if 'a' is a prefix of 'b'
11236 >>> s1 = PrefixOf("ab", "abc")
11239 >>> s2 = PrefixOf("bc", "abc")
11243 ctx = _get_ctx2(a, b)
11244 a = _coerce_seq(a, ctx)
11245 b = _coerce_seq(b, ctx)
11246 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11250 """Check if 'a' is a suffix of 'b'
11251 >>> s1 = SuffixOf("ab", "abc")
11254 >>> s2 = SuffixOf("bc", "abc")
11258 ctx = _get_ctx2(a, b)
11259 a = _coerce_seq(a, ctx)
11260 b = _coerce_seq(b, ctx)
11261 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11265 """Check if 'a' contains 'b'
11266 >>> s1 = Contains("abc", "ab")
11269 >>> s2 = Contains("abc", "bc")
11272 >>> x, y, z = Strings('x y z')
11273 >>> s3 = Contains(Concat(x,y,z), y)
11277 ctx = _get_ctx2(a, b)
11278 a = _coerce_seq(a, ctx)
11279 b = _coerce_seq(b, ctx)
11280 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11283def Replace(s, src, dst):
11284 """Replace the first occurrence of 'src' by 'dst' in 's'
11285 >>> r = Replace("aaa", "a", "b")
11289 ctx = _get_ctx2(dst, s)
11290 if ctx is None and is_expr(src):
11292 src = _coerce_seq(src, ctx)
11293 dst = _coerce_seq(dst, ctx)
11294 s = _coerce_seq(s, ctx)
11295 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11298def IndexOf(s, substr, offset=None):
11299 """Retrieve the index of substring within a string starting at a specified offset.
11300 >>> simplify(IndexOf("abcabc", "bc", 0))
11302 >>> simplify(IndexOf("abcabc", "bc", 2))
11308 if is_expr(offset):
11310 ctx = _get_ctx2(s, substr, ctx)
11311 s = _coerce_seq(s, ctx)
11312 substr = _coerce_seq(substr, ctx)
11313 if _is_int(offset):
11314 offset = IntVal(offset, ctx)
11315 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11318def LastIndexOf(s, substr):
11319 """Retrieve the last index of substring within a string"""
11321 ctx = _get_ctx2(s, substr, ctx)
11322 s = _coerce_seq(s, ctx)
11323 substr = _coerce_seq(substr, ctx)
11324 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11328 """Obtain the length of a sequence 's'
11329 >>> l = Length(StringVal("abc"))
11334 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11337 """Map function 'f' over sequence 's'"""
11338 ctx = _get_ctx2(f, s)
11339 s = _coerce_seq(s, ctx)
11340 return _to_expr_ref(Z3_mk_seq_map(s.ctx_ref(), f.as_ast(), s.as_ast()), ctx)
11342def SeqMapI(f, i, s):
11343 """Map function 'f' over sequence 's' at index 'i'"""
11344 ctx = _get_ctx(f, s)
11345 s = _coerce_seq(s, ctx)
11348 return _to_expr_ref(Z3_mk_seq_mapi(s.ctx_ref(), f.as_ast(), i.as_ast(), s.as_ast()), ctx)
11350def SeqFoldLeft(f, a, s):
11351 ctx = _get_ctx2(f, s)
11352 s = _coerce_seq(s, ctx)
11354 return _to_expr_ref(Z3_mk_seq_foldl(s.ctx_ref(), f.as_ast(), a.as_ast(), s.as_ast()), ctx)
11356def SeqFoldLeftI(f, i, a, s):
11357 ctx = _get_ctx2(f, s)
11358 s = _coerce_seq(s, ctx)
11361 return _to_expr_ref(Z3_mk_seq_foldli(s.ctx_ref(), f.as_ast(), i.as_ast(), a.as_ast(), s.as_ast()), ctx)
11364 """Convert string expression to integer
11365 >>> a = StrToInt("1")
11366 >>> simplify(1 == a)
11368 >>> b = StrToInt("2")
11369 >>> simplify(1 == b)
11371 >>> c = StrToInt(IntToStr(2))
11372 >>> simplify(1 == c)
11376 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11380 """Convert integer expression to string"""
11383 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11387 """Convert a unit length string to integer code"""
11390 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11393 """Convert code to a string"""
11396 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11398def Re(s, ctx=None):
11399 """The regular expression that accepts sequence 's'
11401 >>> s2 = Re(StringVal("ab"))
11402 >>> s3 = Re(Unit(BoolVal(True)))
11404 s = _coerce_seq(s, ctx)
11405 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11408# Regular expressions
11410class ReSortRef(SortRef):
11411 """Regular expression sort."""
11414 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11419 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11420 if s is None or isinstance(s, Context):
11422 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11423 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11426class ReRef(ExprRef):
11427 """Regular expressions."""
11429 def __add__(self, other):
11430 return Union(self, other)
11434 return isinstance(s, ReRef)
11438 """Create regular expression membership test
11439 >>> re = Union(Re("a"),Re("b"))
11440 >>> print (simplify(InRe("a", re)))
11442 >>> print (simplify(InRe("b", re)))
11444 >>> print (simplify(InRe("c", re)))
11447 s = _coerce_seq(s, re.ctx)
11448 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11452 """Create union of regular expressions.
11453 >>> re = Union(Re("a"), Re("b"), Re("c"))
11454 >>> print (simplify(InRe("d", re)))
11457 args = _get_args(args)
11460 _z3_assert(sz > 0, "At least one argument expected.")
11461 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11466 for i in range(sz):
11467 v[i] = args[i].as_ast()
11468 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11471def Intersect(*args):
11472 """Create intersection of regular expressions.
11473 >>> re = Intersect(Re("a"), Re("b"), Re("c"))
11475 args = _get_args(args)
11478 _z3_assert(sz > 0, "At least one argument expected.")
11479 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11484 for i in range(sz):
11485 v[i] = args[i].as_ast()
11486 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11490 """Create the regular expression accepting one or more repetitions of argument.
11491 >>> re = Plus(Re("a"))
11492 >>> print(simplify(InRe("aa", re)))
11494 >>> print(simplify(InRe("ab", re)))
11496 >>> print(simplify(InRe("", re)))
11500 _z3_assert(is_expr(re), "expression expected")
11501 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11505 """Create the regular expression that optionally accepts the argument.
11506 >>> re = Option(Re("a"))
11507 >>> print(simplify(InRe("a", re)))
11509 >>> print(simplify(InRe("", re)))
11511 >>> print(simplify(InRe("aa", re)))
11515 _z3_assert(is_expr(re), "expression expected")
11516 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11520 """Create the complement regular expression."""
11521 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11525 """Create the regular expression accepting zero or more repetitions of argument.
11526 >>> re = Star(Re("a"))
11527 >>> print(simplify(InRe("aa", re)))
11529 >>> print(simplify(InRe("ab", re)))
11531 >>> print(simplify(InRe("", re)))
11535 _z3_assert(is_expr(re), "expression expected")
11536 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11539def Loop(re, lo, hi=0):
11540 """Create the regular expression accepting between a lower and upper bound repetitions
11541 >>> re = Loop(Re("a"), 1, 3)
11542 >>> print(simplify(InRe("aa", re)))
11544 >>> print(simplify(InRe("aaaa", re)))
11546 >>> print(simplify(InRe("", re)))
11550 _z3_assert(is_expr(re), "expression expected")
11551 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11554def Range(lo, hi, ctx=None):
11555 """Create the range regular expression over two sequences of length 1
11556 >>> range = Range("a","z")
11557 >>> print(simplify(InRe("b", range)))
11559 >>> print(simplify(InRe("bb", range)))
11562 lo = _coerce_seq(lo, ctx)
11563 hi = _coerce_seq(hi, ctx)
11565 _z3_assert(is_expr(lo), "expression expected")
11566 _z3_assert(is_expr(hi), "expression expected")
11567 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11569def Diff(a, b, ctx=None):
11570 """Create the difference regular expression
11573 _z3_assert(is_expr(a), "expression expected")
11574 _z3_assert(is_expr(b), "expression expected")
11575 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11577def AllChar(regex_sort, ctx=None):
11578 """Create a regular expression that accepts all single character strings
11580 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11585def PartialOrder(a, index):
11586 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11589def LinearOrder(a, index):
11590 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11593def TreeOrder(a, index):
11594 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11597def PiecewiseLinearOrder(a, index):
11598 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11601def TransitiveClosure(f):
11602 """Given a binary relation R, such that the two arguments have the same sort
11603 create the transitive closure relation R+.
11604 The transitive closure R+ is a new relation.
11606 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11610 super(ctypes.c_void_p, ast).__init__(ptr)
11613def to_ContextObj(ptr,):
11614 ctx = ContextObj(ptr)
11615 super(ctypes.c_void_p, ctx).__init__(ptr)
11618def to_AstVectorObj(ptr,):
11619 v = AstVectorObj(ptr)
11620 super(ctypes.c_void_p, v).__init__(ptr)
11623# NB. my-hacky-class only works for a single instance of OnClause
11624# it should be replaced with a proper correlation between OnClause
11625# and object references that can be passed over the FFI.
11626# for UserPropagator we use a global dictionary, which isn't great code.
11628_my_hacky_class = None
11629def on_clause_eh(ctx, p, n, dep, clause):
11630 onc = _my_hacky_class
11631 p = _to_expr_ref(to_Ast(p), onc.ctx)
11632 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11633 deps = [dep[i] for i in range(n)]
11634 onc.on_clause(p, deps, clause)
11636_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11639 def __init__(self, s, on_clause):
11642 self.on_clause = on_clause
11644 global _my_hacky_class
11645 _my_hacky_class = self
11646 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11650 def __init__(self):
11654 def set_threaded(self):
11655 if self.lock is None:
11657 self.lock = threading.Lock()
11659 def get(self, ctx):
11662 r = self.bases[ctx]
11664 r = self.bases[ctx]
11667 def set(self, ctx, r):
11670 self.bases[ctx] = r
11672 self.bases[ctx] = r
11674 def insert(self, r):
11677 id = len(self.bases) + 3
11680 id = len(self.bases) + 3
11685_prop_closures = None
11688def ensure_prop_closures():
11689 global _prop_closures
11690 if _prop_closures is None:
11691 _prop_closures = PropClosures()
11694def user_prop_push(ctx, cb):
11695 prop = _prop_closures.get(ctx)
11700def user_prop_pop(ctx, cb, num_scopes):
11701 prop = _prop_closures.get(ctx)
11703 prop.pop(num_scopes)
11706def user_prop_fresh(ctx, _new_ctx):
11707 _prop_closures.set_threaded()
11708 prop = _prop_closures.get(ctx)
11710 Z3_del_context(nctx.ctx)
11711 new_ctx = to_ContextObj(_new_ctx)
11713 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11715 new_prop = prop.fresh(nctx)
11716 _prop_closures.set(new_prop.id, new_prop)
11720def user_prop_fixed(ctx, cb, id, value):
11721 prop = _prop_closures.get(ctx)
11724 id = _to_expr_ref(to_Ast(id), prop.ctx())
11725 value = _to_expr_ref(to_Ast(value), prop.ctx())
11726 prop.fixed(id, value)
11729def user_prop_created(ctx, cb, id):
11730 prop = _prop_closures.get(ctx)
11733 id = _to_expr_ref(to_Ast(id), prop.ctx())
11738def user_prop_final(ctx, cb):
11739 prop = _prop_closures.get(ctx)
11745def user_prop_eq(ctx, cb, x, y):
11746 prop = _prop_closures.get(ctx)
11749 x = _to_expr_ref(to_Ast(x), prop.ctx())
11750 y = _to_expr_ref(to_Ast(y), prop.ctx())
11754def user_prop_diseq(ctx, cb, x, y):
11755 prop = _prop_closures.get(ctx)
11758 x = _to_expr_ref(to_Ast(x), prop.ctx())
11759 y = _to_expr_ref(to_Ast(y), prop.ctx())
11763def user_prop_decide(ctx, cb, t_ref, idx, phase):
11764 prop = _prop_closures.get(ctx)
11767 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11768 prop.decide(t, idx, phase)
11772_user_prop_push = Z3_push_eh(user_prop_push)
11773_user_prop_pop = Z3_pop_eh(user_prop_pop)
11774_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11775_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11776_user_prop_created = Z3_created_eh(user_prop_created)
11777_user_prop_final = Z3_final_eh(user_prop_final)
11778_user_prop_eq = Z3_eq_eh(user_prop_eq)
11779_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11780_user_prop_decide = Z3_decide_eh(user_prop_decide)
11783def PropagateFunction(name, *sig):
11784 """Create a function that gets tracked by user propagator.
11785 Every term headed by this function symbol is tracked.
11786 If a term is fixed and the fixed callback is registered a
11787 callback is invoked that the term headed by this function is fixed.
11789 sig = _get_args(sig)
11791 _z3_assert(len(sig) > 0, "At least two arguments expected")
11792 arity = len(sig) - 1
11795 _z3_assert(is_sort(rng), "Z3 sort expected")
11796 dom = (Sort * arity)()
11797 for i in range(arity):
11799 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11800 dom[i] = sig[i].ast
11802 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11806class UserPropagateBase:
11809 # Either solver is set or ctx is set.
11810 # Propagators that are created through callbacks
11811 # to "fresh" inherit the context of that is supplied
11812 # as argument to the callback.
11813 # This context should not be deleted. It is owned by the solver.
11815 def __init__(self, s, ctx=None):
11816 assert s is None or ctx is None
11817 ensure_prop_closures()
11820 self.fresh_ctx = None
11822 self.id = _prop_closures.insert(self)
11828 self.created = None
11830 self.fresh_ctx = ctx
11832 Z3_solver_propagate_init(self.ctx_ref(),
11834 ctypes.c_void_p(self.id),
11841 self._ctx.ctx = None
11845 return self.fresh_ctx
11847 return self.solver.ctx
11850 return self.ctx().ref()
11852 def add_fixed(self, fixed):
11853 assert not self.fixed
11854 assert not self._ctx
11856 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11859 def add_created(self, created):
11860 assert not self.created
11861 assert not self._ctx
11863 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11864 self.created = created
11866 def add_final(self, final):
11867 assert not self.final
11868 assert not self._ctx
11870 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11873 def add_eq(self, eq):
11875 assert not self._ctx
11877 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11880 def add_diseq(self, diseq):
11881 assert not self.diseq
11882 assert not self._ctx
11884 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11887 def add_decide(self, decide):
11888 assert not self.decide
11889 assert not self._ctx
11891 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11892 self.decide = decide
11895 raise Z3Exception("push needs to be overwritten")
11897 def pop(self, num_scopes):
11898 raise Z3Exception("pop needs to be overwritten")
11900 def fresh(self, new_ctx):
11901 raise Z3Exception("fresh needs to be overwritten")
11904 assert not self._ctx
11906 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11908 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11911 # Tell the solver to perform the next split on a given term
11912 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11913 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11915 def next_split(self, t, idx, phase):
11916 return Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11919 # Propagation can only be invoked as during a fixed or final callback.
11921 def propagate(self, e, ids, eqs=[]):
11922 _ids, num_fixed = _to_ast_array(ids)
11924 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11925 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11926 return Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11927 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11929 def conflict(self, deps = [], eqs = []):
11930 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
approx(self, precision=10)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, m=None, ctx=None)
__deepcopy__(self, memo={})
__init__(self, ast, ctx=None)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__init__(self, v=None, ctx=None)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, *args, **kws)
__deepcopy__(self, memo={})
__init__(self, name, ctx=None)
declare(self, name, *args)
declare_core(self, name, rec_name, *args)
__deepcopy__(self, memo={})
__init__(self, entry, ctx)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__deepcopy__(self, memo={})
assert_exprs(self, *args)
dimacs(self, include_names=True)
simplify(self, *arguments, **keywords)
convert_model(self, model)
__init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
__deepcopy__(self, memo={})
eval(self, t, model_completion=False)
project_with_witness(self, vars, fml)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
check(self, *assumptions)
__exit__(self, *exc_info)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_sort Z3_API Z3_mk_int_sort(Z3_context c)
Create the integer type.
Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const *domain, Z3_sort range)
Create an array type with N arguments.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_denominator(Z3_context c, Z3_ast a)
Return the denominator (as a numeral AST) of a numeral AST of sort Real.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
void Z3_API Z3_solver_assert_and_track(Z3_context c, Z3_solver s, Z3_ast a, Z3_ast p)
Assert a constraint a into the solver, and track it (in the unsat) core using the Boolean constant p.
Z3_ast Z3_API Z3_func_interp_get_else(Z3_context c, Z3_func_interp f)
Return the 'else' value of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsge(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than or equal to.
void Z3_API Z3_ast_map_inc_ref(Z3_context c, Z3_ast_map m)
Increment the reference counter of the given AST map.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
Z3_ast Z3_API Z3_mk_bvsle(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than or equal to.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_ast Z3_API Z3_ast_map_find(Z3_context c, Z3_ast_map m, Z3_ast k)
Return the value associated with the key k.
Z3_string Z3_API Z3_ast_map_to_string(Z3_context c, Z3_ast_map m)
Convert the given map into a string.
Z3_string Z3_API Z3_param_descrs_to_string(Z3_context c, Z3_param_descrs p)
Convert a parameter description set into a string. This function is mainly used for printing the cont...
Z3_ast Z3_API Z3_mk_zero_ext(Z3_context c, unsigned i, Z3_ast t1)
Extend the given bit-vector with zeros to the (unsigned) equivalent bit-vector of size m+i,...
void Z3_API Z3_solver_set_params(Z3_context c, Z3_solver s, Z3_params p)
Set the given solver using the given parameters.
Z3_ast Z3_API Z3_mk_set_intersect(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the intersection of a list of sets.
Z3_params Z3_API Z3_mk_params(Z3_context c)
Create a Z3 (empty) parameter set. Starting at Z3 4.0, parameter sets are used to configure many comp...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
Z3_ast Z3_API Z3_mk_set_subset(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Check for subsetness of sets.
Z3_ast Z3_API Z3_mk_bvule(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than or equal to.
Z3_ast Z3_API Z3_mk_full_set(Z3_context c, Z3_sort domain)
Create the full set.
Z3_param_kind Z3_API Z3_param_descrs_get_kind(Z3_context c, Z3_param_descrs p, Z3_symbol n)
Return the kind associated with the given parameter name n.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_mk_set_union(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the union of a list of sets.
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
Z3_ast Z3_API Z3_mk_bvsdiv_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
void Z3_API Z3_ast_vector_set(Z3_context c, Z3_ast_vector v, unsigned i, Z3_ast a)
Update position i of the AST vector v with the AST a.
Z3_ast Z3_API Z3_mk_bvxor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise exclusive-or.
Z3_string Z3_API Z3_stats_to_string(Z3_context c, Z3_stats s)
Convert a statistics into a string.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, unsigned num_bound, Z3_app const bound[], Z3_ast body)
Create a lambda expression using a list of constants that form the set of bound variables.
void Z3_API Z3_solver_dec_ref(Z3_context c, Z3_solver s)
Decrement the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_bvslt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than.
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
bool Z3_API Z3_ast_map_contains(Z3_context c, Z3_ast_map m, Z3_ast k)
Return true if the map m contains the AST key k.
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_symbol Z3_API Z3_get_quantifier_skolem_id(Z3_context c, Z3_ast a)
Obtain skolem id of quantifier.
Z3_ast Z3_API Z3_get_numerator(Z3_context c, Z3_ast a)
Return the numerator (as a numeral AST) of a numeral AST of sort Real.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_ast Z3_API Z3_mk_and(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] and ... and args[num_args-1].
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
Z3_symbol Z3_API Z3_param_descrs_get_name(Z3_context c, Z3_param_descrs p, unsigned i)
Return the name of the parameter at given index i.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
Z3_ast Z3_API Z3_mk_false(Z3_context c)
Create an AST node representing false.
Z3_ast_vector Z3_API Z3_ast_map_keys(Z3_context c, Z3_ast_map m)
Return the keys stored in the given map.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null,...
void Z3_API Z3_del_constructor(Z3_context c, Z3_constructor constr)
Reclaim memory allocated to constructor.
Z3_ast Z3_API Z3_mk_bvsgt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than.
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context....
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_mk_set_complement(Z3_context c, Z3_ast arg)
Take the complement of a set.
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.
bool Z3_API Z3_stats_is_uint(Z3_context c, Z3_stats s, unsigned idx)
Return true if the given statistical data is a unsigned integer.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_ast Z3_API Z3_mk_extract(Z3_context c, unsigned high, unsigned low, Z3_ast t1)
Extract the bits high down to low from a bit-vector of size m to yield a new bit-vector of size n,...
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
Z3_ast Z3_API Z3_mk_set_add(Z3_context c, Z3_ast set, Z3_ast elem)
Add an element to a set.
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.
Z3_ast Z3_API Z3_mk_bvadd_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
Z3_ast Z3_API Z3_mk_bvadd_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
Z3_ast Z3_API Z3_mk_array_default(Z3_context c, Z3_ast array)
Access the array default value. Produces the default range value, for arrays that can be represented ...
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.
Z3_constructor Z3_API Z3_mk_constructor(Z3_context c, Z3_symbol name, Z3_symbol recognizer, unsigned num_fields, Z3_symbol const field_names[], Z3_sort_opt const sorts[], unsigned sort_refs[])
Create a constructor.
Z3_ast_vector Z3_API Z3_ast_vector_translate(Z3_context s, Z3_ast_vector v, Z3_context t)
Translate the AST vector v from context s into an AST vector in context t.
void Z3_API Z3_func_entry_inc_ref(Z3_context c, Z3_func_entry e)
Increment the reference counter of the given Z3_func_entry object.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.
Z3_ast Z3_API Z3_mk_bvsub_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
void Z3_API Z3_solver_push(Z3_context c, Z3_solver s)
Create a backtracking point.
Z3_ast Z3_API Z3_mk_bvsub_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
Z3_ast Z3_API Z3_mk_bvudiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned division.
Z3_string Z3_API Z3_ast_vector_to_string(Z3_context c, Z3_ast_vector v)
Convert AST vector into a string.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
bool Z3_API Z3_is_numeral_ast(Z3_context c, Z3_ast a)
Z3_ast Z3_API Z3_mk_bvsrem(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows dividend).
bool Z3_API Z3_is_as_array(Z3_context c, Z3_ast a)
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3....
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
Z3_ast Z3_API Z3_mk_is_int(Z3_context c, Z3_ast t1)
Check if a real number is an integer.
void Z3_API Z3_params_set_bool(Z3_context c, Z3_params p, Z3_symbol k, bool v)
Add a Boolean parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.
Z3_ast Z3_API Z3_mk_sign_ext(Z3_context c, unsigned i, Z3_ast t1)
Sign-extend of the given bit-vector to the (signed) equivalent bit-vector of size m+i,...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
void Z3_API Z3_stats_inc_ref(Z3_context c, Z3_stats s)
Increment the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs)
n-ary Array read. The argument a is the array and idxs are the indices of the array that gets read.
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
void Z3_API Z3_func_interp_inc_ref(Z3_context c, Z3_func_interp f)
Increment the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_set_double(Z3_context c, Z3_params p, Z3_symbol k, double v)
Add a double parameter k with value v to the parameter set p.
Z3_string Z3_API Z3_param_descrs_get_documentation(Z3_context c, Z3_param_descrs p, Z3_symbol s)
Retrieve documentation string corresponding to parameter name s.
Z3_sort Z3_API Z3_mk_datatype_sort(Z3_context c, Z3_symbol name)
create a forward reference to a recursive datatype being declared. The forward reference can be used ...
Z3_solver Z3_API Z3_mk_solver(Z3_context c)
Create a new solver. This solver is a "combined solver" (see combined_solver module) that internally ...
Z3_model Z3_API Z3_solver_get_model(Z3_context c, Z3_solver s)
Retrieve the model for the last Z3_solver_check or Z3_solver_check_assumptions.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
Z3_func_decl Z3_API Z3_get_as_array_func_decl(Z3_context c, Z3_ast a)
Return the function declaration f associated with a (_ as_array f) node.
Z3_ast Z3_API Z3_mk_ext_rotate_left(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the left t2 times.
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
void Z3_API Z3_params_set_uint(Z3_context c, Z3_params p, Z3_symbol k, unsigned v)
Add a unsigned parameter k with value v to the parameter set p.
Z3_lbool Z3_API Z3_solver_check_assumptions(Z3_context c, Z3_solver s, unsigned num_assumptions, Z3_ast const assumptions[])
Check whether the assertions in the given solver and optional assumptions are consistent or not.
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.
Z3_ast Z3_API Z3_mk_bvashr(Z3_context c, Z3_ast t1, Z3_ast t2)
Arithmetic shift right.
Z3_ast Z3_API Z3_mk_bv2int(Z3_context c, Z3_ast t1, bool is_signed)
Create an integer from the bit-vector argument t1. If is_signed is false, then the bit-vector t1 is t...
Z3_sort Z3_API Z3_get_array_sort_domain_n(Z3_context c, Z3_sort t, unsigned idx)
Return the i'th domain sort of an n-dimensional array.
Z3_ast Z3_API Z3_mk_set_del(Z3_context c, Z3_ast set, Z3_ast elem)
Remove an element to a set.
Z3_ast Z3_API Z3_mk_bvmul_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
Z3_ast Z3_API Z3_mk_bvor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise or.
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th constructor.
void Z3_API Z3_ast_vector_resize(Z3_context c, Z3_ast_vector v, unsigned n)
Resize the AST vector v.
Z3_ast Z3_API Z3_mk_quantifier_const_ex(Z3_context c, bool is_forall, unsigned weight, Z3_symbol quantifier_id, Z3_symbol skolem_id, unsigned num_bound, Z3_app const bound[], unsigned num_patterns, Z3_pattern const patterns[], unsigned num_no_patterns, Z3_ast const no_patterns[], Z3_ast body)
Create a universal or existential quantifier using a list of constants that will form the set of boun...
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[])
Create a pattern for quantifier instantiation.
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
unsigned Z3_API Z3_stats_get_uint_value(Z3_context c, Z3_stats s, unsigned idx)
Return the unsigned value of the given statistical data.
Z3_sort Z3_API Z3_get_array_sort_domain(Z3_context c, Z3_sort t)
Return the domain of the given array sort. In the case of a multi-dimensional array,...
Z3_ast Z3_API Z3_mk_bvmul_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflo...
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
Z3_ast Z3_API Z3_mk_bvadd(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement addition.
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.
void Z3_API Z3_params_dec_ref(Z3_context c, Z3_params p)
Decrement the reference counter of the given parameter set.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
unsigned Z3_API Z3_ast_map_size(Z3_context c, Z3_ast_map m)
Return the size of the given map.
unsigned Z3_API Z3_param_descrs_size(Z3_context c, Z3_param_descrs p)
Return the number of parameters in the given parameter description set.
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
double Z3_API Z3_stats_get_double_value(Z3_context c, Z3_stats s, unsigned idx)
Return the double value of the given statistical data.
Z3_ast Z3_API Z3_mk_bvugt(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than.
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_ast Z3_API Z3_pattern_to_ast(Z3_context c, Z3_pattern p)
Convert a Z3_pattern into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_bvnot(Z3_context c, Z3_ast t1)
Bitwise negation.
Z3_ast Z3_API Z3_mk_bvurem(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned remainder.
void Z3_API Z3_mk_datatypes(Z3_context c, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort sorts[], Z3_constructor_list constructor_lists[])
Create mutually recursive datatypes.
unsigned Z3_API Z3_func_interp_get_arity(Z3_context c, Z3_func_interp f)
Return the arity (number of arguments) of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.
Z3_ast Z3_API Z3_mk_seq_concat(Z3_context c, unsigned n, Z3_ast const args[])
Concatenate sequences.
Z3_sort Z3_API Z3_mk_enumeration_sort(Z3_context c, Z3_symbol name, unsigned n, Z3_symbol const enum_names[], Z3_func_decl enum_consts[], Z3_func_decl enum_testers[])
Create a enumeration sort.
unsigned Z3_API Z3_get_bv_sort_size(Z3_context c, Z3_sort t)
Return the size of the given bit-vector sort.
Z3_ast Z3_API Z3_mk_set_member(Z3_context c, Z3_ast elem, Z3_ast set)
Check for set membership.
void Z3_API Z3_ast_vector_dec_ref(Z3_context c, Z3_ast_vector v)
Decrement the reference counter of the given AST vector.
void Z3_API Z3_func_interp_dec_ref(Z3_context c, Z3_func_interp f)
Decrement the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_inc_ref(Z3_context c, Z3_params p)
Increment the reference counter of the given parameter set.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
Z3_sort Z3_API Z3_mk_bv_sort(Z3_context c, unsigned sz)
Create a bit-vector type of the given size.
Z3_ast Z3_API Z3_mk_bvult(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than.
void Z3_API Z3_ast_map_dec_ref(Z3_context c, Z3_ast_map m)
Decrement the reference counter of the given AST map.
Z3_string Z3_API Z3_params_to_string(Z3_context c, Z3_params p)
Convert a parameter set into a string. This function is mainly used for printing the contents of a pa...
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.
void Z3_API Z3_func_entry_dec_ref(Z3_context c, Z3_func_entry e)
Decrement the reference counter of the given Z3_func_entry object.
unsigned Z3_API Z3_stats_size(Z3_context c, Z3_stats s)
Return the number of statistical data in s.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.
void Z3_API Z3_param_descrs_dec_ref(Z3_context c, Z3_param_descrs p)
Decrement the reference counter of the given parameter description set.
Z3_model Z3_API Z3_mk_model(Z3_context c)
Create a fresh model object. It has reference count 0.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
Z3_ast Z3_API Z3_mk_bvneg_no_overflow(Z3_context c, Z3_ast t1)
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
Z3_string Z3_API Z3_stats_get_key(Z3_context c, Z3_stats s, unsigned idx)
Return the key (a string) for a particular statistical data.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast Z3_API Z3_mk_bvsmod(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows divisor).
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_ast Z3_API Z3_mk_int2bv(Z3_context c, unsigned n, Z3_ast t1)
Create an n bit bit-vector from the integer argument t1.
void Z3_API Z3_solver_assert(Z3_context c, Z3_solver s, Z3_ast a)
Assert a constraint into the solver.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.
unsigned Z3_API Z3_solver_get_num_scopes(Z3_context c, Z3_solver s)
Return the number of backtracking points.
Z3_sort Z3_API Z3_get_array_sort_range(Z3_context c, Z3_sort t)
Return the range of the given array sort.
void Z3_API Z3_del_constructor_list(Z3_context c, Z3_constructor_list clist)
Reclaim memory allocated for constructor list.
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_ast Z3_API Z3_func_entry_get_arg(Z3_context c, Z3_func_entry e, unsigned i)
Return an argument of a Z3_func_entry object.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
void Z3_API Z3_ast_vector_inc_ref(Z3_context c, Z3_ast_vector v)
Increment the reference counter of the given AST vector.
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_ast Z3_API Z3_mk_set_has_size(Z3_context c, Z3_ast set, Z3_ast k)
Create predicate that holds if Boolean array set has k elements set to true.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
void Z3_API Z3_solver_pop(Z3_context c, Z3_solver s, unsigned n)
Backtrack n backtracking points.
void Z3_API Z3_ast_map_erase(Z3_context c, Z3_ast_map m, Z3_ast k)
Erase a key from the map.
Z3_ast Z3_API Z3_mk_int2real(Z3_context c, Z3_ast t1)
Coerce an integer to a real.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
void Z3_API Z3_params_validate(Z3_context c, Z3_params p, Z3_param_descrs d)
Validate the parameter set p against the parameter description set d.
Z3_func_decl Z3_API Z3_get_datatype_sort_recognizer(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th recognizer.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_ast_vector_push(Z3_context c, Z3_ast_vector v, Z3_ast a)
Add the AST a in the end of the AST vector v. The size of v is increased by one.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
Z3_ast Z3_API Z3_mk_map(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast const *args)
Map f on the argument arrays.
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
void Z3_API Z3_param_descrs_inc_ref(Z3_context c, Z3_param_descrs p)
Increment the reference counter of the given parameter description set.
void Z3_API Z3_stats_dec_ref(Z3_context c, Z3_stats s)
Decrement the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_array_ext(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create array extensionality index given two arrays with the same sort. The meaning is given by the ax...
Z3_ast Z3_API Z3_mk_re_concat(Z3_context c, unsigned n, Z3_ast const args[])
Create the concatenation of the regular languages.
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
Z3_func_entry Z3_API Z3_func_interp_get_entry(Z3_context c, Z3_func_interp f, unsigned i)
Return a "point" of the given function interpretation. It represents the value of f in a particular p...
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....
Z3_ast Z3_API Z3_mk_concat(Z3_context c, Z3_ast t1, Z3_ast t2)
Concatenate the given bit-vectors.
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
Z3_constructor_list Z3_API Z3_mk_constructor_list(Z3_context c, unsigned num_constructors, Z3_constructor const constructors[])
Create list of constructors.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
Z3_ast Z3_API Z3_mk_bvneg(Z3_context c, Z3_ast t1)
Standard two's complement unary minus.
Z3_ast Z3_API Z3_mk_store_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs, Z3_ast v)
n-ary Array update.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
Z3_sort Z3_API Z3_mk_bool_sort(Z3_context c)
Create the Boolean type.
void Z3_API Z3_params_set_symbol(Z3_context c, Z3_params p, Z3_symbol k, Z3_symbol v)
Add a symbol parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_ast_vector_get(Z3_context c, Z3_ast_vector v, unsigned i)
Return the AST at position i in the AST vector v.
Z3_func_decl Z3_API Z3_to_func_decl(Z3_context c, Z3_ast a)
Convert an AST into a FUNC_DECL_AST. This is just type casting.
Z3_ast Z3_API Z3_mk_set_difference(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Take the set difference between two sets.
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_ast Z3_API Z3_mk_bvlshr(Z3_context c, Z3_ast t1, Z3_ast t2)
Logical shift right.
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_not(Z3_context c, Z3_ast a)
Create an AST node representing not(a).
Z3_ast Z3_API Z3_mk_or(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] or ... or args[num_args-1].
Z3_sort Z3_API Z3_mk_array_sort(Z3_context c, Z3_sort domain, Z3_sort range)
Create an array type.
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
Z3_ast Z3_API Z3_mk_seq_extract(Z3_context c, Z3_ast s, Z3_ast offset, Z3_ast length)
Extract subsequence starting at offset of length.
Z3_sort Z3_API Z3_mk_type_variable(Z3_context c, Z3_symbol s)
Create a type variable.
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.
Z3_ast Z3_API Z3_mk_bvuge(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than or equal to.
Z3_string Z3_API Z3_get_numeral_binary_string(Z3_context c, Z3_ast a)
Return numeral value, as a binary string of a numeric constant term.
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
unsigned Z3_API Z3_func_interp_get_num_entries(Z3_context c, Z3_func_interp f)
Return the number of entries in the given function interpretation.
void Z3_API Z3_ast_map_insert(Z3_context c, Z3_ast_map m, Z3_ast k, Z3_ast v)
Store/Replace a new key, value pair in the given map.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
double Z3_API Z3_get_numeral_double(Z3_context c, Z3_ast a)
Return numeral as a double.
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_real2int(Z3_context c, Z3_ast t1)
Coerce a real to an integer.
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.
Z3_ast Z3_API Z3_mk_ext_rotate_right(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the right t2 times.
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor_accessor(Z3_context c, Z3_sort t, unsigned idx_c, unsigned idx_a)
Return idx_a'th accessor for the idx_c'th constructor.
Z3_ast Z3_API Z3_mk_bvredor(Z3_context c, Z3_ast t1)
Take disjunction of bits in vector, return vector of length 1.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
void Z3_API Z3_solver_reset(Z3_context c, Z3_solver s)
Remove all assertions from the solver.
bool Z3_API Z3_is_algebraic_number(Z3_context c, Z3_ast a)
Return true if the given AST is a real algebraic number.
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
_ctx_from_ast_args(*args)
_to_func_decl_ref(a, ctx)
_valid_accessor(acc)
Datatypes.
BitVec(name, bv, ctx=None)
DeclareSort(name, ctx=None)
RecAddDefinition(f, args, body)
DeclareTypeVar(name, ctx=None)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
_coerce_expr_list(alist, ctx=None)
RealVector(prefix, sz, ctx=None)
BitVecs(names, bv, ctx=None)
BoolVector(prefix, sz, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
FreshReal(prefix="b", ctx=None)
_reduce(func, sequence, initial)
BVAddNoOverflow(a, b, signed)
FreshBool(prefix="b", ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
IntVector(prefix, sz, ctx=None)
RealVarVector(n, ctx=None)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])