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.
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.
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.
248 >>> x2 =
Real(
'x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
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
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.
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
445 >>> n1.hash() == n2.hash()
452 """Return `True` if `a` is an AST node.
469 return isinstance(a, AstRef)
473 """Return `True` if `a` and `b` are structurally identical AST nodes.
517 _args = (FuncDecl * sz)()
519 _args[i] = args[i].as_func_decl()
527 _args[i] = args[i].as_ast()
535 _args[i] = args[i].as_ast()
543 elif k == Z3_FUNC_DECL_AST:
560 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
569 """Return the Z3 internal kind of a sort.
570 This method can be used to test if `self`
is one of the Z3 builtin sorts.
573 >>> b.kind() == Z3_BOOL_SORT
575 >>> b.kind() == Z3_INT_SORT
578 >>> A.kind() == Z3_ARRAY_SORT
580 >>> A.kind() == Z3_INT_SORT
586 """Return `True` if `self` is a subsort of `other`.
594 """Try to cast `val` as an element of sort `self`.
596 This method is used
in Z3Py to convert Python objects such
as integers,
597 floats, longs
and strings into Z3 expressions.
609 """Return the name (string) of sort `self`.
619 """Return `True` if `self` and `other` are the same Z3 sort.
632 """Return `True` if `self` and `other` are not the same Z3 sort.
644 return AstRef.__hash__(self)
648 """Return `True` if `s` is a Z3 sort.
657 return isinstance(s, SortRef)
662 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
664 if k == Z3_BOOL_SORT:
666 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
668 elif k == Z3_BV_SORT:
670 elif k == Z3_ARRAY_SORT:
672 elif k == Z3_DATATYPE_SORT:
674 elif k == Z3_FINITE_DOMAIN_SORT:
676 elif k == Z3_FLOATING_POINT_SORT:
678 elif k == Z3_ROUNDING_MODE_SORT:
680 elif k == Z3_RE_SORT:
682 elif k == Z3_SEQ_SORT:
684 elif k == Z3_CHAR_SORT:
686 elif k == Z3_TYPE_VAR:
696 """Create a new uninterpreted sort named `name`.
698 If `ctx=None`, then the new sort
is declared
in the
global Z3Py context.
701 >>> a =
Const(
'a', A)
702 >>> b =
Const(
'b', A)
714 """Type variable reference"""
724 """Create a new type variable named `name`.
726 If `ctx=None`, then the new sort
is declared
in the
global Z3Py context.
741 """Function declaration. Every constant and function have an associated declaration.
743 The declaration assigns a name, a sort (i.e., type), and for function
744 the sort (i.e., type) of each of its arguments. Note that,
in Z3,
745 a constant
is a function
with 0 arguments.
758 """Return the name of the function declaration `self`.
763 >>> isinstance(f.name(), str)
769 """Return the number of arguments of a function declaration.
770 If `self` is a constant, then `self.
arity()`
is 0.
779 """Return the sort of the argument `i` of a function declaration.
780 This method assumes that `0 <= i < self.arity()`.
791 """Return the sort of the range of a function declaration.
792 For constants, this is the sort of the constant.
801 """Return the internal kind of a function declaration.
802 It can be used to identify Z3 built-in functions such
as addition, multiplication, etc.
805 >>> d = (x + 1).decl()
806 >>> d.kind() == Z3_OP_ADD
808 >>> d.kind() == Z3_OP_MUL
816 result = [
None for i
in range(n)]
819 if k == Z3_PARAMETER_INT:
821 elif k == Z3_PARAMETER_DOUBLE:
823 elif k == Z3_PARAMETER_RATIONAL:
825 elif k == Z3_PARAMETER_SYMBOL:
827 elif k == Z3_PARAMETER_SORT:
829 elif k == Z3_PARAMETER_AST:
831 elif k == Z3_PARAMETER_FUNC_DECL:
838 """Create a Z3 application expression using the function `self`, and the given arguments.
840 The arguments must be Z3 expressions. This method assumes that
841 the sorts of the elements in `args` match the sorts of the
842 domain. Limited coercion
is supported. For example,
if
843 args[0]
is a Python integer,
and the function expects a Z3
844 integer, then the argument
is automatically converted into a
857 _args = (Ast * num)()
862 tmp = self.
domain(i).cast(args[i])
864 _args[i] = tmp.as_ast()
869 """Return `True` if `a` is a Z3 function declaration.
878 return isinstance(a, FuncDeclRef)
882 """Create a new Z3 uninterpreted function with the given sorts.
890 _z3_assert(len(sig) > 0,
"At least two arguments expected")
895 dom = (Sort * arity)()
896 for i
in range(arity):
905 """Create a new fresh Z3 uninterpreted function with the given sorts.
909 _z3_assert(len(sig) > 0,
"At least two arguments expected")
914 dom = (z3.Sort * arity)()
915 for i
in range(arity):
928 """Create a new Z3 recursive with the given sorts."""
931 _z3_assert(len(sig) > 0,
"At least two arguments expected")
936 dom = (Sort * arity)()
937 for i
in range(arity):
946 """Set the body of a recursive function.
947 Recursive definitions can be simplified if they are applied to ground
951 >>> n =
Int(
'n', ctx)
956 >>> s.add(fac(n) < 3)
959 >>> s.model().eval(fac(5))
969 _args[i] = args[i].ast
980 """Constraints, formulas and terms are expressions in Z3.
982 Expressions are ASTs. Every expression has a sort.
983 There are three main kinds of expressions:
984 function applications, quantifiers and bounded variables.
985 A constant
is a function application
with 0 arguments.
986 For quantifier free problems, all expressions are
987 function applications.
997 """Return the sort of expression `self`.
1009 """Shorthand for `self.sort().kind()`.
1012 >>> a.sort_kind() == Z3_ARRAY_SORT
1014 >>> a.sort_kind() == Z3_INT_SORT
1017 return self.
sort().kind()
1020 """Return a Z3 expression that represents the constraint `self == other`.
1022 If `other` is `
None`, then this method simply returns `
False`.
1038 return AstRef.__hash__(self)
1041 """Return a Z3 expression that represents the constraint `self != other`.
1043 If `other` is `
None`, then this method simply returns `
True`.
1062 """Return the Z3 function declaration associated with a Z3 application.
1077 """Return the number of arguments of a Z3 application.
1093 """Return argument `idx` of the application `self`.
1095 This method assumes that `self` is a function application
with at least `idx+1` arguments.
1114 """Return a list containing the children of the given expression
1124 return [self.
arg(i)
for i
in range(self.
num_args())]
1138 """inverse function to the serialize method on ExprRef.
1139 It is made available to make it easier
for users to serialize expressions back
and forth between
1140 strings. Solvers can be serialized using the
'sexpr()' method.
1144 if len(s.assertions()) != 1:
1145 raise Z3Exception(
"single assertion expected")
1146 fml = s.assertions()[0]
1147 if fml.num_args() != 1:
1148 raise Z3Exception(
"dummy function 'F' expected")
1152 if isinstance(a, Pattern):
1156 if k == Z3_QUANTIFIER_AST:
1159 if sk == Z3_BOOL_SORT:
1161 if sk == Z3_INT_SORT:
1162 if k == Z3_NUMERAL_AST:
1165 if sk == Z3_REAL_SORT:
1166 if k == Z3_NUMERAL_AST:
1171 if sk == Z3_BV_SORT:
1172 if k == Z3_NUMERAL_AST:
1176 if sk == Z3_ARRAY_SORT:
1178 if sk == Z3_DATATYPE_SORT:
1180 if sk == Z3_FLOATING_POINT_SORT:
1184 return FPRef(a, ctx)
1185 if sk == Z3_FINITE_DOMAIN_SORT:
1186 if k == Z3_NUMERAL_AST:
1190 if sk == Z3_ROUNDING_MODE_SORT:
1192 if sk == Z3_SEQ_SORT:
1194 if sk == Z3_CHAR_SORT:
1196 if sk == Z3_RE_SORT:
1197 return ReRef(a, ctx)
1214 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1224 if isinstance(a, str)
and isinstance(b, SeqRef):
1226 if isinstance(b, str)
and isinstance(a, SeqRef):
1228 if isinstance(a, float)
and isinstance(b, ArithRef):
1230 if isinstance(b, float)
and isinstance(a, ArithRef):
1243 for element
in sequence:
1244 result = func(result, element)
1255 alist = [
_py2expr(a, ctx)
for a
in alist]
1256 s =
_reduce(_coerce_expr_merge, alist,
None)
1257 return [s.cast(a)
for a
in alist]
1261 """Return `True` if `a` is a Z3 expression.
1280 return isinstance(a, ExprRef)
1284 """Return `True` if `a` is a Z3 function application.
1286 Note that, constants are function applications with 0 arguments.
1303 if not isinstance(a, ExprRef):
1306 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1310 """Return `True` if `a` is Z3 constant/variable expression.
1325 return is_app(a)
and a.num_args() == 0
1329 """Return `True` if `a` is variable.
1331 Z3 uses de-Bruijn indices for representing bound variables
in
1341 >>> q =
ForAll(x, f(x) == x)
1354 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1364 >>> q =
ForAll([x, y], f(x, y) == x + y)
1370 >>> v1 = b.arg(0).arg(0)
1371 >>> v2 = b.arg(0).arg(1)
1387 """Return `True` if `a` is an application of the given kind `k`.
1396 return is_app(a)
and a.decl().kind() == k
1399def If(a, b, c, ctx=None):
1400 """Create a Z3 if-then-else expression.
1404 >>> max =
If(x > y, x, y)
1410 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1411 return Cond(a, b, c, ctx)
1418 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1423 """Create a Z3 distinct expression.
1440 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1449 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1450 args[0] = a.as_ast()
1451 args[1] = b.as_ast()
1452 return f(a.ctx.ref(), 2, args)
1456 """Create a constant of the given sort.
1462 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1468 """Create several constants of the given sort.
1470 `names` is a string containing the names of all constants to be created.
1471 Blank spaces separate the names of different constants.
1477 if isinstance(names, str):
1478 names = names.split(
" ")
1479 return [
Const(name, sort)
for name
in names]
1483 """Create a fresh constant of a specified sort"""
1489 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1490 A free variable with index n
is bound when it occurs within the scope of n+1 quantified
1505 Create a real free variable. Free variables are used to create quantified formulas.
1506 They are also used to create polynomials.
1516 Create a list of Real free variables.
1517 The variables have ids: 0, 1, ..., n-1
1523 return [
RealVar(i, ctx)
for i
in range(n)]
1536 """Try to cast `val` as a Boolean.
1548 if isinstance(val, bool):
1552 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1554 if not self.
eq(val.sort()):
1555 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1559 return isinstance(other, ArithSortRef)
1569 """All Boolean expressions are instances of this class."""
1575 if isinstance(other, BoolRef):
1576 other =
If(other, 1, 0)
1577 return If(self, 1, 0) + other
1586 """Create the Z3 expression `self * other`.
1588 if isinstance(other, int)
and other == 1:
1589 return If(self, 1, 0)
1590 if isinstance(other, int)
and other == 0:
1592 if isinstance(other, BoolRef):
1593 other =
If(other, 1, 0)
1594 return If(self, other, 0)
1597 return And(self, other)
1600 return Or(self, other)
1603 return Xor(self, other)
1612 """Return `True` if `a` is a Z3 Boolean expression.
1626 return isinstance(a, BoolRef)
1630 """Return `True` if `a` is the Z3 true expression.
1648 """Return `True` if `a` is the Z3 false expression.
1662 """Return `True` if `a` is a Z3 and expression.
1664 >>> p, q = Bools('p q')
1674 """Return `True` if `a` is a Z3 or expression.
1676 >>> p, q = Bools('p q')
1686 """Return `True` if `a` is a Z3 implication expression.
1688 >>> p, q = Bools('p q')
1698 """Return `True` if `a` is a Z3 not expression.
1710 """Return `True` if `a` is a Z3 equality expression.
1712 >>> x, y = Ints('x y')
1720 """Return `True` if `a` is a Z3 distinct expression.
1722 >>> x, y, z = Ints('x y z')
1732 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1750 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1769 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1781 """Return a tuple of Boolean constants.
1783 `names` is a single string containing all names separated by blank spaces.
1784 If `ctx=
None`, then the
global context
is used.
1786 >>> p, q, r =
Bools(
'p q r')
1787 >>>
And(p,
Or(q, r))
1791 if isinstance(names, str):
1792 names = names.split(
" ")
1793 return [
Bool(name, ctx)
for name
in names]
1797 """Return a list of Boolean constants of size `sz`.
1799 The constants are named using the given prefix.
1800 If `ctx=None`, then the
global context
is used.
1806 And(p__0, p__1, p__2)
1808 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1812 """Return a fresh Boolean constant in the given context using the given prefix.
1814 If `ctx=None`, then the
global context
is used.
1826 """Create a Z3 implies expression.
1828 >>> p, q = Bools('p q')
1840 """Create a Z3 Xor expression.
1842 >>> p, q = Bools('p q')
1856 """Create a Z3 not expression or probe.
1882 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1890 """Create a Z3 and-expression or and-probe.
1892 >>> p, q, r = Bools('p q r')
1897 And(p__0, p__1, p__2, p__3, p__4)
1901 last_arg = args[len(args) - 1]
1902 if isinstance(last_arg, Context):
1903 ctx = args[len(args) - 1]
1904 args = args[:len(args) - 1]
1905 elif len(args) == 1
and isinstance(args[0], AstVector):
1907 args = [a
for a
in args[0]]
1913 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1923 """Create a Z3 or-expression or or-probe.
1925 >>> p, q, r = Bools('p q r')
1930 Or(p__0, p__1, p__2, p__3, p__4)
1934 last_arg = args[len(args) - 1]
1935 if isinstance(last_arg, Context):
1936 ctx = args[len(args) - 1]
1937 args = args[:len(args) - 1]
1938 elif len(args) == 1
and isinstance(args[0], AstVector):
1940 args = [a
for a
in args[0]]
1946 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1962 """Patterns are hints for quantifier instantiation.
1974 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
1978 >>> q =
ForAll(x, f(x) == 0, patterns = [ f(x) ])
1981 >>> q.num_patterns()
1988 return isinstance(a, PatternRef)
1992 """Create a Z3 multi-pattern using the given expressions `*args`
2000 >>> q.num_patterns()
2008 _z3_assert(len(args) > 0,
"At least one argument expected")
2029 """Universally and Existentially quantified formulas."""
2038 """Return the Boolean sort or sort of Lambda."""
2044 """Return `True` if `self` is a universal quantifier.
2048 >>> q =
ForAll(x, f(x) == 0)
2051 >>> q =
Exists(x, f(x) != 0)
2058 """Return `True` if `self` is an existential quantifier.
2062 >>> q =
ForAll(x, f(x) == 0)
2065 >>> q =
Exists(x, f(x) != 0)
2072 """Return `True` if `self` is a lambda expression.
2079 >>> q =
Exists(x, f(x) != 0)
2086 """Return the Z3 expression `self[arg]`.
2093 """Return the weight annotation of `self`.
2097 >>> q =
ForAll(x, f(x) == 0)
2100 >>> q =
ForAll(x, f(x) == 0, weight=10)
2107 """Return the skolem id of `self`.
2112 """Return the quantifier id of `self`.
2117 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2122 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2123 >>> q.num_patterns()
2129 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2134 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2135 >>> q.num_patterns()
2147 """Return the number of no-patterns."""
2151 """Return a no-pattern."""
2157 """Return the expression being quantified.
2161 >>> q =
ForAll(x, f(x) == 0)
2168 """Return the number of variables bounded by this quantifier.
2173 >>> q =
ForAll([x, y], f(x, y) >= x)
2180 """Return a string representing a name used when displaying the quantifier.
2185 >>> q =
ForAll([x, y], f(x, y) >= x)
2196 """Return the sort of a bound variable.
2201 >>> q =
ForAll([x, y], f(x, y) >= x)
2212 """Return a list containing a single element self.body()
2216 >>> q =
ForAll(x, f(x) == 0)
2220 return [self.
body()]
2224 """Return `True` if `a` is a Z3 quantifier.
2228 >>> q =
ForAll(x, f(x) == 0)
2234 return isinstance(a, QuantifierRef)
2237def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2242 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2253 _vs = (Ast * num_vars)()
2254 for i
in range(num_vars):
2256 _vs[i] = vs[i].as_ast()
2258 num_pats = len(patterns)
2259 _pats = (Pattern * num_pats)()
2260 for i
in range(num_pats):
2261 _pats[i] = patterns[i].ast
2268 num_no_pats, _no_pats,
2269 body.as_ast()), ctx)
2272def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2273 """Create a Z3 forall formula.
2275 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2280 >>>
ForAll([x, y], f(x, y) >= x)
2281 ForAll([x, y], f(x, y) >= x)
2282 >>>
ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2283 ForAll([x, y], f(x, y) >= x)
2284 >>>
ForAll([x, y], f(x, y) >= x, weight=10)
2285 ForAll([x, y], f(x, y) >= x)
2287 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2290def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2291 """Create a Z3 exists formula.
2293 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2299 >>> q =
Exists([x, y], f(x, y) >= x, skid=
"foo")
2301 Exists([x, y], f(x, y) >= x)
2304 >>> r =
Tactic(
'nnf')(q).as_expr()
2308 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2312 """Create a Z3 lambda expression.
2316 >>> lo, hi, e, i =
Ints(
'lo hi e i')
2317 >>> mem1 =
Lambda([i],
If(
And(lo <= i, i <= hi), e, mem0[i]))
2325 _vs = (Ast * num_vars)()
2326 for i
in range(num_vars):
2328 _vs[i] = vs[i].as_ast()
2339 """Real and Integer sorts."""
2342 """Return `True` if `self` is of the sort Real.
2353 return self.
kind() == Z3_REAL_SORT
2356 """Return `True` if `self` is of the sort Integer.
2367 return self.
kind() == Z3_INT_SORT
2373 """Return `True` if `self` is a subsort of `other`."""
2377 """Try to cast `val` as an Integer or Real.
2396 if val_s.is_int()
and self.
is_real():
2398 if val_s.is_bool()
and self.
is_int():
2399 return If(val, 1, 0)
2400 if val_s.is_bool()
and self.
is_real():
2403 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2410 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2415 """Return `True` if s is an arithmetical sort (type).
2423 >>> n =
Int(
'x') + 1
2427 return isinstance(s, ArithSortRef)
2431 """Integer and Real expressions."""
2434 """Return the sort (type) of the arithmetical expression `self`.
2444 """Return `True` if `self` is an integer expression.
2458 """Return `True` if `self` is an real expression.
2469 """Create the Z3 expression `self + other`.
2482 """Create the Z3 expression `other + self`.
2492 """Create the Z3 expression `self * other`.
2501 if isinstance(other, BoolRef):
2502 return If(other, self, 0)
2507 """Create the Z3 expression `other * self`.
2517 """Create the Z3 expression `self - other`.
2530 """Create the Z3 expression `other - self`.
2540 """Create the Z3 expression `self**other` (** is the power operator).
2554 """Create the Z3 expression `other**self` (** is the power operator).
2568 """Create the Z3 expression `other/self`.
2591 """Create the Z3 expression `other/self`."""
2595 """Create the Z3 expression `other/self`.
2612 """Create the Z3 expression `other/self`."""
2616 """Create the Z3 expression `other%self`.
2627 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2631 """Create the Z3 expression `other%self`.
2639 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2643 """Return an expression representing `-self`.
2663 """Create the Z3 expression `other <= self`.
2665 >>> x, y = Ints('x y')
2676 """Create the Z3 expression `other < self`.
2678 >>> x, y = Ints('x y')
2689 """Create the Z3 expression `other > self`.
2691 >>> x, y = Ints('x y')
2702 """Create the Z3 expression `other >= self`.
2704 >>> x, y = Ints('x y')
2716 """Return `True` if `a` is an arithmetical expression.
2733 return isinstance(a, ArithRef)
2737 """Return `True` if `a` is an integer expression.
2756 """Return `True` if `a` is a real expression.
2783 """Return `True` if `a` is an integer value of sort Int.
2791 >>> n =
Int(
'x') + 1
2807 """Return `True` if `a` is rational value of sort Real.
2817 >>> n =
Real(
'x') + 1
2829 """Return `True` if `a` is an algebraic value of sort Real.
2843 """Return `True` if `a` is an expression of the form b + c.
2845 >>> x, y = Ints('x y')
2855 """Return `True` if `a` is an expression of the form b * c.
2857 >>> x, y = Ints('x y')
2867 """Return `True` if `a` is an expression of the form b - c.
2869 >>> x, y = Ints('x y')
2879 """Return `True` if `a` is an expression of the form b / c.
2881 >>> x, y = Reals('x y')
2886 >>> x, y =
Ints(
'x y')
2896 """Return `True` if `a` is an expression of the form b div c.
2898 >>> x, y = Ints('x y')
2908 """Return `True` if `a` is an expression of the form b % c.
2910 >>> x, y = Ints('x y')
2920 """Return `True` if `a` is an expression of the form b <= c.
2922 >>> x, y = Ints('x y')
2932 """Return `True` if `a` is an expression of the form b < c.
2934 >>> x, y = Ints('x y')
2944 """Return `True` if `a` is an expression of the form b >= c.
2946 >>> x, y = Ints('x y')
2956 """Return `True` if `a` is an expression of the form b > c.
2958 >>> x, y = Ints('x y')
2968 """Return `True` if `a` is an expression of the form IsInt(b).
2980 """Return `True` if `a` is an expression of the form ToReal(b).
2995 """Return `True` if `a` is an expression of the form ToInt(b).
3010 """Integer values."""
3013 """Return a Z3 integer numeral as a Python long (bignum) numeral.
3026 """Return a Z3 integer numeral as a Python string.
3034 """Return a Z3 integer numeral as a Python binary string.
3036 >>> v.as_binary_string()
3043 """Rational values."""
3046 """ Return the numerator of a Z3 rational numeral.
3061 """ Return the denominator of a Z3 rational numeral.
3072 """ Return the numerator as a Python long.
3079 >>> v.numerator_as_long() + 1 == 10000000001
3085 """ Return the denominator as a Python long.
3090 >>> v.denominator_as_long()
3109 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3121 """Return a Z3 rational numeral as a Python string.
3130 """Return a Z3 rational as a Python Fraction object.
3140 """Algebraic irrational values."""
3143 """Return a Z3 rational number that approximates the algebraic number `self`.
3144 The result `r` is such that |r - self| <= 1/10^precision
3148 6838717160008073720548335/4835703278458516698824704
3155 """Return a string representation of the algebraic number `self` in decimal notation
3156 using `prec` decimal places.
3159 >>> x.as_decimal(10)
3161 >>> x.as_decimal(20)
3162 '1.41421356237309504880?'
3174 if isinstance(a, bool):
3178 if isinstance(a, float):
3180 if isinstance(a, str):
3185 _z3_assert(
False,
"Python bool, int, long or float expected")
3189 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3206 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3223 if isinstance(val, float):
3224 return str(int(val))
3225 elif isinstance(val, bool):
3235 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3247 """Return a Z3 real value.
3249 `val` may be a Python int, long, float or string representing a number
in decimal
or rational notation.
3250 If `ctx=
None`, then the
global context
is used.
3266 """Return a Z3 rational a/b.
3268 If `ctx=None`, then the
global context
is used.
3276 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3277 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3281def Q(a, b, ctx=None):
3282 """Return a Z3 rational a/b.
3284 If `ctx=None`, then the
global context
is used.
3295 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3308 """Return a tuple of Integer constants.
3310 >>> x, y, z = Ints('x y z')
3315 if isinstance(names, str):
3316 names = names.split(
" ")
3317 return [
Int(name, ctx)
for name
in names]
3321 """Return a list of integer constants of size `sz`.
3330 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3334 """Return a fresh integer constant in the given context using the given prefix.
3348 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3361 """Return a tuple of real constants.
3363 >>> x, y, z = Reals('x y z')
3366 >>>
Sum(x, y, z).sort()
3370 if isinstance(names, str):
3371 names = names.split(
" ")
3372 return [
Real(name, ctx)
for name
in names]
3376 """Return a list of real constants of size `sz`.
3387 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3391 """Return a fresh real constant in the given context using the given prefix.
3405 """ Return the Z3 expression ToReal(a).
3417 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3423 """ Return the Z3 expression ToInt(a).
3435 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3441 """ Return the Z3 predicate IsInt(a).
3444 >>>
IsInt(x +
"1/2")
3448 >>>
solve(
IsInt(x +
"1/2"), x > 0, x < 1, x !=
"1/2")
3452 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3458 """ Return a Z3 expression which represents the square root of a.
3471 """ Return a Z3 expression which represents the cubic root of a.
3490 """Bit-vector sort."""
3493 """Return the size (number of bits) of the bit-vector sort `self`.
3505 """Try to cast `val` as a Bit-Vector.
3510 >>> b.cast(10).sexpr()
3523 """Return True if `s` is a Z3 bit-vector sort.
3530 return isinstance(s, BitVecSortRef)
3534 """Bit-vector expressions."""
3537 """Return the sort of the bit-vector expression `self`.
3548 """Return the number of bits of the bit-vector expression `self`.
3559 """Create the Z3 expression `self + other`.
3572 """Create the Z3 expression `other + self`.
3582 """Create the Z3 expression `self * other`.
3595 """Create the Z3 expression `other * self`.
3605 """Create the Z3 expression `self - other`.
3618 """Create the Z3 expression `other - self`.
3628 """Create the Z3 expression bitwise-or `self | other`.
3641 """Create the Z3 expression bitwise-or `other | self`.
3651 """Create the Z3 expression bitwise-and `self & other`.
3664 """Create the Z3 expression bitwise-or `other & self`.
3674 """Create the Z3 expression bitwise-xor `self ^ other`.
3687 """Create the Z3 expression bitwise-xor `other ^ self`.
3706 """Return an expression representing `-self`.
3717 """Create the Z3 expression bitwise-not `~self`.
3728 """Create the Z3 expression (signed) division `self / other`.
3730 Use the function UDiv() for unsigned division.
3747 """Create the Z3 expression (signed) division `self / other`."""
3751 """Create the Z3 expression (signed) division `other / self`.
3753 Use the function UDiv() for unsigned division.
3758 >>> (10 / x).
sexpr()
3759 '(bvsdiv #x0000000a x)'
3761 '(bvudiv #x0000000a x)'
3767 """Create the Z3 expression (signed) division `other / self`."""
3771 """Create the Z3 expression (signed) mod `self % other`.
3773 Use the function URem() for unsigned remainder,
and SRem()
for signed remainder.
3792 """Create the Z3 expression (signed) mod `other % self`.
3794 Use the function URem() for unsigned remainder,
and SRem()
for signed remainder.
3799 >>> (10 % x).
sexpr()
3800 '(bvsmod #x0000000a x)'
3802 '(bvurem #x0000000a x)'
3804 '(bvsrem #x0000000a x)'
3810 """Create the Z3 expression (signed) `other <= self`.
3812 Use the function ULE() for unsigned less than
or equal to.
3817 >>> (x <= y).
sexpr()
3826 """Create the Z3 expression (signed) `other < self`.
3828 Use the function ULT() for unsigned less than.
3842 """Create the Z3 expression (signed) `other > self`.
3844 Use the function UGT() for unsigned greater than.
3858 """Create the Z3 expression (signed) `other >= self`.
3860 Use the function UGE() for unsigned greater than
or equal to.
3865 >>> (x >= y).
sexpr()
3874 """Create the Z3 expression (arithmetical) right shift `self >> other`
3876 Use the function LShR() for the right logical shift
3881 >>> (x >> y).
sexpr()
3904 """Create the Z3 expression left shift `self << other`
3909 >>> (x << y).
sexpr()
3918 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3920 Use the function LShR() for the right logical shift
3925 >>> (10 >> x).
sexpr()
3926 '(bvashr #x0000000a x)'
3932 """Create the Z3 expression left shift `other << self`.
3934 Use the function LShR() for the right logical shift
3939 >>> (10 << x).
sexpr()
3940 '(bvshl #x0000000a x)'
3947 """Bit-vector values."""
3950 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3955 >>> print("0x%.8x" % v.as_long())
3961 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3962 The most significant bit is assumed to be the sign.
3977 if val >= 2**(sz - 1):
3979 if val < -2**(sz - 1):
3991 """Return `True` if `a` is a Z3 bit-vector expression.
4001 return isinstance(a, BitVecRef)
4005 """Return `True` if `a` is a Z3 bit-vector numeral value.
4020 """Return the Z3 expression BV2Int(a).
4028 >>> x >
BV2Int(b, is_signed=
False)
4030 >>> x >
BV2Int(b, is_signed=
True)
4036 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4043 """Return the z3 expression Int2BV(a, num_bits).
4044 It is a bit-vector of width num_bits
and represents the
4045 modulo of a by 2^num_bits
4052 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4058 >>> x = Const('x', Byte)
4067 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4072 >>> print("0x%.8x" % v.as_long())
4084 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4085 If `ctx=None`, then the
global context
is used.
4095 >>> x2 =
BitVec(
'x', word)
4099 if isinstance(bv, BitVecSortRef):
4108 """Return a tuple of bit-vector constants of size bv.
4110 >>> x, y, z = BitVecs('x y z', 16)
4123 if isinstance(names, str):
4124 names = names.split(
" ")
4125 return [
BitVec(name, bv, ctx)
for name
in names]
4129 """Create a Z3 bit-vector concatenation expression.
4142 _z3_assert(sz >= 2,
"At least two arguments expected.")
4149 if is_seq(args[0])
or isinstance(args[0], str):
4152 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4155 v[i] = args[i].as_ast()
4160 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4163 v[i] = args[i].as_ast()
4167 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4169 for i
in range(sz - 1):
4175 """Create a Z3 bit-vector extraction expression.
4176 Extract is overloaded to also work on sequence extraction.
4177 The functions SubString
and SubSeq are redirected to Extract.
4178 For this case, the arguments are reinterpreted
as:
4179 high -
is a sequence (string)
4181 a -
is the length to be extracted
4191 if isinstance(high, str):
4198 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4200 "First and second arguments must be non negative integers")
4201 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4207 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4211 """Create the Z3 expression (unsigned) `other <= self`.
4213 Use the operator <= for signed less than
or equal to.
4218 >>> (x <= y).sexpr()
4220 >>>
ULE(x, y).sexpr()
4229 """Create the Z3 expression (unsigned) `other < self`.
4231 Use the operator < for signed less than.
4238 >>>
ULT(x, y).sexpr()
4247 """Create the Z3 expression (unsigned) `other >= self`.
4249 Use the operator >= for signed greater than
or equal to.
4254 >>> (x >= y).sexpr()
4256 >>>
UGE(x, y).sexpr()
4265 """Create the Z3 expression (unsigned) `other > self`.
4267 Use the operator > for signed greater than.
4274 >>>
UGT(x, y).sexpr()
4283 """Create the Z3 expression (unsigned) division `self / other`.
4285 Use the operator / for signed division.
4291 >>>
UDiv(x, y).sort()
4295 >>>
UDiv(x, y).sexpr()
4304 """Create the Z3 expression (unsigned) remainder `self % other`.
4306 Use the operator % for signed modulus,
and SRem()
for signed remainder.
4312 >>>
URem(x, y).sort()
4316 >>>
URem(x, y).sexpr()
4325 """Create the Z3 expression signed remainder.
4327 Use the operator % for signed modulus,
and URem()
for unsigned remainder.
4333 >>>
SRem(x, y).sort()
4337 >>>
SRem(x, y).sexpr()
4346 """Create the Z3 expression logical right shift.
4348 Use the operator >> for the arithmetical right shift.
4353 >>> (x >> y).sexpr()
4355 >>>
LShR(x, y).sexpr()
4378 """Return an expression representing `a` rotated to the left `b` times.
4394 """Return an expression representing `a` rotated to the right `b` times.
4410 """Return a bit-vector expression with `n` extra sign-bits.
4430 >>> print(
"%.x" % v.as_long())
4435 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4440 """Return a bit-vector expression with `n` extra zero-bits.
4463 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4468 """Return an expression representing `n` copies of `a`.
4477 >>> print(
"%.x" % v0.as_long())
4482 >>> print(
"%.x" % v.as_long())
4487 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4492 """Return the reduction-and expression of `a`."""
4494 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4499 """Return the reduction-or expression of `a`."""
4501 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4506 """A predicate the determines that bit-vector addition does not overflow"""
4513 """A predicate the determines that signed bit-vector addition does not underflow"""
4520 """A predicate the determines that bit-vector subtraction does not overflow"""
4527 """A predicate the determines that bit-vector subtraction does not underflow"""
4534 """A predicate the determines that bit-vector signed division does not overflow"""
4541 """A predicate the determines that bit-vector unary negation does not overflow"""
4543 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4548 """A predicate the determines that bit-vector multiplication does not overflow"""
4555 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4571 """Return the domain of the array sort `self`.
4580 """Return the domain of the array sort `self`.
4585 """Return the range of the array sort `self`.
4595 """Array expressions. """
4598 """Return the array sort of the array expression `self`.
4607 """Shorthand for `self.sort().domain()`.
4616 """Shorthand for self.sort().domain_n(i)`."""
4620 """Shorthand for `self.sort().range()`.
4629 """Return the Z3 expression `self[arg]`.
4645 if isinstance(arg, tuple):
4646 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4649 arg = ar.sort().domain().cast(arg)
4658 """Return `True` if `a` is a Z3 array expression.
4668 return isinstance(a, ArrayRef)
4672 """Return `True` if `a` is a Z3 constant array.
4685 """Return `True` if `a` is a Z3 constant array.
4698 """Return `True` if `a` is a Z3 map array expression.
4714 """Return `True` if `a` is a Z3 default array expression.
4719 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4723 """Return the function declaration associated with a Z3 map array expression.
4747 """Return the Z3 array sort with the given domain and range sorts.
4762 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4763 arity = len(sig) - 1
4769 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4773 dom = (Sort * arity)()
4774 for i
in range(arity):
4780 """Return an array constant named `name` with the given domain and range sorts.
4794 """Return a Z3 store array expression.
4797 >>> i, v =
Ints(
'i v')
4801 >>>
prove(s[i] == v)
4812 raise Z3Exception(
"array update requires index and value arguments")
4816 i = a.sort().domain().cast(i)
4817 v = a.sort().range().cast(v)
4819 v = a.sort().range().cast(args[-1])
4820 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4826 """ Return a default value for array expression.
4837 """Return a Z3 store array expression.
4840 >>> i, v =
Ints(
'i v')
4841 >>> s =
Store(a, i, v)
4844 >>>
prove(s[i] == v)
4854 """Return a Z3 select array expression.
4870 """Return a Z3 map array expression.
4875 >>> b =
Map(f, a1, a2)
4878 >>>
prove(b[0] == f(a1[0], a2[0]))
4883 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4886 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4893 """Return a Z3 constant array expression.
4915 """Return extensionality index for one-dimensional arrays.
4933 """Return `True` if `a` is a Z3 array select application.
4946 """Return `True` if `a` is a Z3 array store application.
4964 """ Create a set sort over element sort s"""
4969 """Create the empty set
4978 """Create the full set
4987 """ Take the union of sets
5000 """ Take the union of sets
5013 """ Add element e to set s
5024 """ Remove element e to set s
5035 """ The complement of set s
5045 """ The set difference of a and b
5056 """ Check if e is a member of set s
5067 """ Check if a is a subset of b
5084 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5085 if not isinstance(acc, tuple):
5089 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5093 """Helper class for declaring Z3 datatypes.
5096 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5097 >>> List.declare(
'nil')
5098 >>> List = List.create()
5102 >>> List.cons(10, List.nil)
5104 >>> List.cons(10, List.nil).sort()
5106 >>> cons = List.cons
5110 >>> n = cons(1, cons(0, nil))
5112 cons(1, cons(0, nil))
5131 _z3_assert(isinstance(name, str),
"String expected")
5132 _z3_assert(isinstance(rec_name, str),
"String expected")
5135 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5140 """Declare constructor named `name` with the given accessors `args`.
5141 Each accessor is a pair `(name, sort)`, where `name`
is a string
and `sort` a Z3 sort
5142 or a reference to the datatypes being declared.
5144 In the following example `List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))`
5145 declares the constructor named `cons` that builds a new List using an integer
and a List.
5146 It also declares the accessors `car`
and `cdr`. The accessor `car` extracts the integer
5147 of a `cons` cell,
and `cdr` the list of a `cons` cell. After all constructors were declared,
5148 we use the method
create() to create the actual datatype
in Z3.
5151 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5152 >>> List.declare(
'nil')
5153 >>> List = List.create()
5156 _z3_assert(isinstance(name, str),
"String expected")
5157 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5164 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5166 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5169 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5170 >>> List.declare(
'nil')
5171 >>> List = List.create()
5174 >>> List.cons(10, List.nil)
5181 """Auxiliary object used to create Z3 datatypes."""
5188 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5193 """Auxiliary object used to create Z3 datatypes."""
5200 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5205 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5207 In the following example we define a Tree-List using two mutually recursive datatypes.
5209 >>> TreeList = Datatype('TreeList')
5212 >>> Tree.declare(
'leaf', (
'val',
IntSort()))
5214 >>> Tree.declare(
'node', (
'children', TreeList))
5215 >>> TreeList.declare(
'nil')
5216 >>> TreeList.declare(
'cons', (
'car', Tree), (
'cdr', TreeList))
5218 >>> Tree.val(Tree.leaf(10))
5220 >>>
simplify(Tree.val(Tree.leaf(10)))
5222 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5224 node(cons(leaf(10), cons(leaf(20), nil)))
5225 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5228 >>>
simplify(TreeList.car(Tree.children(n2)) == n1)
5233 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5234 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5235 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5236 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5239 names = (Symbol * num)()
5240 out = (Sort * num)()
5241 clists = (ConstructorList * num)()
5243 for i
in range(num):
5246 num_cs = len(d.constructors)
5247 cs = (Constructor * num_cs)()
5248 for j
in range(num_cs):
5249 c = d.constructors[j]
5254 fnames = (Symbol * num_fs)()
5255 sorts = (Sort * num_fs)()
5256 refs = (ctypes.c_uint * num_fs)()
5257 for k
in range(num_fs):
5261 if isinstance(ftype, Datatype):
5264 ds.count(ftype) == 1,
5265 "One and only one occurrence of each datatype is expected",
5268 refs[k] = ds.index(ftype)
5272 sorts[k] = ftype.ast
5281 for i
in range(num):
5283 num_cs = dref.num_constructors()
5284 for j
in range(num_cs):
5285 cref = dref.constructor(j)
5286 cref_name = cref.name()
5287 cref_arity = cref.arity()
5288 if cref.arity() == 0:
5290 setattr(dref, cref_name, cref)
5291 rref = dref.recognizer(j)
5292 setattr(dref,
"is_" + cref_name, rref)
5293 for k
in range(cref_arity):
5294 aref = dref.accessor(j, k)
5295 setattr(dref, aref.name(), aref)
5297 return tuple(result)
5301 """Datatype sorts."""
5304 """Return the number of constructors in the given Z3 datatype.
5307 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5308 >>> List.declare(
'nil')
5309 >>> List = List.create()
5311 >>> List.num_constructors()
5317 """Return a constructor of the datatype `self`.
5320 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5321 >>> List.declare(
'nil')
5322 >>> List = List.create()
5324 >>> List.num_constructors()
5326 >>> List.constructor(0)
5328 >>> List.constructor(1)
5336 """In Z3, each constructor has an associated recognizer predicate.
5338 If the constructor is named `name`, then the recognizer `is_name`.
5341 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5342 >>> List.declare(
'nil')
5343 >>> List = List.create()
5345 >>> List.num_constructors()
5347 >>> List.recognizer(0)
5349 >>> List.recognizer(1)
5351 >>>
simplify(List.is_nil(List.cons(10, List.nil)))
5353 >>>
simplify(List.is_cons(List.cons(10, List.nil)))
5355 >>> l =
Const(
'l', List)
5364 """In Z3, each constructor has 0 or more accessor.
5365 The number of accessors is equal to the arity of the constructor.
5368 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5369 >>> List.declare(
'nil')
5370 >>> List = List.create()
5371 >>> List.num_constructors()
5373 >>> List.constructor(0)
5375 >>> num_accs = List.constructor(0).arity()
5378 >>> List.accessor(0, 0)
5380 >>> List.accessor(0, 1)
5382 >>> List.constructor(1)
5384 >>> num_accs = List.constructor(1).arity()
5398 """Datatype expressions."""
5401 """Return the datatype sort of the datatype expression `self`."""
5405 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5410 """Create a named tuple sort base on a set of underlying sorts
5415 projects = [("project%d" % i, sorts[i])
for i
in range(len(sorts))]
5416 tuple.declare(name, *projects)
5417 tuple = tuple.create()
5418 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5422 """Create a named tagged union sort base on a set of underlying sorts
5427 for i
in range(len(sorts)):
5428 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5430 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5434 """Return a new enumeration sort named `name` containing the given values.
5436 The result is a pair (sort, list of constants).
5438 >>> Color, (red, green, blue) =
EnumSort(
'Color', [
'red',
'green',
'blue'])
5441 _z3_assert(isinstance(name, str),
"Name must be a string")
5442 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Enumeration sort values must be strings")
5443 _z3_assert(len(values) > 0,
"At least one value expected")
5446 _val_names = (Symbol * num)()
5447 for i
in range(num):
5449 _values = (FuncDecl * num)()
5450 _testers = (FuncDecl * num)()
5454 for i
in range(num):
5456 V = [a()
for a
in V]
5467 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5469 Consider using the function `args2params` to create instances of this object.
5484 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5488 """Set parameter name with value val."""
5490 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5492 if isinstance(val, bool):
5496 elif isinstance(val, float):
5498 elif isinstance(val, str):
5508 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5513 """Convert python arguments into a Z3_params object.
5514 A ':' is added to the keywords,
and '_' is replaced
with '-'
5516 >>>
args2params([
'model',
True,
'relevancy', 2], {
'elim_and' :
True})
5517 (params model true relevancy 2 elim_and true)
5520 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5536 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5540 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5546 return ParamsDescrsRef(self.
descr, self.
ctx)
5549 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5553 """Return the size of in the parameter description `self`.
5558 """Return the size of in the parameter description `self`.
5563 """Return the i-th parameter name in the parameter description `self`.
5568 """Return the kind of the parameter named `n`.
5573 """Return the documentation string of the parameter named `n`.
5594 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5596 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5597 A goal has a solution if one of its subgoals has a solution.
5598 A goal
is unsatisfiable
if all subgoals are unsatisfiable.
5601 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5604 "If goal is different from None, then ctx must be also different from None")
5607 if self.
goal is None:
5612 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5616 """Return the depth of the goal `self`.
5617 The depth corresponds to the number of tactics applied to `self`.
5619 >>> x, y = Ints('x y')
5621 >>> g.add(x == 0, y >= x + 1)
5624 >>> r =
Then(
'simplify',
'solve-eqs')(g)
5634 """Return `True` if `self` contains the `False` constraints.
5636 >>> x, y = Ints('x y')
5638 >>> g.inconsistent()
5640 >>> g.add(x == 0, x == 1)
5643 >>> g.inconsistent()
5645 >>> g2 =
Tactic(
'propagate-values')(g)[0]
5646 >>> g2.inconsistent()
5652 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5655 >>> g.prec() == Z3_GOAL_PRECISE
5657 >>> x, y =
Ints(
'x y')
5658 >>> g.add(x == y + 1)
5659 >>> g.prec() == Z3_GOAL_PRECISE
5661 >>> t =
With(
Tactic(
'add-bounds'), add_bound_lower=0, add_bound_upper=10)
5664 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5665 >>> g2.prec() == Z3_GOAL_PRECISE
5667 >>> g2.prec() == Z3_GOAL_UNDER
5673 """Alias for `prec()`.
5676 >>> g.precision() == Z3_GOAL_PRECISE
5682 """Return the number of constraints in the goal `self`.
5687 >>> x, y = Ints('x y')
5688 >>> g.add(x == 0, y > x)
5695 """Return the number of constraints in the goal `self`.
5700 >>> x, y = Ints('x y')
5701 >>> g.add(x == 0, y > x)
5708 """Return a constraint in the goal `self`.
5711 >>> x, y = Ints('x y')
5712 >>> g.add(x == 0, y > x)
5721 """Return a constraint in the goal `self`.
5724 >>> x, y = Ints('x y')
5725 >>> g.add(x == 0, y > x)
5731 if arg >= len(self):
5733 return self.
get(arg)
5736 """Assert constraints into the goal.
5740 >>> g.assert_exprs(x > 0, x < 2)
5755 >>> g.append(x > 0, x < 2)
5766 >>> g.insert(x > 0, x < 2)
5777 >>> g.add(x > 0, x < 2)
5784 """Retrieve model from a satisfiable goal
5785 >>> a, b = Ints('a b')
5787 >>> g.add(
Or(a == 0, a == 1),
Or(b == 0, b == 1), a > b)
5791 [
Or(b == 0, b == 1),
Not(0 <= b)]
5793 [
Or(b == 0, b == 1),
Not(1 <= b)]
5809 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5813 return obj_to_string(self)
5816 """Return a textual representation of the s-expression representing the goal."""
5820 """Return a textual representation of the goal in DIMACS format."""
5824 """Copy goal `self` to context `target`.
5832 >>> g2 = g.translate(c2)
5843 _z3_assert(isinstance(target, Context),
"target must be a context")
5853 """Return a new simplified goal.
5855 This method is essentially invoking the simplify tactic.
5859 >>> g.add(x + 1 >= 2)
5862 >>> g2 = g.simplify()
5870 return t.apply(self, *arguments, **keywords)[0]
5873 """Return goal `self` as a single Z3 expression.
5892 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5902 """A collection (vector) of ASTs."""
5911 assert ctx
is not None
5916 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5920 """Return the size of the vector `self`.
5925 >>> A.push(Int('x'))
5926 >>> A.push(
Int(
'x'))
5933 """Return the AST at position `i`.
5936 >>> A.push(Int('x') + 1)
5937 >>> A.push(
Int(
'y'))
5944 if isinstance(i, int):
5952 elif isinstance(i, slice):
5954 for ii
in range(*i.indices(self.
__len__())):
5962 """Update AST at position `i`.
5965 >>> A.push(Int('x') + 1)
5966 >>> A.push(
Int(
'y'))
5978 """Add `v` in the end of the vector.
5983 >>> A.push(Int('x'))
5990 """Resize the vector to `sz` elements.
5996 >>> for i
in range(10): A[i] =
Int(
'x')
6003 """Return `True` if the vector contains `item`.
6026 """Copy vector `self` to context `other_ctx`.
6032 >>> B = A.translate(c2)
6048 return obj_to_string(self)
6051 """Return a textual representation of the s-expression representing the vector."""
6062 """A mapping from ASTs to ASTs."""
6071 assert ctx
is not None
6079 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6083 """Return the size of the map.
6096 """Return `True` if the map contains key `key`.
6109 """Retrieve the value associated with key `key`.
6120 """Add/Update key `k` with value `v`.
6139 """Remove the entry associated with key `k`.
6153 """Remove all entries from the map.
6168 """Return an AstVector containing all keys in the map.
6187 """Store the value of the interpretation of a function in a particular point."""
6198 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6202 """Return the number of arguments in the given entry.
6206 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6211 >>> f_i.num_entries()
6213 >>> e = f_i.entry(0)
6220 """Return the value of argument `idx`.
6224 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6229 >>> f_i.num_entries()
6231 >>> e = f_i.entry(0)
6242 ...
except IndexError:
6243 ... print(
"index error")
6251 """Return the value of the function at point `self`.
6255 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6260 >>> f_i.num_entries()
6262 >>> e = f_i.entry(0)
6273 """Return entry `self` as a Python list.
6276 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6281 >>> f_i.num_entries()
6283 >>> e = f_i.entry(0)
6288 args.append(self.
value())
6296 """Stores the interpretation of a function in a Z3 model."""
6301 if self.
f is not None:
6305 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6310 Return the `else` value
for a function interpretation.
6311 Return
None if Z3 did
not specify the `
else` value
for
6316 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6332 """Return the number of entries/points in the function interpretation `self`.
6336 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6348 """Return the number of arguments for each entry in the function interpretation `self`.
6352 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6362 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6366 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6382 """Copy model 'self' to context 'other_ctx'.
6393 """Return the function interpretation as a Python list.
6396 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6410 return obj_to_string(self)
6414 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6417 assert ctx
is not None
6423 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6427 return obj_to_string(self)
6430 """Return a textual representation of the s-expression representing the model."""
6433 def eval(self, t, model_completion=False):
6434 """Evaluate the expression `t` in the model `self`.
6435 If `model_completion` is enabled, then a default interpretation
is automatically added
6436 for symbols that do
not have an interpretation
in the model `self`.
6440 >>> s.add(x > 0, x < 2)
6453 >>> m.eval(y, model_completion=
True)
6462 raise Z3Exception(
"failed to evaluate expression in the model")
6465 """Alias for `eval`.
6469 >>> s.add(x > 0, x < 2)
6473 >>> m.evaluate(x + 1)
6475 >>> m.evaluate(x == 1)
6478 >>> m.evaluate(y + x)
6482 >>> m.evaluate(y, model_completion=
True)
6485 >>> m.evaluate(y + x)
6488 return self.
eval(t, model_completion)
6491 """Return the number of constant and function declarations in the model `self`.
6496 >>> s.add(x > 0, f(x) != x)
6505 return num_consts + num_funcs
6508 """Return the interpretation for a given declaration or constant.
6513 >>> s.add(x > 0, x < 2, f(x) == 0)
6523 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6527 if decl.arity() == 0:
6529 if _r.value
is None:
6545 sz = fi.num_entries()
6549 e =
Store(e, fe.arg_value(0), fe.value())
6560 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6563 >>> a, b =
Consts(
'a b', A)
6575 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6579 >>> a1, a2 =
Consts(
'a1 a2', A)
6580 >>> b1, b2 =
Consts(
'b1 b2', B)
6582 >>> s.add(a1 != a2, b1 != b2)
6598 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6602 >>> a1, a2 =
Consts(
'a1 a2', A)
6603 >>> b1, b2 =
Consts(
'b1 b2', B)
6605 >>> s.add(a1 != a2, b1 != b2)
6615 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6618 >>> a, b =
Consts(
'a b', A)
6624 >>> m.get_universe(A)
6628 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6635 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6636 If `idx` is a declaration, then the actual interpretation
is returned.
6638 The elements can be retrieved using position
or the actual declaration.
6643 >>> s.add(x > 0, x < 2, f(x) == 0)
6657 >>>
for d
in m: print(
"%s -> %s" % (d, m[d]))
6662 if idx >= len(self):
6665 if (idx < num_consts):
6669 if isinstance(idx, FuncDeclRef):
6673 if isinstance(idx, SortRef):
6676 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6680 """Return a list with all symbols that have an interpretation in the model `self`.
6684 >>> s.add(x > 0, x < 2, f(x) == 0)
6699 """Update the interpretation of a constant"""
6702 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6706 for i
in range(value.num_entries()):
6711 v.push(e.arg_value(j))
6716 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6721 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6724 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6741 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6742 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6746 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6759 """Statistics for `Solver.check()`."""
6770 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6777 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6780 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6783 out.write(u(
"<tr>"))
6785 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6786 out.write(u(
"</table>"))
6787 return out.getvalue()
6792 """Return the number of statistical counters.
6795 >>> s =
Then(
'simplify',
'nlsat').solver()
6799 >>> st = s.statistics()
6806 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6809 >>> s =
Then(
'simplify',
'nlsat').solver()
6813 >>> st = s.statistics()
6817 (
'nlsat propagations', 2)
6821 if idx >= len(self):
6830 """Return the list of statistical counters.
6833 >>> s =
Then(
'simplify',
'nlsat').solver()
6837 >>> st = s.statistics()
6842 """Return the value of a particular statistical counter.
6845 >>> s =
Then(
'simplify',
'nlsat').solver()
6849 >>> st = s.statistics()
6850 >>> st.get_key_value(
'nlsat propagations')
6853 for idx
in range(len(self)):
6859 raise Z3Exception(
"unknown key")
6862 """Access the value of statistical using attributes.
6864 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6865 we should use
'_' (e.g.,
'nlsat_propagations').
6868 >>> s =
Then(
'simplify',
'nlsat').solver()
6872 >>> st = s.statistics()
6873 >>> st.nlsat_propagations
6878 key = name.replace("_",
" ")
6882 raise AttributeError
6892 """Represents the result of a satisfiability check: sat, unsat, unknown.
6898 >>> isinstance(r, CheckSatResult)
6909 return isinstance(other, CheckSatResult)
and self.
r == other.r
6912 return not self.
__eq__(other)
6916 if self.
r == Z3_L_TRUE:
6918 elif self.
r == Z3_L_FALSE:
6919 return "<b>unsat</b>"
6921 return "<b>unknown</b>"
6923 if self.
r == Z3_L_TRUE:
6925 elif self.
r == Z3_L_FALSE:
6931 in_html = in_html_mode()
6934 set_html_mode(in_html)
6945 Solver API provides methods for implementing the main SMT 2.0 commands:
6946 push, pop, check, get-model, etc.
6949 def __init__(self, solver=None, ctx=None, logFile=None):
6950 assert solver
is None or ctx
is not None
6959 if logFile
is not None:
6960 self.
set(
"smtlib2_log", logFile)
6963 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
6974 """Set a configuration option.
6975 The method `help()` return a string containing all available options.
6979 >>> s.set(mbqi=
True)
6980 >>> s.set(
'MBQI',
True)
6981 >>> s.set(
':mbqi',
True)
6987 """Create a backtracking point.
7009 """Backtrack \\c num backtracking points.
7031 """Return the current number of backtracking points.
7049 """Remove all asserted constraints and backtracking points created using `push()`.
7063 """Assert constraints into the solver.
7067 >>> s.assert_exprs(x > 0, x < 2)
7074 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7082 """Assert constraints into the solver.
7086 >>> s.add(x > 0, x < 2)
7097 """Assert constraints into the solver.
7101 >>> s.append(x > 0, x < 2)
7108 """Assert constraints into the solver.
7112 >>> s.insert(x > 0, x < 2)
7119 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7121 If `p` is a string, it will be automatically converted into a Boolean constant.
7126 >>> s.set(unsat_core=
True)
7127 >>> s.assert_and_track(x > 0,
'p1')
7128 >>> s.assert_and_track(x != 1,
'p2')
7129 >>> s.assert_and_track(x < 0, p3)
7130 >>> print(s.check())
7132 >>> c = s.unsat_core()
7142 if isinstance(p, str):
7144 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7149 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7155 >>> s.add(x > 0, x < 2)
7158 >>> s.model().eval(x)
7164 >>> s.add(2**x == 4)
7170 num = len(assumptions)
7171 _assumptions = (Ast * num)()
7172 for i
in range(num):
7173 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7178 """Return a model for the last `check()`.
7180 This function raises an exception if
7181 a model
is not available (e.g., last `
check()` returned unsat).
7185 >>> s.add(a + 2 == 0)
7194 raise Z3Exception(
"model is not available")
7197 """Import model converter from other into the current solver"""
7201 """Interrupt the execution of the solver object.
7202 Remarks: This ensures that the interrupt applies only
7203 to the given solver object and it applies only
if it
is running.
7208 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7210 These are the assumptions Z3 used in the unsatisfiability proof.
7211 Assumptions are available
in Z3. They are used to extract unsatisfiable cores.
7212 They may be also used to
"retract" assumptions. Note that, assumptions are
not really
7213 "soft constraints", but they can be used to implement them.
7215 >>> p1, p2, p3 =
Bools(
'p1 p2 p3')
7216 >>> x, y =
Ints(
'x y')
7221 >>> s.add(
Implies(p3, y > -3))
7222 >>> s.check(p1, p2, p3)
7224 >>> core = s.unsat_core()
7240 """Determine fixed values for the variables based on the solver state and assumptions.
7242 >>> a, b, c, d = Bools('a b c d')
7244 >>> s.consequences([a],[b,c,d])
7246 >>> s.consequences([
Not(c),d],[a,b,c,d])
7249 if isinstance(assumptions, list):
7251 for a
in assumptions:
7254 if isinstance(variables, list):
7259 _z3_assert(isinstance(assumptions, AstVector),
"ast vector expected")
7260 _z3_assert(isinstance(variables, AstVector),
"ast vector expected")
7263 variables.vector, consequences.vector)
7264 sz = len(consequences)
7265 consequences = [consequences[i]
for i
in range(sz)]
7269 """Parse assertions from a file"""
7273 """Parse assertions from a string"""
7278 The method takes an optional set of variables that restrict which
7279 variables may be used as a starting point
for cubing.
7280 If vars
is not None, then the first case split
is based on a variable
in
7284 if vars
is not None:
7291 if (len(r) == 1
and is_false(r[0])):
7298 """Access the set of variables that were touched by the most recently generated cube.
7299 This set of variables can be used as a starting point
for additional cubes.
7300 The idea
is that variables that appear
in clauses that are reduced by the most recent
7301 cube are likely more useful to cube on.
"""
7306 """Retrieve congruence closure root of the term t relative to the current search state
7307 The function primarily works for SimpleSolver. Terms
and variables that are
7308 eliminated during pre-processing are
not visible to the congruence closure.
7314 """Retrieve congruence closure sibling of the term t relative to the current search state
7315 The function primarily works for SimpleSolver. Terms
and variables that are
7316 eliminated during pre-processing are
not visible to the congruence closure.
7321 """Return a proof for the last `check()`. Proof construction must be enabled."""
7325 """Return an AST vector containing all added constraints.
7339 """Return an AST vector containing all currently inferred units.
7344 """Return an AST vector containing all atomic formulas in solver state that are not units.
7349 """Return trail and decision levels of the solver state after a check() call.
7351 trail = self.trail()
7352 levels = (ctypes.c_uint * len(trail))()
7354 return trail, levels
7357 """Return trail of the solver state after a check() call.
7362 """Return statistics for the last `check()`.
7369 >>> st = s.statistics()
7370 >>> st.get_key_value(
'final checks')
7380 """Return a string describing why the last `check()` returned `unknown`.
7384 >>> s.add(2**x == 4)
7387 >>> s.reason_unknown()
7388 '(incomplete (theory arithmetic))'
7393 """Display a string describing all available options."""
7397 """Return the parameter description set."""
7401 """Return a formatted string with all added constraints."""
7402 return obj_to_string(self)
7405 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7410 >>> s2 = s1.translate(c2)
7413 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
7415 return Solver(solver, target)
7424 """Return a formatted string (in Lisp-like format) with all added constraints.
7425 We say the string is in s-expression format.
7436 """Return a textual representation of the solver in DIMACS format."""
7440 """return SMTLIB2 formatted benchmark for solver's assertions"""
7447 for i
in range(sz1):
7448 v[i] = es[i].as_ast()
7450 e = es[sz1].as_ast()
7454 self.
ctx.ref(),
"benchmark generated from python API",
"",
"unknown",
"", sz1, v, e,
7459 """Create a solver customized for the given logic.
7461 The parameter `logic` is a string. It should be contains
7462 the name of a SMT-LIB logic.
7463 See http://www.smtlib.org/
for the name of all available logics.
7480 """Return a simple general purpose solver with limited amount of preprocessing.
7499 """Fixedpoint API provides methods for solving with recursive predicates"""
7502 assert fixedpoint
is None or ctx
is not None
7505 if fixedpoint
is None:
7516 if self.
fixedpoint is not None and self.
ctx.ref()
is not None and Z3_fixedpoint_dec_ref
is not None:
7520 """Set a configuration option. The method `help()` return a string containing all available options.
7526 """Display a string describing all available options."""
7530 """Return the parameter description set."""
7534 """Assert constraints as background axioms for the fixedpoint solver."""
7538 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7548 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7556 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7560 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7564 """Assert rules defining recursive predicates to the fixedpoint solver.
7568 >>> s.register_relation(a.decl())
7569 >>> s.register_relation(b.decl())
7586 def rule(self, head, body=None, name=None):
7587 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7591 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7595 """Query the fixedpoint engine whether formula is derivable.
7596 You can also pass an tuple
or list of recursive predicates.
7600 if sz >= 1
and isinstance(query[0], FuncDeclRef):
7601 _decls = (FuncDecl * sz)()
7611 query =
And(query, self.
ctx)
7612 query = self.
abstract(query,
False)
7617 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7621 if sz >= 1
and isinstance(query[0], FuncDecl):
7628 query = self.
abstract(query,
False)
7629 r = Z3_fixedpoint_query_from_lvl(self.
ctx.ref(), self.
fixedpoint, query.as_ast(), lvl)
7642 """Retrieve answer from last query call."""
7647 """Retrieve a ground cex from last query call."""
7648 r = Z3_fixedpoint_get_ground_sat_answer(self.
ctx.ref(), self.
fixedpoint)
7652 """retrieve rules along the counterexample trace"""
7656 """retrieve rule names along the counterexample trace"""
7661 return names.split(
";")
7664 """Retrieve number of levels used for predicate in PDR engine"""
7668 """Retrieve properties known about predicate for the level'th unfolding.
7669 -1 is treated
as the limit (infinity)
7675 """Add property to predicate for the level'th unfolding.
7676 -1 is treated
as infinity (infinity)
7681 """Register relation as recursive"""
7687 """Control how relation is represented"""
7688 representations =
_get_args(representations)
7689 representations = [
to_symbol(s)
for s
in representations]
7690 sz = len(representations)
7691 args = (Symbol * sz)()
7693 args[i] = representations[i]
7697 """Parse rules and queries from a string"""
7701 """Parse rules and queries from a file"""
7705 """retrieve rules that have been added to fixedpoint context"""
7709 """retrieve assertions that have been added to fixedpoint context"""
7713 """Return a formatted string with all added rules and constraints."""
7717 """Return a formatted string (in Lisp-like format) with all added constraints.
7718 We say the string is in s-expression format.
7723 """Return a formatted string (in Lisp-like format) with all added constraints.
7724 We say the string is in s-expression format.
7725 Include also queries.
7731 """Return statistics for the last `query()`.
7736 """Return a string describing why the last `query()` returned `unknown`.
7741 """Add variable or several variables.
7742 The added variable or variables will be bound
in the rules
7765 """Finite domain sort."""
7768 """Return the size of the finite domain sort"""
7769 r = (ctypes.c_ulonglong * 1)()
7773 raise Z3Exception(
"Failed to retrieve finite domain sort size")
7777 """Create a named finite domain sort of a given size sz"""
7778 if not isinstance(name, Symbol):
7785 """Return True if `s` is a Z3 finite-domain sort.
7792 return isinstance(s, FiniteDomainSortRef)
7796 """Finite-domain expressions."""
7799 """Return the sort of the finite-domain expression `self`."""
7803 """Return a Z3 floating point expression as a Python string."""
7808 """Return `True` if `a` is a Z3 finite-domain expression.
7811 >>> b =
Const(
'b', s)
7817 return isinstance(a, FiniteDomainRef)
7821 """Integer values."""
7824 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7836 """Return a Z3 finite-domain numeral as a Python string.
7847 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7862 """Return `True` if `a` is a Z3 finite-domain value.
7865 >>> b =
Const(
'b', s)
7919 (fn, mdl) = _on_models[ctx]
7923_on_model_eh = on_model_eh_type(_global_on_model)
7927 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
7939 if self.
optimize is not None and self.
ctx.ref()
is not None and Z3_optimize_dec_ref
is not None:
7945 """Set a configuration option.
7946 The method `help()` return a string containing all available options.
7952 """Display a string describing all available options."""
7956 """Return the parameter description set."""
7960 """Assert constraints as background axioms for the optimize solver."""
7964 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7972 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
7980 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7982 If `p` is a string, it will be automatically converted into a Boolean constant.
7987 >>> s.assert_and_track(x > 0,
'p1')
7988 >>> s.assert_and_track(x != 1,
'p2')
7989 >>> s.assert_and_track(x < 0, p3)
7990 >>> print(s.check())
7992 >>> c = s.unsat_core()
8002 if isinstance(p, str):
8004 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
8009 """Add soft constraint with optional weight and optional identifier.
8010 If no weight is supplied, then the penalty
for violating the soft constraint
8012 Soft constraints are grouped by identifiers. Soft constraints that are
8013 added without identifiers are grouped by default.
8016 weight =
"%d" % weight
8017 elif isinstance(weight, float):
8018 weight =
"%f" % weight
8019 if not isinstance(weight, str):
8020 raise Z3Exception(
"weight should be a string or an integer")
8028 if sys.version_info.major >= 3
and isinstance(arg, Iterable):
8029 return [asoft(a)
for a
in arg]
8033 """Add objective function to maximize."""
8041 """Add objective function to minimize."""
8049 """create a backtracking point for added rules, facts and assertions"""
8053 """restore to previously created backtracking point"""
8057 """Check consistency and produce optimal values."""
8059 num = len(assumptions)
8060 _assumptions = (Ast * num)()
8061 for i
in range(num):
8062 _assumptions[i] = assumptions[i].as_ast()
8066 """Return a string that describes why the last `check()` returned `unknown`."""
8070 """Return a model for the last check()."""
8074 raise Z3Exception(
"model is not available")
8080 if not isinstance(obj, OptimizeObjective):
8081 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8085 if not isinstance(obj, OptimizeObjective):
8086 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8090 if not isinstance(obj, OptimizeObjective):
8091 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8092 return obj.lower_values()
8095 if not isinstance(obj, OptimizeObjective):
8096 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8097 return obj.upper_values()
8100 """Parse assertions and objectives from a file"""
8104 """Parse assertions and objectives from a string"""
8108 """Return an AST vector containing all added constraints."""
8112 """returns set of objective functions"""
8116 """Return a formatted string with all added rules and constraints."""
8120 """Return a formatted string (in Lisp-like format) with all added constraints.
8121 We say the string is in s-expression format.
8126 """Return statistics for the last check`.
8131 """Register a callback that is invoked with every incremental improvement to
8132 objective values. The callback takes a model as argument.
8133 The life-time of the model
is limited to the callback so the
8134 model has to be (deep) copied
if it
is to be used after the callback
8136 id = len(_on_models) + 41
8138 _on_models[id] = (on_model, mdl)
8141 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8151 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8152 It also contains model and proof converters.
8164 if self.
ctx.ref()
is not None and Z3_apply_result_dec_ref
is not None:
8168 """Return the number of subgoals in `self`.
8170 >>> a, b = Ints('a b')
8172 >>> g.add(
Or(a == 0, a == 1),
Or(b == 0, b == 1), a > b)
8173 >>> t =
Tactic(
'split-clause')
8187 """Return one of the subgoals stored in ApplyResult object `self`.
8189 >>> a, b = Ints('a b')
8191 >>> g.add(
Or(a == 0, a == 1),
Or(b == 0, b == 1), a > b)
8192 >>> t =
Tactic(
'split-clause')
8195 [a == 0,
Or(b == 0, b == 1), a > b]
8197 [a == 1,
Or(b == 0, b == 1), a > b]
8199 if idx >= len(self):
8204 return obj_to_string(self)
8207 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8211 """Return a Z3 expression consisting of all subgoals.
8216 >>> g.add(
Or(x == 2, x == 3))
8217 >>> r =
Tactic(
'simplify')(g)
8219 [[
Not(x <= 1),
Or(x == 2, x == 3)]]
8221 And(
Not(x <= 1),
Or(x == 2, x == 3))
8222 >>> r =
Tactic(
'split-clause')(g)
8224 [[x > 1, x == 2], [x > 1, x == 3]]
8226 Or(
And(x > 1, x == 2),
And(x > 1, x == 3))
8234 return Or([self[i].
as_expr()
for i
in range(len(self))])
8243 """Simplifiers act as pre-processing utilities for solvers.
8244 Build a custom simplifier and add it to a solver
"""
8249 if isinstance(simplifier, SimplifierObj):
8251 elif isinstance(simplifier, list):
8252 simps = [
Simplifier(s, ctx)
for s
in simplifier]
8254 for i
in range(1, len(simps)):
8260 _z3_assert(isinstance(simplifier, str),
"simplifier name expected")
8264 raise Z3Exception(
"unknown simplifier '%s'" % simplifier)
8271 if self.
simplifier is not None and self.
ctx.ref()
is not None and Z3_simplifier_dec_ref
is not None:
8275 """Return a simplifier that uses the given configuration options"""
8280 """Return a solver that applies the simplification pre-processing specified by the simplifier"""
8284 """Display a string containing a description of the available options for the `self` simplifier."""
8288 """Return the parameter description set."""
8300 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8301 A Tactic can be converted into a Solver using the method solver().
8303 Several combinators are available for creating new tactics using the built-
in ones:
8310 if isinstance(tactic, TacticObj):
8314 _z3_assert(isinstance(tactic, str),
"tactic name expected")
8318 raise Z3Exception(
"unknown tactic '%s'" % tactic)
8325 if self.
tactic is not None and self.
ctx.ref()
is not None and Z3_tactic_dec_ref
is not None:
8329 """Create a solver using the tactic `self`.
8331 The solver supports the methods `push()` and `pop()`, but it
8332 will always solve each `check()`
from scratch.
8334 >>> t =
Then(
'simplify',
'nlsat')
8337 >>> s.add(x**2 == 2, x > 0)
8345 def apply(self, goal, *arguments, **keywords):
8346 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8348 >>> x, y = Ints('x y')
8349 >>> t =
Tactic(
'solve-eqs')
8350 >>> t.apply(
And(x == 0, y >= x + 1))
8354 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expressions expected")
8356 if len(arguments) > 0
or len(keywords) > 0:
8363 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8365 >>> x, y = Ints('x y')
8366 >>> t =
Tactic(
'solve-eqs')
8367 >>> t(
And(x == 0, y >= x + 1))
8370 return self.
apply(goal, *arguments, **keywords)
8373 """Display a string containing a description of the available options for the `self` tactic."""
8377 """Return the parameter description set."""
8382 if isinstance(a, BoolRef):
8383 goal =
Goal(ctx=a.ctx)
8391 if isinstance(t, Tactic):
8401 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8409 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8414 """Return a tactic that applies the tactics in `*ts` in sequence.
8416 >>> x, y = Ints('x y')
8418 >>> t(
And(x == 0, y > x + 1))
8420 >>> t(
And(x == 0, y > x + 1)).as_expr()
8424 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8425 ctx = ks.get(
"ctx",
None)
8428 for i
in range(num - 1):
8434 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8436 >>> x, y = Ints('x y')
8438 >>> t(
And(x == 0, y > x + 1))
8440 >>> t(
And(x == 0, y > x + 1)).as_expr()
8447 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8454 >>> t(
Or(x == 0, x == 1))
8455 [[x == 0], [x == 1]]
8458 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8459 ctx = ks.get(
"ctx",
None)
8462 for i
in range(num - 1):
8468 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8476 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8477 ctx =
_get_ctx(ks.get(
"ctx",
None))
8480 _args = (TacticObj * sz)()
8482 _args[i] = ts[i].tactic
8487 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8488 The subgoals are processed in parallel.
8490 >>> x, y =
Ints(
'x y')
8492 >>> t(
And(
Or(x == 1, x == 2), y == x + 1))
8493 [[x == 1, y == 2], [x == 2, y == 3]]
8498 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8503 """Alias for ParThen(t1, t2, ctx)."""
8508 """Return a tactic that applies tactic `t` using the given configuration options.
8510 >>> x, y = Ints('x y')
8512 >>> t((x + 1)*(y + 2) == 0)
8513 [[2*x + y + x*y == -2]]
8515 ctx = keys.pop("ctx",
None)
8522 """Return a tactic that applies tactic `t` using the given configuration options.
8524 >>> x, y = Ints('x y')
8526 >>> p.set(
"som",
True)
8528 >>> t((x + 1)*(y + 2) == 0)
8529 [[2*x + y + x*y == -2]]
8536 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8537 or the maximum number of iterations `max`
is reached.
8539 >>> x, y =
Ints(
'x y')
8540 >>> c =
And(
Or(x == 0, x == 1),
Or(y == 0, y == 1), x > y)
8543 >>>
for subgoal
in r: print(subgoal)
8544 [x == 0, y == 0, x > y]
8545 [x == 0, y == 1, x > y]
8546 [x == 1, y == 0, x > y]
8547 [x == 1, y == 1, x > y]
8557 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8559 If `t` does not terminate
in `ms` milliseconds, then it fails.
8566 """Return a list of all available tactics in Z3.
8569 >>> l.count('simplify') == 1
8577 """Return a short description for the tactic named `name`.
8586 """Display a (tabular) description of all available tactics in Z3."""
8589 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8592 print(
'<tr style="background-color:#CFCFCF">')
8597 print(
"<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(
tactic_description(t), 40)))
8605 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8606 to decide which solver and/
or preprocessing step will be used.
8612 if isinstance(probe, ProbeObj):
8614 elif isinstance(probe, float):
8618 elif isinstance(probe, bool):
8625 _z3_assert(isinstance(probe, str),
"probe name expected")
8629 raise Z3Exception(
"unknown probe '%s'" % probe)
8636 if self.
probe is not None and self.
ctx.ref()
is not None and Z3_probe_dec_ref
is not None:
8640 """Return a probe that evaluates to "true" when the value returned by `self`
8641 is less than the value returned by `other`.
8643 >>> p =
Probe(
'size') < 10
8654 """Return a probe that evaluates to "true" when the value returned by `self`
8655 is greater than the value returned by `other`.
8657 >>> p =
Probe(
'size') > 10
8668 """Return a probe that evaluates to "true" when the value returned by `self`
8669 is less than
or equal to the value returned by `other`.
8671 >>> p =
Probe(
'size') <= 2
8682 """Return a probe that evaluates to "true" when the value returned by `self`
8683 is greater than
or equal to the value returned by `other`.
8685 >>> p =
Probe(
'size') >= 2
8696 """Return a probe that evaluates to "true" when the value returned by `self`
8697 is equal to the value returned by `other`.
8699 >>> p =
Probe(
'size') == 2
8710 """Return a probe that evaluates to "true" when the value returned by `self`
8711 is not equal to the value returned by `other`.
8713 >>> p =
Probe(
'size') != 2
8725 """Evaluate the probe `self` in the given goal.
8727 >>> p = Probe('size')
8737 >>> p =
Probe(
'num-consts')
8740 >>> p =
Probe(
'is-propositional')
8743 >>> p =
Probe(
'is-qflia')
8748 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expression expected")
8754 """Return `True` if `p` is a Z3 probe.
8761 return isinstance(p, Probe)
8768 return Probe(p, ctx)
8772 """Return a list of all available probes in Z3.
8775 >>> l.count('memory') == 1
8783 """Return a short description for the probe named `name`.
8792 """Display a (tabular) description of all available probes in Z3."""
8795 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8798 print(
'<tr style="background-color:#CFCFCF">')
8803 print(
"<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(
probe_description(p), 40)))
8812 _z3_assert(len(args) > 0,
"At least one argument expected")
8815 for i
in range(num - 1):
8816 r =
Probe(f(ctx.ref(), r.probe,
_to_probe(args[i + 1], ctx).probe), ctx)
8829 """Return a tactic that fails if the probe `p` evaluates to true.
8830 Otherwise, it returns the input goal unmodified.
8832 In the following example, the tactic applies 'simplify' if and only
if there are
8833 more than 2 constraints
in the goal.
8836 >>> x, y =
Ints(
'x y')
8842 >>> g.add(x == y + 1)
8844 [[
Not(x <= 0),
Not(y <= 0), x == 1 + y]]
8851 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8852 Otherwise, it returns the input goal unmodified.
8855 >>> x, y =
Ints(
'x y')
8861 >>> g.add(x == y + 1)
8863 [[
Not(x <= 0),
Not(y <= 0), x == 1 + y]]
8871 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8888 """Simplify the expression `a` using the given options.
8890 This function has many options. Use `help_simplify` to obtain the complete list.
8896 >>>
simplify((x + 1)*(y + 1), som=
True)
8905 if len(arguments) > 0
or len(keywords) > 0:
8913 """Return a string describing all options available for Z3 `simplify` procedure."""
8918 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
8923 """Apply substitution m on t, m is a list of pairs of the form (from, to).
8924 Every occurrence in t of
from is replaced
with to.
8934 if isinstance(m, tuple):
8936 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8941 all([isinstance(p, tuple)
and is_expr(p[0])
and is_expr(p[1])
for p
in m]),
8942 "Z3 invalid substitution, expression pairs expected.")
8944 all([p[0].sort().
eq(p[1].sort())
for p
in m]),
8945 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
8947 _from = (Ast * num)()
8949 for i
in range(num):
8950 _from[i] = m[i][0].as_ast()
8951 _to[i] = m[i][1].as_ast()
8956 """Substitute the free variables in t with the expression in m.
8968 _z3_assert(all([
is_expr(n)
for n
in m]),
"Z3 invalid substitution, list of expressions expected.")
8971 for i
in range(num):
8972 _to[i] = m[i].as_ast()
8976 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
8977 Every occurrence in to of the function
from is replaced
with the expression to.
8978 The expression to can have free variables, that refer to the arguments of
from.
8981 if isinstance(m, tuple):
8983 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8987 _z3_assert(all([isinstance(p, tuple)
and is_func_decl(p[0])
and is_expr(p[1])
for p
in m]),
"Z3 invalid substitution, funcion pairs expected.")
8989 _from = (FuncDecl * num)()
8991 for i
in range(num):
8992 _from[i] = m[i][0].as_func_decl()
8993 _to[i] = m[i][1].as_ast()
8998 """Create the sum of the Z3 expressions.
9000 >>> a, b, c = Ints('a b c')
9007 a__0 + a__1 + a__2 + a__3 + a__4
9014 return _reduce(
lambda a, b: a + b, args, 0)
9017 return _reduce(
lambda a, b: a + b, args, 0)
9024 """Create the product of the Z3 expressions.
9026 >>> a, b, c = Ints('a b c')
9033 a__0*a__1*a__2*a__3*a__4
9040 return _reduce(
lambda a, b: a * b, args, 1)
9043 return _reduce(
lambda a, b: a * b, args, 1)
9049 """Create the absolute value of an arithmetic expression"""
9050 return If(arg > 0, arg, -arg)
9054 """Create an at-most Pseudo-Boolean k constraint.
9056 >>> a, b, c = Bools('a b c')
9057 >>> f =
AtMost(a, b, c, 2)
9061 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
9064 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9072 """Create an at-most Pseudo-Boolean k constraint.
9074 >>> a, b, c = Bools('a b c')
9079 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
9082 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9099 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9101 args, coeffs = zip(*args)
9103 _z3_assert(len(args) > 0,
"Non empty list of arguments expected")
9106 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9109 _coeffs = (ctypes.c_int * len(coeffs))()
9110 for i
in range(len(coeffs)):
9112 _coeffs[i] = coeffs[i]
9113 return ctx, sz, _args, _coeffs, args
9117 """Create a Pseudo-Boolean inequality k constraint.
9119 >>> a, b, c = Bools('a b c')
9120 >>> f =
PbLe(((a,1),(b,3),(c,2)), 3)
9128 """Create a Pseudo-Boolean inequality k constraint.
9130 >>> a, b, c = Bools('a b c')
9131 >>> f =
PbGe(((a,1),(b,3),(c,2)), 3)
9139 """Create a Pseudo-Boolean equality k constraint.
9141 >>> a, b, c = Bools('a b c')
9142 >>> f =
PbEq(((a,1),(b,3),(c,2)), 3)
9150 """Solve the constraints `*args`.
9152 This is a simple function
for creating demonstrations. It creates a solver,
9153 configure it using the options
in `keywords`, adds the constraints
9154 in `args`,
and invokes check.
9157 >>>
solve(a > 0, a < 2)
9160 show = keywords.pop("show",
False)
9168 print(
"no solution")
9170 print(
"failed to solve")
9180 """Solve the constraints `*args` using solver `s`.
9182 This is a simple function
for creating demonstrations. It
is similar to `solve`,
9183 but it uses the given solver `s`.
9184 It configures solver `s` using the options
in `keywords`, adds the constraints
9185 in `args`,
and invokes check.
9187 show = keywords.pop("show",
False)
9189 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9197 print(
"no solution")
9199 print(
"failed to solve")
9210def prove(claim, show=False, **keywords):
9211 """Try to prove the given claim.
9213 This is a simple function
for creating demonstrations. It tries to prove
9214 `claim` by showing the negation
is unsatisfiable.
9216 >>> p, q =
Bools(
'p q')
9231 print(
"failed to prove")
9234 print(
"counterexample")
9239 """Version of function `solve` that renders HTML output."""
9240 show = keywords.pop(
"show",
False)
9245 print(
"<b>Problem:</b>")
9249 print(
"<b>no solution</b>")
9251 print(
"<b>failed to solve</b>")
9258 print(
"<b>Solution:</b>")
9263 """Version of function `solve_using` that renders HTML."""
9264 show = keywords.pop(
"show",
False)
9266 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9270 print(
"<b>Problem:</b>")
9274 print(
"<b>no solution</b>")
9276 print(
"<b>failed to solve</b>")
9283 print(
"<b>Solution:</b>")
9288 """Version of function `prove` that renders HTML."""
9298 print(
"<b>proved</b>")
9300 print(
"<b>failed to prove</b>")
9303 print(
"<b>counterexample</b>")
9309 _names = (Symbol * sz)()
9310 _sorts = (Sort * sz)()
9315 _z3_assert(isinstance(k, str),
"String expected")
9320 return sz, _names, _sorts
9325 _names = (Symbol * sz)()
9326 _decls = (FuncDecl * sz)()
9331 _z3_assert(isinstance(k, str),
"String expected")
9335 _decls[i] = v.decl().ast
9339 return sz, _names, _decls
9348 if self.
ctx.ref()
is not None and self.
pctx is not None and Z3_parser_context_dec_ref
is not None:
9362 """Parse a string in SMT 2.0 format using the given sorts and decls.
9364 The arguments sorts and decls are Python dictionaries used to initialize
9365 the symbol table used
for the SMT 2.0 parser.
9367 >>>
parse_smt2_string(
'(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9369 >>> x, y =
Ints(
'x y')
9371 >>>
parse_smt2_string(
'(assert (> (+ foo (g bar)) 0))', decls={
'foo' : x,
'bar' : y,
'g' : f})
9383 """Parse a file in SMT 2.0 format using the given sorts and decls.
9401_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9402_dflt_fpsort_ebits = 11
9403_dflt_fpsort_sbits = 53
9407 """Retrieves the global default rounding mode."""
9408 global _dflt_rounding_mode
9409 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9411 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9413 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9415 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9417 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9421_ROUNDING_MODES = frozenset({
9422 Z3_OP_FPA_RM_TOWARD_ZERO,
9423 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9424 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9425 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9426 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9431 global _dflt_rounding_mode
9433 _dflt_rounding_mode = rm.decl().kind()
9435 _z3_assert(_dflt_rounding_mode
in _ROUNDING_MODES,
"illegal rounding mode")
9436 _dflt_rounding_mode = rm
9440 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9444 global _dflt_fpsort_ebits
9445 global _dflt_fpsort_sbits
9446 _dflt_fpsort_ebits = ebits
9447 _dflt_fpsort_sbits = sbits
9459 first_fp_sort =
None
9462 if first_fp_sort
is None:
9463 first_fp_sort = a.sort()
9464 elif first_fp_sort == a.sort():
9469 first_fp_sort =
None
9473 for i
in range(len(alist)):
9475 is_repr = isinstance(a, str)
and a.contains(
"2**(")
and a.endswith(
")")
9476 if is_repr
or _is_int(a)
or isinstance(a, (float, bool)):
9477 r.append(
FPVal(a,
None, first_fp_sort, ctx))
9486 """Floating-point sort."""
9489 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9497 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9505 """Try to cast `val` as a floating-point expression.
9509 >>> b.cast(1.0).sexpr()
9510 '(fp #b0 #x7f #b00000000000000000000000)'
9521 """Floating-point 16-bit (half) sort."""
9527 """Floating-point 16-bit (half) sort."""
9533 """Floating-point 32-bit (single) sort."""
9539 """Floating-point 32-bit (single) sort."""
9545 """Floating-point 64-bit (double) sort."""
9551 """Floating-point 64-bit (double) sort."""
9557 """Floating-point 128-bit (quadruple) sort."""
9563 """Floating-point 128-bit (quadruple) sort."""
9569 """"Floating-point rounding mode sort."""
9573 """Return True if `s` is a Z3 floating-point sort.
9580 return isinstance(s, FPSortRef)
9584 """Return True if `s` is a Z3 floating-point rounding mode sort.
9591 return isinstance(s, FPRMSortRef)
9597 """Floating-point expressions."""
9600 """Return the sort of the floating-point expression `self`.
9605 >>> x.sort() ==
FPSort(8, 24)
9611 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9619 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9627 """Return a Z3 floating point expression as a Python string."""
9643 """Create the Z3 expression `self + other`.
9656 """Create the Z3 expression `other + self`.
9666 """Create the Z3 expression `self - other`.
9679 """Create the Z3 expression `other - self`.
9689 """Create the Z3 expression `self * other`.
9704 """Create the Z3 expression `other * self`.
9717 """Create the Z3 expression `+self`."""
9721 """Create the Z3 expression `-self`.
9730 """Create the Z3 expression `self / other`.
9745 """Create the Z3 expression `other / self`.
9758 """Create the Z3 expression division `self / other`."""
9762 """Create the Z3 expression division `other / self`."""
9766 """Create the Z3 expression mod `self % other`."""
9767 return fpRem(self, other)
9770 """Create the Z3 expression mod `other % self`."""
9771 return fpRem(other, self)
9775 """Floating-point rounding mode expressions"""
9778 """Return a Z3 floating point expression as a Python string."""
9833 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9842 return isinstance(a, FPRMRef)
9846 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9853 """The sign of the numeral.
9864 num = (ctypes.c_int)()
9867 raise Z3Exception(
"error retrieving the sign of a numeral.")
9868 return num.value != 0
9870 """The sign of a floating-point numeral as a bit-vector expression.
9872 Remark: NaN's are invalid arguments.
9878 """The significand of the numeral.
9888 """The significand of the numeral as a long.
9891 >>> x.significand_as_long()
9896 ptr = (ctypes.c_ulonglong * 1)()
9898 raise Z3Exception(
"error retrieving the significand of a numeral.")
9901 """The significand of the numeral as a bit-vector expression.
9903 Remark: NaN are invalid arguments.
9909 """The exponent of the numeral.
9919 """The exponent of the numeral as a long.
9922 >>> x.exponent_as_long()
9927 ptr = (ctypes.c_longlong * 1)()
9929 raise Z3Exception(
"error retrieving the exponent of a numeral.")
9932 """The exponent of the numeral as a bit-vector expression.
9934 Remark: NaNs are invalid arguments.
9940 """Indicates whether the numeral is a NaN."""
9945 """Indicates whether the numeral is +oo or -oo."""
9950 """Indicates whether the numeral is +zero or -zero."""
9955 """Indicates whether the numeral is normal."""
9960 """Indicates whether the numeral is subnormal."""
9965 """Indicates whether the numeral is positive."""
9970 """Indicates whether the numeral is negative."""
9976 The string representation of the numeral.
9985 return (
"FPVal(%s, %s)" % (s, self.
sortsort()))
9989 """Return `True` if `a` is a Z3 floating-point expression.
9999 return isinstance(a, FPRef)
10003 """Return `True` if `a` is a Z3 floating-point numeral value.
10018 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
10020 >>> Single = FPSort(8, 24)
10021 >>> Double = FPSort(11, 53)
10024 >>> x = Const('x', Single)
10033 if isinstance(val, float):
10034 if math.isnan(val):
10037 sone = math.copysign(1.0, val)
10042 elif val == float(
"+inf"):
10044 elif val == float(
"-inf"):
10047 v = val.as_integer_ratio()
10050 rvs = str(num) +
"/" + str(den)
10052 elif isinstance(val, bool):
10059 elif isinstance(val, str):
10060 inx = val.find(
"*(2**")
10063 elif val[-1] ==
")":
10065 exp = str(int(val[inx + 5:-1]) + int(exp))
10067 _z3_assert(
False,
"String does not have floating-point numeral form.")
10069 _z3_assert(
False,
"Python value cannot be used to create floating-point numerals.")
10073 return res +
"p" + exp
10077 """Create a Z3 floating-point NaN term.
10080 >>> set_fpa_pretty(True)
10083 >>> pb = get_fpa_pretty()
10084 >>> set_fpa_pretty(
False)
10087 >>> set_fpa_pretty(pb)
10089 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10094 """Create a Z3 floating-point +oo term.
10097 >>> pb = get_fpa_pretty()
10098 >>> set_fpa_pretty(True)
10101 >>> set_fpa_pretty(
False)
10104 >>> set_fpa_pretty(pb)
10106 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10111 """Create a Z3 floating-point -oo term."""
10112 _z3_assert(isinstance(s, FPSortRef),
"sort mismatch")
10117 """Create a Z3 floating-point +oo or -oo term."""
10118 _z3_assert(isinstance(s, FPSortRef),
"sort mismatch")
10119 _z3_assert(isinstance(negative, bool),
"expected Boolean flag")
10124 """Create a Z3 floating-point +0.0 term."""
10125 _z3_assert(isinstance(s, FPSortRef),
"sort mismatch")
10130 """Create a Z3 floating-point -0.0 term."""
10131 _z3_assert(isinstance(s, FPSortRef),
"sort mismatch")
10136 """Create a Z3 floating-point +0.0 or -0.0 term."""
10137 _z3_assert(isinstance(s, FPSortRef),
"sort mismatch")
10138 _z3_assert(isinstance(negative, bool),
"expected Boolean flag")
10142def FPVal(sig, exp=None, fps=None, ctx=None):
10143 """Return a floating-point value of value `val` and sort `fps`.
10144 If `ctx=None`, then the
global context
is used.
10149 >>> print(
"0x%.8x" % v.exponent_as_long(
False))
10174 if val ==
"NaN" or val ==
"nan":
10176 elif val ==
"-0.0":
10178 elif val ==
"0.0" or val ==
"+0.0":
10180 elif val ==
"+oo" or val ==
"+inf" or val ==
"+Inf":
10182 elif val ==
"-oo" or val ==
"-inf" or val ==
"-Inf":
10188def FP(name, fpsort, ctx=None):
10189 """Return a floating-point constant named `name`.
10190 `fpsort` is the floating-point sort.
10191 If `ctx=
None`, then the
global context
is used.
10200 >>> word =
FPSort(8, 24)
10201 >>> x2 =
FP(
'x', word)
10205 if isinstance(fpsort, FPSortRef)
and ctx
is None:
10213 """Return an array of floating-point constants.
10215 >>> x, y, z = FPs('x y z',
FPSort(8, 24))
10226 if isinstance(names, str):
10227 names = names.split(
" ")
10228 return [
FP(name, fpsort, ctx)
for name
in names]
10232 """Create a Z3 floating-point absolute value expression.
10236 >>> x = FPVal(1.0, s)
10239 >>> y = FPVal(-20.0, s)
10243 fpAbs(-1.25*(2**4))
10244 >>> fpAbs(-1.25*(2**4))
10245 fpAbs(-1.25*(2**4))
10246 >>> fpAbs(x).sort()
10255 """Create a Z3 floating-point addition expression.
10262 >>>
fpNeg(x).sort()
10274 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10275 _z3_assert(
is_fp(a),
"Second argument must be a Z3 floating-point expression")
10276 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10283 _z3_assert(
is_fp(a),
"First argument must be a Z3 floating-point expression")
10284 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10291 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10292 _z3_assert(
is_fp(a)
or is_fp(b),
"Second or third argument must be a Z3 floating-point expression")
10293 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10300 _z3_assert(
is_fp(a)
or is_fp(b),
"First or second argument must be a Z3 floating-point expression")
10301 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10308 _z3_assert(
is_fp(a)
or is_fp(b),
"First or second argument must be a Z3 floating-point expression")
10309 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10316 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10318 c),
"Second, third or fourth argument must be a Z3 floating-point expression")
10319 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10323 """Create a Z3 floating-point addition expression.
10329 >>>
fpAdd(rm, x, y)
10333 >>>
fpAdd(rm, x, y).sort()
10336 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10340 """Create a Z3 floating-point subtraction expression.
10346 >>>
fpSub(rm, x, y)
10348 >>>
fpSub(rm, x, y).sort()
10351 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10355 """Create a Z3 floating-point multiplication expression.
10361 >>>
fpMul(rm, x, y)
10363 >>>
fpMul(rm, x, y).sort()
10366 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10370 """Create a Z3 floating-point division expression.
10376 >>>
fpDiv(rm, x, y)
10378 >>>
fpDiv(rm, x, y).sort()
10381 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10385 """Create a Z3 floating-point remainder expression.
10392 >>>
fpRem(x, y).sort()
10399 """Create a Z3 floating-point minimum expression.
10407 >>>
fpMin(x, y).sort()
10414 """Create a Z3 floating-point maximum expression.
10422 >>>
fpMax(x, y).sort()
10429 """Create a Z3 floating-point fused multiply-add expression.
10431 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10435 """Create a Z3 floating-point square root expression.
10441 """Create a Z3 floating-point roundToIntegral expression.
10443 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10447 """Create a Z3 floating-point isNaN expression.
10459 """Create a Z3 floating-point isInfinite expression.
10470 """Create a Z3 floating-point isZero expression.
10476 """Create a Z3 floating-point isNormal expression.
10482 """Create a Z3 floating-point isSubnormal expression.
10488 """Create a Z3 floating-point isNegative expression.
10494 """Create a Z3 floating-point isPositive expression.
10501 _z3_assert(
is_fp(a)
or is_fp(b),
"First or second argument must be a Z3 floating-point expression")
10505 """Create the Z3 floating-point expression `other < self`.
10510 >>> (x < y).sexpr()
10517 """Create the Z3 floating-point expression `other <= self`.
10522 >>> (x <= y).sexpr()
10529 """Create the Z3 floating-point expression `other > self`.
10534 >>> (x > y).sexpr()
10541 """Create the Z3 floating-point expression `other >= self`.
10546 >>> (x >= y).sexpr()
10553 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10558 >>>
fpEQ(x, y).sexpr()
10565 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10570 >>> (x != y).sexpr()
10577 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10582 fpFP(1, 127, 4194304)
10583 >>> xv = FPVal(-1.5, s)
10587 >>> slvr.add(fpEQ(x, xv))
10590 >>> xv = FPVal(+1.5, s)
10594 >>> slvr.add(fpEQ(x, xv))
10599 _z3_assert(sgn.sort().size() == 1,
"sort mismatch")
10601 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx,
"context mismatch")
10606 """Create a Z3 floating-point conversion expression from other term sorts
10609 From a bit-vector term in IEEE 754-2008 format:
10615 From a floating-point term
with different precision:
10626 From a signed bit-vector term:
10641 raise Z3Exception(
"Unsupported combination of arguments for conversion to floating-point term.")
10645 """Create a Z3 floating-point conversion expression that represents the
10646 conversion from a bit-vector term to a floating-point term.
10655 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10662 """Create a Z3 floating-point conversion expression that represents the
10663 conversion from a floating-point term to a floating-point term of different precision.
10674 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10675 _z3_assert(
is_fp(v),
"Second argument must be a Z3 floating-point expression.")
10682 """Create a Z3 floating-point conversion expression that represents the
10683 conversion from a real term to a floating-point term.
10692 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10693 _z3_assert(
is_real(v),
"Second argument must be a Z3 expression or real sort.")
10700 """Create a Z3 floating-point conversion expression that represents the
10701 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10710 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10711 _z3_assert(
is_bv(v),
"Second argument must be a Z3 bit-vector expression")
10718 """Create a Z3 floating-point conversion expression that represents the
10719 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10728 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10729 _z3_assert(
is_bv(v),
"Second argument must be a Z3 bit-vector expression")
10736 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10738 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10739 _z3_assert(
is_bv(x),
"Second argument must be a Z3 bit-vector expression")
10746 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10750 >>> print(
is_fp(x))
10752 >>> print(
is_bv(y))
10754 >>> print(
is_fp(y))
10756 >>> print(
is_bv(x))
10760 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10761 _z3_assert(
is_fp(x),
"Second argument must be a Z3 floating-point expression")
10768 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10772 >>> print(
is_fp(x))
10774 >>> print(
is_bv(y))
10776 >>> print(
is_fp(y))
10778 >>> print(
is_bv(x))
10782 _z3_assert(
is_fprm(rm),
"First argument must be a Z3 floating-point rounding mode expression")
10783 _z3_assert(
is_fp(x),
"Second argument must be a Z3 floating-point expression")
10790 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10794 >>> print(
is_fp(x))
10798 >>> print(
is_fp(y))
10804 _z3_assert(
is_fp(x),
"First argument must be a Z3 floating-point expression")
10810 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10812 The size of the resulting bit-vector is automatically determined.
10814 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10815 knows only one NaN
and it will always produce the same bit-vector representation of
10820 >>> print(
is_fp(x))
10822 >>> print(
is_bv(y))
10824 >>> print(
is_fp(y))
10826 >>> print(
is_bv(x))
10830 _z3_assert(
is_fp(x),
"First argument must be a Z3 floating-point expression")
10842 """Sequence sort."""
10845 """Determine if sort is a string
10859 """Character sort."""
10863 """Create a string sort
10872 """Create a character sort
10882 """Create a sequence sort over elements provided in the argument
10891 """Sequence expression."""
10897 return Concat(self, other)
10900 return Concat(other, self)
10919 """Return a string representation of sequence expression."""
10921 string_length = ctypes.c_uint()
10923 return string_at(chars, size=string_length.value).decode(
"latin-1")
10940 if isinstance(ch, str):
10944 raise Z3Exception(
"Character expression expected")
10948 """Character expression."""
10966 if isinstance(ch, str):
10968 if not isinstance(ch, int):
10969 raise Z3Exception(
"character value should be an ordinal")
10974 raise Z3Exception(
"Bit-vector expression needed")
10987 return ch.is_digit()
10990 if isinstance(s, str):
10994 raise Z3Exception(
"Non-expression passed as a sequence")
10996 raise Z3Exception(
"Non-sequence passed as a sequence")
11011 """Return `True` if `a` is a Z3 sequence expression.
11017 return isinstance(a, SeqRef)
11021 """Return `True` if `a` is a Z3 string expression.
11025 return isinstance(a, SeqRef)
and a.is_string()
11029 """return 'True' if 'a' is a Z3 string constant expression.
11035 return isinstance(a, SeqRef)
and a.is_string_value()
11038 """create a string expression"""
11039 s =
"".join(str(ch)
if 32 <= ord(ch)
and ord(ch) < 127
else "\\u{%x}" % (ord(ch))
for ch
in s)
11045 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
11054 """Return a tuple of String constants. """
11056 if isinstance(names, str):
11057 names = names.split(
" ")
11058 return [
String(name, ctx)
for name
in names]
11062 """Extract substring or subsequence starting at offset"""
11063 return Extract(s, offset, length)
11067 """Extract substring or subsequence starting at offset"""
11068 return Extract(s, offset, length)
11072 """Create the empty sequence of the given sort
11075 >>> print(e.eq(e2))
11084 if isinstance(s, SeqSortRef):
11086 if isinstance(s, ReSortRef):
11088 raise Z3Exception(
"Non-sequence, non-regular expression sort passed to Empty")
11092 """Create the regular expression that accepts the universal language
11100 if isinstance(s, ReSortRef):
11102 raise Z3Exception(
"Non-sequence, non-regular expression sort passed to Full")
11107 """Create a singleton sequence"""
11112 """Check if 'a' is a prefix of 'b'
11127 """Check if 'a' is a suffix of 'b'
11142 """Check if 'a' contains 'b'
11149 >>> x, y, z =
Strings(
'x y z')
11161 """Replace the first occurrence of 'src' by 'dst' in 's'
11162 >>> r = Replace("aaa",
"a",
"b")
11167 if ctx
is None and is_expr(src):
11176 """Retrieve the index of substring within a string starting at a specified offset.
11191 offset =
IntVal(offset, ctx)
11196 """Retrieve the last index of substring within a string"""
11205 """Obtain the length of a sequence 's'
11215 """Convert string expression to integer
11231 """Convert integer expression to string"""
11238 """Convert a unit length string to integer code"""
11244 """Convert code to a string"""
11250 """The regular expression that accepts sequence 's'
11262 """Regular expression sort."""
11271 if s
is None or isinstance(s, Context):
11274 raise Z3Exception(
"Regular expression sort constructor expects either a string or a context or no argument")
11278 """Regular expressions."""
11281 return Union(self, other)
11285 return isinstance(s, ReRef)
11289 """Create regular expression membership test
11303 """Create union of regular expressions.
11311 _z3_assert(sz > 0,
"At least one argument expected.")
11312 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
11317 for i
in range(sz):
11318 v[i] = args[i].as_ast()
11323 """Create intersection of regular expressions.
11329 _z3_assert(sz > 0,
"At least one argument expected.")
11330 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
11335 for i
in range(sz):
11336 v[i] = args[i].as_ast()
11341 """Create the regular expression accepting one or more repetitions of argument.
11356 """Create the regular expression that optionally accepts the argument.
11371 """Create the complement regular expression."""
11376 """Create the regular expression accepting zero or more repetitions of argument.
11391 """Create the regular expression accepting between a lower and upper bound repetitions
11392 >>> re = Loop(Re("a"), 1, 3)
11406 """Create the range regular expression over two sequences of length 1
11407 >>> range = Range("a",
"z")
11421 """Create the difference regular expression
11429 """Create a regular expression that accepts all single character strings
11453 """Given a binary relation R, such that the two arguments have the same sort
11454 create the transitive closure relation R+.
11455 The transitive closure R+ is a new relation.
11461 super(ctypes.c_void_p, ast).__init__(ptr)
11465 ctx = ContextObj(ptr)
11466 super(ctypes.c_void_p, ctx).__init__(ptr)
11470 v = AstVectorObj(ptr)
11471 super(ctypes.c_void_p, v).__init__(ptr)
11479_my_hacky_class =
None
11481 onc = _my_hacky_class
11484 deps = [dep[i]
for i
in range(n)]
11485 onc.on_clause(p, deps, clause)
11487_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11495 global _my_hacky_class
11496 _my_hacky_class = self
11506 if self.
lock is None:
11508 self.
lock = threading.Lock()
11513 r = self.
bases[ctx]
11515 r = self.
bases[ctx]
11521 self.
bases[ctx] = r
11523 self.
bases[ctx] = r
11528 id = len(self.
bases) + 3
11531 id = len(self.
bases) + 3
11536_prop_closures =
None
11540 global _prop_closures
11541 if _prop_closures
is None:
11546 prop = _prop_closures.get(ctx)
11552 prop = _prop_closures.get(ctx)
11554 prop.pop(num_scopes)
11558 _prop_closures.set_threaded()
11559 prop = _prop_closures.get(ctx)
11566 new_prop = prop.fresh(nctx)
11567 _prop_closures.set(new_prop.id, new_prop)
11572 prop = _prop_closures.get(ctx)
11576 prop.fixed(id, value)
11580 prop = _prop_closures.get(ctx)
11587 prop = _prop_closures.get(ctx)
11593 prop = _prop_closures.get(ctx)
11601 prop = _prop_closures.get(ctx)
11609 prop = _prop_closures.get(ctx)
11612 prop.decide(t, idx, phase)
11616_user_prop_push = Z3_push_eh(user_prop_push)
11617_user_prop_pop = Z3_pop_eh(user_prop_pop)
11618_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11619_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11620_user_prop_created = Z3_created_eh(user_prop_created)
11621_user_prop_final = Z3_final_eh(user_prop_final)
11622_user_prop_eq = Z3_eq_eh(user_prop_eq)
11623_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11624_user_prop_decide = Z3_decide_eh(user_prop_decide)
11628 """Create a function that gets tracked by user propagator.
11629 Every term headed by this function symbol is tracked.
11630 If a term
is fixed
and the fixed callback
is registered a
11631 callback
is invoked that the term headed by this function
is fixed.
11635 _z3_assert(len(sig) > 0,
"At least two arguments expected")
11636 arity = len(sig) - 1
11640 dom = (Sort * arity)()
11641 for i
in range(arity):
11644 dom[i] = sig[i].ast
11660 assert s
is None or ctx
is None
11666 self.
id = _prop_closures.insert(self)
11677 ctypes.c_void_p(self.
id),
11684 self.
_ctx.ctx =
None
11693 return self.
ctx().ref()
11696 assert not self.
fixed
11697 assert not self.
_ctx
11704 assert not self.
_ctx
11710 assert not self.
final
11711 assert not self.
_ctx
11718 assert not self.
_ctx
11724 assert not self.
diseq
11725 assert not self.
_ctx
11732 assert not self.
_ctx
11738 raise Z3Exception(
"push needs to be overwritten")
11741 raise Z3Exception(
"pop needs to be overwritten")
11744 raise Z3Exception(
"fresh needs to be overwritten")
11747 assert not self.
_ctx
11770 self.
cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
approx(self, precision=10)
__deepcopy__(self, memo={})
__init__(self, result, ctx)
__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)
significand_as_long(self)
exponent_as_long(self, biased=True)
exponent_as_bv(self, biased=True)
exponent(self, biased=True)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
get_rule_names_along_trace(self)
fact(self, head, name=None)
update_rule(self, head, body, name)
get_ground_sat_answer(self)
register_relation(self, *relations)
get_cover_delta(self, level, predicate)
set_predicate_representation(self, f, *representations)
assert_exprs(self, *args)
get_rules_along_trace(self)
abstract(self, fml, is_forall=True)
get_num_levels(self, predicate)
__init__(self, fixedpoint=None, ctx=None)
rule(self, head, body=None, name=None)
add_cover(self, level, predicate, property)
query_from_lvl(self, lvl, *query)
add_rule(self, head, body=None, name=None)
__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)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__init__(self, s, on_clause)
__deepcopy__(self, memo={})
assert_and_track(self, a, p)
assert_exprs(self, *args)
set_on_model(self, on_model)
from_file(self, filename)
add_soft(self, arg, weight="1", id=None)
check(self, *assumptions)
__init__(self, opt, value, is_max)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
__deepcopy__(self, memo={})
__init__(self, probe, ctx=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__deepcopy__(self, memo={})
__init__(self, simplifier, ctx=None)
using_params(self, *args, **keys)
__deepcopy__(self, memo={})
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
dimacs(self, include_names=True)
from_file(self, filename)
check(self, *assumptions)
__exit__(self, *exc_info)
consequences(self, assumptions, variables)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
__deepcopy__(self, memo={})
__call__(self, goal, *arguments, **keywords)
__init__(self, tactic, ctx=None)
solver(self, logFile=None)
apply(self, goal, *arguments, **keywords)
propagate(self, e, ids, eqs=[])
conflict(self, deps=[], eqs=[])
add_created(self, created)
__init__(self, s, ctx=None)
next_split(self, t, idx, phase)
Z3_ast Z3_API Z3_mk_pbeq(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
Z3_ast_vector Z3_API Z3_optimize_get_assertions(Z3_context c, Z3_optimize o)
Return the set of asserted formulas on the optimization context.
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_simplifier Z3_API Z3_simplifier_and_then(Z3_context c, Z3_simplifier t1, Z3_simplifier t2)
Return a simplifier that applies t1 to a given goal and t2 to every subgoal produced by t1.
Z3_probe Z3_API Z3_probe_lt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than the value returned...
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_char_to_bv(Z3_context c, Z3_ast ch)
Create a bit-vector (code point) from character.
void Z3_API Z3_solver_propagate_diseq(Z3_context c, Z3_solver s, Z3_eq_eh eq_eh)
register a callback on expression dis-equalities.
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.
void Z3_API Z3_fixedpoint_inc_ref(Z3_context c, Z3_fixedpoint d)
Increment the reference counter of the given fixedpoint context.
Z3_tactic Z3_API Z3_tactic_using_params(Z3_context c, Z3_tactic t, Z3_params p)
Return a tactic that applies t using the given set of parameters.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
void Z3_API Z3_simplifier_inc_ref(Z3_context c, Z3_simplifier t)
Increment the reference counter of the given simplifier.
void Z3_API Z3_fixedpoint_add_rule(Z3_context c, Z3_fixedpoint d, Z3_ast rule, Z3_symbol name)
Add a universal Horn clause as a named rule. The horn_rule should be of the form:
Z3_probe Z3_API Z3_probe_eq(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is equal to the value returned ...
Z3_ast_vector Z3_API Z3_optimize_get_unsat_core(Z3_context c, Z3_optimize o)
Retrieve the unsat core for the last Z3_optimize_check The unsat core is a subset of the assumptions ...
void Z3_API Z3_fixedpoint_set_predicate_representation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f, unsigned num_relations, Z3_symbol const relation_kinds[])
Configure the predicate representation.
Z3_sort Z3_API Z3_mk_char_sort(Z3_context c)
Create a sort for unicode characters.
Z3_ast Z3_API Z3_mk_re_option(Z3_context c, Z3_ast re)
Create the regular language [re].
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_ast Z3_API Z3_substitute(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const from[], Z3_ast const to[])
Substitute every occurrence of from[i] in a with to[i], for i smaller than num_exprs....
Z3_ast Z3_API Z3_mk_mul(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] * ... * args[num_args-1].
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_mk_fpa_to_fp_bv(Z3_context c, Z3_ast bv, Z3_sort s)
Conversion of a single IEEE 754-2008 bit-vector into a floating-point number.
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_ast Z3_API Z3_mk_seq_replace(Z3_context c, Z3_ast s, Z3_ast src, Z3_ast dst)
Replace the first occurrence of src with dst in s.
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_ast Z3_API Z3_mk_str_le(Z3_context c, Z3_ast prefix, Z3_ast s)
Check if s1 is equal or lexicographically strictly less than s2.
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_simplify(Z3_context c, Z3_ast a)
Interface to simplifier.
Z3_ast Z3_API Z3_mk_fpa_to_ieee_bv(Z3_context c, Z3_ast t)
Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
Z3_lbool Z3_API Z3_solver_get_consequences(Z3_context c, Z3_solver s, Z3_ast_vector assumptions, Z3_ast_vector variables, Z3_ast_vector consequences)
retrieve consequences from solver that determine values of the supplied function symbols.
Z3_ast_vector Z3_API Z3_fixedpoint_from_file(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 file with fixedpoint rules. Add the rules to the current fixedpoint context....
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.
Z3_ast Z3_API Z3_mk_char_le(Z3_context c, Z3_ast ch1, Z3_ast ch2)
Create less than or equal to between two characters.
Z3_ast Z3_API Z3_mk_fpa_to_fp_signed(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a 2's complement signed bit-vector term into a term of FloatingPoint sort.
Z3_ast_vector Z3_API Z3_optimize_get_upper_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
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_param_descrs Z3_API Z3_solver_get_param_descrs(Z3_context c, Z3_solver s)
Return the parameter description set for the given solver object.
Z3_ast Z3_API Z3_mk_fpa_to_sbv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz)
Conversion of a floating-point term into a signed bit-vector.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_optimize_get_lower(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective.
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_model Z3_API Z3_optimize_get_model(Z3_context c, Z3_optimize o)
Retrieve the model for the last Z3_optimize_check.
void Z3_API Z3_apply_result_inc_ref(Z3_context c, Z3_apply_result r)
Increment the reference counter of the given Z3_apply_result object.
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.
void Z3_API Z3_parser_context_add_decl(Z3_context c, Z3_parser_context pc, Z3_func_decl f)
Add a function declaration.
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_param_descrs Z3_API Z3_fixedpoint_get_param_descrs(Z3_context c, Z3_fixedpoint f)
Return the parameter description set for the given fixedpoint object.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_string_from_code(Z3_context c, Z3_ast a)
Code to string conversion.
void Z3_API Z3_optimize_from_file(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 file with assertions, soft constraints and optimization objectives....
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.
Z3_string Z3_API Z3_simplifier_get_help(Z3_context c, Z3_simplifier t)
Return a string containing a description of parameters accepted by the given simplifier.
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.
Z3_tactic Z3_API Z3_tactic_par_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and then t2 to every subgoal produced by t1....
void Z3_API Z3_fixedpoint_update_rule(Z3_context c, Z3_fixedpoint d, Z3_ast a, Z3_symbol name)
Update a named rule. A rule with the same name must have been previously created.
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_seq_length(Z3_context c, Z3_ast s)
Return the length of the sequence s.
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_ast Z3_API Z3_simplify_ex(Z3_context c, Z3_ast a, Z3_params p)
Interface to simplifier.
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_sort Z3_API Z3_get_seq_sort_basis(Z3_context c, Z3_sort s)
Retrieve basis sort for sequence sort.
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.
bool Z3_API Z3_fpa_get_numeral_sign(Z3_context c, Z3_ast t, int *sgn)
Retrieves the sign of a floating-point literal.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_probe Z3_API Z3_probe_ge(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than or equal to the...
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_simplifier_dec_ref(Z3_context c, Z3_simplifier g)
Decrement the reference counter of the given simplifier.
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
Z3_ast Z3_API Z3_mk_str_to_int(Z3_context c, Z3_ast s)
Convert string to integer.
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_mk_re_allchar(Z3_context c, Z3_sort regex_sort)
Create a regular expression that accepts all singleton sequences of the regular expression sort.
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_ast_vector Z3_API Z3_fixedpoint_from_string(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 string with fixedpoint rules. Add the rules to the current fixedpoint context....
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
void Z3_API Z3_optimize_pop(Z3_context c, Z3_optimize d)
Backtrack one level.
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_fpa_to_ubv(Z3_context c, Z3_ast rm, Z3_ast t, unsigned sz)
Conversion of a floating-point term into an unsigned bit-vector.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_ast Z3_API Z3_mk_seq_at(Z3_context c, Z3_ast s, Z3_ast index)
Retrieve from s the unit sequence positioned at position index. The sequence is empty if the index is...
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_ast Z3_API Z3_mk_re_complement(Z3_context c, Z3_ast re)
Create the complement of the regular language re.
Z3_sort Z3_API Z3_mk_fpa_sort_half(Z3_context c)
Create the half-precision (16-bit) FloatingPoint sort.
Z3_ast_vector Z3_API Z3_fixedpoint_get_assertions(Z3_context c, Z3_fixedpoint f)
Retrieve set of background assertions from fixedpoint context.
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....
unsigned Z3_API Z3_fpa_get_ebits(Z3_context c, Z3_sort s)
Retrieves the number of bits reserved for the exponent in a FloatingPoint sort.
Z3_ast_vector Z3_API Z3_solver_get_assertions(Z3_context c, Z3_solver s)
Return the set of asserted formulas on the solver.
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_solver Z3_API Z3_mk_solver_from_tactic(Z3_context c, Z3_tactic t)
Create a new solver that is implemented using the given tactic. The solver supports the commands Z3_s...
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.
Z3_string Z3_API Z3_simplify_get_help(Z3_context c)
Return a string describing all available parameters.
unsigned Z3_API Z3_get_num_probes(Z3_context c)
Return the number of builtin probes available in Z3.
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.
bool Z3_API Z3_fpa_is_numeral_positive(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is positive.
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_char_ptr Z3_API Z3_get_lstring(Z3_context c, Z3_ast s, unsigned *length)
Retrieve the string constant stored in s. The string can contain escape sequences....
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.
void Z3_API Z3_solver_interrupt(Z3_context c, Z3_solver s)
Solver local interrupt. Normally you should use Z3_interrupt to cancel solvers because only one solve...
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
bool Z3_API Z3_fpa_get_numeral_exponent_int64(Z3_context c, Z3_ast t, int64_t *n, bool biased)
Return the exponent value of a floating-point numeral as a signed 64-bit integer.
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.
bool Z3_API Z3_solver_propagate_consequence(Z3_context c, Z3_solver_callback cb, unsigned num_fixed, Z3_ast const *fixed, unsigned num_eqs, Z3_ast const *eq_lhs, Z3_ast const *eq_rhs, Z3_ast conseq)
propagate a consequence based on fixed values and equalities. A client may invoke it during the pro...
bool Z3_API Z3_fpa_is_numeral_nan(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is a NaN.
unsigned Z3_API Z3_fpa_get_sbits(Z3_context c, Z3_sort s)
Retrieves the number of bits reserved for the significand in a FloatingPoint sort.
Z3_ast_vector Z3_API Z3_optimize_get_lower_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective. The returned vector ...
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.
void Z3_API Z3_parser_context_dec_ref(Z3_context c, Z3_parser_context pc)
Decrement the reference counter of the given Z3_parser_context object.
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_param_descrs Z3_API Z3_tactic_get_param_descrs(Z3_context c, Z3_tactic t)
Return the parameter description set for the given tactic object.
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.
Z3_ast Z3_API Z3_mk_fpa_round_toward_negative(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardNegative rounding mode.
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.
void Z3_API Z3_optimize_assert_and_track(Z3_context c, Z3_optimize o, Z3_ast a, Z3_ast t)
Assert tracked hard constraint to the optimization context.
unsigned Z3_API Z3_optimize_assert_soft(Z3_context c, Z3_optimize o, Z3_ast a, Z3_string weight, Z3_symbol id)
Assert soft constraint to the optimization context.
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_fpa_to_fp_real(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a term of real sort into a term of FloatingPoint sort.
Z3_ast_vector Z3_API Z3_solver_get_trail(Z3_context c, Z3_solver s)
Return the trail modulo model conversion, in order of decision level The decision level can be retrie...
bool Z3_API Z3_fpa_get_numeral_significand_uint64(Z3_context c, Z3_ast t, uint64_t *n)
Return the significand value of a floating-point numeral as a uint64.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
Z3_func_decl Z3_API Z3_mk_tree_order(Z3_context c, Z3_sort a, unsigned id)
create a tree ordering relation over signature a identified using index id.
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).
Z3_ast Z3_API Z3_solver_congruence_next(Z3_context c, Z3_solver s, Z3_ast a)
retrieve the next expression in the congruence class. The set of congruent siblings form a cyclic lis...
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_solver Z3_API Z3_mk_solver_for_logic(Z3_context c, Z3_symbol logic)
Create a new solver customized for the given logic. It behaves like Z3_mk_solver if the logic is unkn...
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.
unsigned Z3_API Z3_apply_result_get_num_subgoals(Z3_context c, Z3_apply_result r)
Return the number of subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
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,...
Z3_ast Z3_API Z3_mk_seq_unit(Z3_context c, Z3_ast a)
Create a unit sequence of a.
Z3_ast Z3_API Z3_mk_re_intersect(Z3_context c, unsigned n, Z3_ast const args[])
Create the intersection of the regular languages.
Z3_ast_vector Z3_API Z3_solver_cube(Z3_context c, Z3_solver s, Z3_ast_vector vars, unsigned backtrack_level)
extract a next cube for a solver. The last cube is the constant true or false. The number of (non-con...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
Z3_func_decl Z3_API Z3_solver_propagate_declare(Z3_context c, Z3_symbol name, unsigned n, Z3_sort *domain, Z3_sort range)
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.
bool Z3_API Z3_is_string_sort(Z3_context c, Z3_sort s)
Check if s is a string sort.
Z3_string Z3_API Z3_fpa_get_numeral_exponent_string(Z3_context c, Z3_ast t, bool biased)
Return the exponent value of a floating-point numeral as a string.
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.
Z3_ast Z3_API Z3_mk_pbge(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
Z3_param_descrs Z3_API Z3_optimize_get_param_descrs(Z3_context c, Z3_optimize o)
Return the parameter description set for the given optimize object.
Z3_sort Z3_API Z3_mk_re_sort(Z3_context c, Z3_sort seq)
Create a regular expression sort out of a sequence sort.
Z3_ast Z3_API Z3_mk_pble(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
void Z3_API Z3_optimize_inc_ref(Z3_context c, Z3_optimize d)
Increment the reference counter of the given optimize context.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
Z3_ast Z3_API Z3_mk_fpa_inf(Z3_context c, Z3_sort s, bool negative)
Create a floating-point infinity of sort s.
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.
Z3_func_decl Z3_API Z3_mk_piecewise_linear_order(Z3_context c, Z3_sort a, unsigned id)
create a piecewise linear ordering relation over signature a and index id.
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_tactic Z3_API Z3_tactic_par_or(Z3_context c, unsigned num, Z3_tactic const ts[])
Return a tactic that applies the given tactics in parallel.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
Z3_ast Z3_API Z3_mk_fpa_nan(Z3_context c, Z3_sort s)
Create a floating-point NaN of sort s.
bool Z3_API Z3_fpa_is_numeral_subnormal(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is subnormal.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
Z3_ast Z3_API Z3_optimize_get_upper(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
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_simplifier Z3_API Z3_simplifier_using_params(Z3_context c, Z3_simplifier t, Z3_params p)
Return a simplifier that applies t using the given set of parameters.
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.
void Z3_API Z3_solver_import_model_converter(Z3_context ctx, Z3_solver src, Z3_solver dst)
Ad-hoc method for importing model conversion from solver.
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_re_union(Z3_context c, unsigned n, Z3_ast const args[])
Create the union of the regular languages.
Z3_param_descrs Z3_API Z3_simplifier_get_param_descrs(Z3_context c, Z3_simplifier t)
Return the parameter description set for the given simplifier object.
void Z3_API Z3_optimize_set_params(Z3_context c, Z3_optimize o, Z3_params p)
Set parameters on optimization context.
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_ast Z3_API Z3_mk_fpa_round_toward_positive(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardPositive rounding mode.
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_seq_empty(Z3_context c, Z3_sort seq)
Create an empty sequence of the sequence sort seq.
Z3_probe Z3_API Z3_mk_probe(Z3_context c, Z3_string name)
Return a probe associated with the given name. The complete list of probes may be obtained using the ...
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_tactic Z3_API Z3_tactic_when(Z3_context c, Z3_probe p, Z3_tactic t)
Return a tactic that applies t to a given goal is the probe p evaluates to true. If p evaluates to fa...
Z3_ast Z3_API Z3_mk_seq_suffix(Z3_context c, Z3_ast suffix, Z3_ast s)
Check if suffix is a suffix of s.
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...
Z3_sort Z3_API Z3_get_re_sort_basis(Z3_context c, Z3_sort s)
Retrieve basis sort for regex sort.
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
Z3_solver Z3_API Z3_solver_translate(Z3_context source, Z3_solver s, Z3_context target)
Copy a solver s from the context source to the context target.
void Z3_API Z3_optimize_push(Z3_context c, Z3_optimize d)
Create a backtracking point.
Z3_string Z3_API Z3_solver_get_help(Z3_context c, Z3_solver s)
Return a string describing all solver available parameters.
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.
void Z3_API Z3_probe_inc_ref(Z3_context c, Z3_probe p)
Increment the reference counter of the given probe.
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,...
void Z3_API Z3_solver_propagate_register_cb(Z3_context c, Z3_solver_callback cb, Z3_ast e)
register an expression to propagate on with the solver. Only expressions of type Bool and type Bit-Ve...
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_string Z3_API Z3_get_probe_name(Z3_context c, unsigned i)
Return the name of the i probe.
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.
Z3_sort Z3_API Z3_mk_fpa_sort_16(Z3_context c)
Create the half-precision (16-bit) FloatingPoint sort.
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.
void Z3_API Z3_fixedpoint_dec_ref(Z3_context c, Z3_fixedpoint d)
Decrement the reference counter of the given fixedpoint context.
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_ast Z3_API Z3_mk_str_lt(Z3_context c, Z3_ast prefix, Z3_ast s)
Check if s1 is lexicographically strictly less than s2.
Z3_ast Z3_API Z3_solver_congruence_root(Z3_context c, Z3_solver s, Z3_ast a)
retrieve the congruence closure root of an expression. The root is retrieved relative to the state wh...
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_string Z3_API Z3_tactic_get_help(Z3_context c, Z3_tactic t)
Return a string containing a description of parameters accepted by the given tactic.
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.
void Z3_API Z3_solver_propagate_final(Z3_context c, Z3_solver s, Z3_final_eh final_eh)
register a callback on final check. This provides freedom to the propagator to delay actions or imple...
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_ast_vector Z3_API Z3_parse_smtlib2_string(Z3_context c, Z3_string str, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort const sorts[], unsigned num_decls, Z3_symbol const decl_names[], Z3_func_decl const decls[])
Parse the given string using the SMT-LIB2 parser.
void Z3_API Z3_solver_register_on_clause(Z3_context c, Z3_solver s, void *user_context, Z3_on_clause_eh on_clause_eh)
register a callback to that retrieves assumed, inferred and deleted clauses during search.
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.
Z3_lbool Z3_API Z3_fixedpoint_query(Z3_context c, Z3_fixedpoint d, Z3_ast query)
Pose a query against the asserted rules.
unsigned Z3_API Z3_get_num_tactics(Z3_context c)
Return the number of builtin tactics available in Z3.
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_simplifier Z3_API Z3_mk_simplifier(Z3_context c, Z3_string name)
Return a simplifier associated with the given name. The complete list of simplifiers may be obtained ...
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.
bool Z3_API Z3_fpa_is_numeral_negative(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is negative.
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_vector Z3_API Z3_solver_get_non_units(Z3_context c, Z3_solver s)
Return the set of non units in the solver state.
Z3_ast Z3_API Z3_mk_seq_to_re(Z3_context c, Z3_ast seq)
Create a regular expression that accepts the sequence seq.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast_vector Z3_API Z3_optimize_get_objectives(Z3_context c, Z3_optimize o)
Return objectives on the optimization context. If the objective function is a max-sat objective it is...
bool Z3_API Z3_get_finite_domain_sort_size(Z3_context c, Z3_sort s, uint64_t *r)
Store the size of the sort in r. Return false if the call failed. That is, Z3_get_sort_kind(s) == Z3_...
Z3_ast Z3_API Z3_mk_seq_index(Z3_context c, Z3_ast s, Z3_ast substr, Z3_ast offset)
Return index of the first occurrence of substr in s starting from offset offset. If s does not contai...
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.
Z3_ast Z3_API Z3_mk_re_range(Z3_context c, Z3_ast lo, Z3_ast hi)
Create the range regular expression over two sequences of length 1.
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_vector Z3_API Z3_fixedpoint_get_rules(Z3_context c, Z3_fixedpoint f)
Retrieve set of rules from fixedpoint context.
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.
Z3_ast Z3_API Z3_fpa_get_numeral_significand_bv(Z3_context c, Z3_ast t)
Retrieves the significand of a floating-point literal as a bit-vector expression.
Z3_tactic Z3_API Z3_tactic_fail_if(Z3_context c, Z3_probe p)
Return a tactic that fails if the probe p evaluates to false.
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.
Z3_sort Z3_API Z3_mk_fpa_sort_quadruple(Z3_context c)
Create the quadruple-precision (128-bit) FloatingPoint sort.
void Z3_API Z3_probe_dec_ref(Z3_context c, Z3_probe p)
Decrement the reference counter of the given probe.
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_ast Z3_API Z3_mk_seq_prefix(Z3_context c, Z3_ast prefix, Z3_ast s)
Check if prefix is a prefix of s.
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_fixedpoint Z3_API Z3_mk_fixedpoint(Z3_context c)
Create a new fixedpoint context.
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_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_away(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToAway rounding mode.
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
void Z3_API Z3_solver_propagate_init(Z3_context c, Z3_solver s, void *user_context, Z3_push_eh push_eh, Z3_pop_eh pop_eh, Z3_fresh_eh fresh_eh)
register a user-propagator with the solver.
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.
void Z3_API Z3_tactic_dec_ref(Z3_context c, Z3_tactic g)
Decrement the reference counter of the given tactic.
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_solver Z3_API Z3_mk_simple_solver(Z3_context c)
Create a new incremental solver.
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.
void Z3_API Z3_optimize_assert(Z3_context c, Z3_optimize o, Z3_ast a)
Assert hard constraint to the optimization context.
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.
Z3_string Z3_API Z3_benchmark_to_smtlib_string(Z3_context c, Z3_string name, Z3_string logic, Z3_string status, Z3_string attributes, unsigned num_assumptions, Z3_ast const assumptions[], Z3_ast formula)
Convert the given benchmark into SMT-LIB formatted string.
Z3_ast Z3_API Z3_mk_re_star(Z3_context c, Z3_ast re)
Create the regular language re*.
Z3_ast Z3_API Z3_mk_char(Z3_context c, unsigned ch)
Create a character literal.
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.
Z3_string Z3_API Z3_optimize_to_string(Z3_context c, Z3_optimize o)
Print the current context as a string.
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_ast Z3_API Z3_mk_re_full(Z3_context c, Z3_sort re)
Create an universal regular expression of sort re.
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_re_diff(Z3_context c, Z3_ast re1, Z3_ast re2)
Create the difference of regular expressions.
unsigned Z3_API Z3_fixedpoint_get_num_levels(Z3_context c, Z3_fixedpoint d, Z3_func_decl pred)
Query the PDR engine for the maximal levels properties are known about predicate.
Z3_ast Z3_API Z3_mk_fpa_to_real(Z3_context c, Z3_ast t)
Conversion of a floating-point term into a real-numbered term.
Z3_ast Z3_API Z3_mk_re_empty(Z3_context c, Z3_sort re)
Create an empty regular expression of sort re.
void Z3_API Z3_solver_from_string(Z3_context c, Z3_solver s, Z3_string file_name)
load solver assertions from a string.
Z3_sort Z3_API Z3_mk_fpa_sort_128(Z3_context c)
Create the quadruple-precision (128-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_param_descrs Z3_API Z3_simplify_get_param_descrs(Z3_context c)
Return the parameter description set for the simplify procedure.
Z3_sort Z3_API Z3_mk_finite_domain_sort(Z3_context c, Z3_symbol name, uint64_t size)
Create a named finite domain sort.
Z3_ast Z3_API Z3_mk_add(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] + ... + args[num_args-1].
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast_vector Z3_API Z3_parse_smtlib2_file(Z3_context c, Z3_string file_name, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort const sorts[], unsigned num_decls, Z3_symbol const decl_names[], Z3_func_decl const decls[])
Similar to Z3_parse_smtlib2_string, but reads the benchmark from a file.
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_tactic Z3_API Z3_tactic_cond(Z3_context c, Z3_probe p, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal if the probe p evaluates to true, and t2 if p evaluat...
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
Z3_string Z3_API Z3_fixedpoint_to_string(Z3_context c, Z3_fixedpoint f, unsigned num_queries, Z3_ast queries[])
Print the current rules and background axioms as a string.
void Z3_API Z3_solver_get_levels(Z3_context c, Z3_solver s, Z3_ast_vector literals, unsigned sz, unsigned levels[])
retrieve the decision depth of Boolean literals (variables or their negations). Assumes a check-sat c...
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_fixedpoint_get_cover_delta(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred)
Z3_ast Z3_API Z3_mk_fpa_to_fp_unsigned(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a 2's complement unsigned bit-vector term into a term of FloatingPoint sort.
Z3_apply_result Z3_API Z3_tactic_apply_ex(Z3_context c, Z3_tactic t, Z3_goal g, Z3_params p)
Apply tactic t to the goal g using the parameter set p.
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.
Z3_tactic Z3_API Z3_mk_tactic(Z3_context c, Z3_string name)
Return a tactic associated with the given name. The complete list of tactics may be obtained using th...
Z3_ast Z3_API Z3_mk_fpa_abs(Z3_context c, Z3_ast t)
Floating-point absolute value.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
Z3_optimize Z3_API Z3_mk_optimize(Z3_context c)
Create a new optimize context.
void Z3_API Z3_parser_context_add_sort(Z3_context c, Z3_parser_context pc, Z3_sort s)
Add a sort declaration.
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_substitute_funs(Z3_context c, Z3_ast a, unsigned num_funs, Z3_func_decl const from[], Z3_ast const to[])
Substitute functions in from with new expressions in to.
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.
Z3_ast Z3_API Z3_mk_atleast(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
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_parser_context_inc_ref(Z3_context c, Z3_parser_context pc)
Increment the reference counter of the given Z3_parser_context object.
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_solver_get_unsat_core(Z3_context c, Z3_solver s)
Retrieve the unsat core for the last Z3_solver_check_assumptions The unsat core is a subset of the as...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
void Z3_API Z3_optimize_dec_ref(Z3_context c, Z3_optimize d)
Decrement the reference counter of the given optimize context.
Z3_ast Z3_API Z3_mk_fpa_fp(Z3_context c, Z3_ast sgn, Z3_ast exp, Z3_ast sig)
Create an expression of FloatingPoint sort from three bit-vector expressions.
Z3_func_decl Z3_API Z3_mk_partial_order(Z3_context c, Z3_sort a, unsigned id)
create a partial ordering relation over signature a and index id.
Z3_ast Z3_API Z3_fpa_get_numeral_exponent_bv(Z3_context c, Z3_ast t, bool biased)
Retrieves the exponent of a floating-point literal as a bit-vector expression.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_sort Z3_API Z3_mk_fpa_sort_single(Z3_context c)
Create the single-precision (32-bit) FloatingPoint sort.
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_string Z3_API Z3_get_tactic_name(Z3_context c, unsigned i)
Return the name of the idx tactic.
bool Z3_API Z3_is_string(Z3_context c, Z3_ast s)
Determine if s is a string constant.
Z3_ast Z3_API Z3_mk_re_loop(Z3_context c, Z3_ast r, unsigned lo, unsigned hi)
Create a regular expression loop. The supplied regular expression r is repeated between lo and hi tim...
Z3_ast Z3_API Z3_mk_char_to_int(Z3_context c, Z3_ast ch)
Create an integer (code point) from character.
Z3_ast Z3_API Z3_mk_fpa_neg(Z3_context c, Z3_ast t)
Floating-point negation.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_string Z3_API Z3_tactic_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the tactic with the given name.
Z3_ast Z3_API Z3_mk_re_plus(Z3_context c, Z3_ast re)
Create the regular language re+.
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_string Z3_API Z3_optimize_get_help(Z3_context c, Z3_optimize t)
Return a string containing a description of parameters accepted by optimize.
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.
Z3_sort Z3_API Z3_mk_fpa_sort_32(Z3_context c)
Create the single-precision (32-bit) FloatingPoint sort.
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_stats Z3_API Z3_optimize_get_statistics(Z3_context c, Z3_optimize d)
Retrieve statistics information from the last call to Z3_optimize_check.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_probe Z3_API Z3_probe_gt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than the value retur...
Z3_sort Z3_API Z3_mk_fpa_sort_64(Z3_context c)
Create the double-precision (64-bit) FloatingPoint sort.
Z3_ast Z3_API Z3_solver_get_proof(Z3_context c, Z3_solver s)
Retrieve the proof for the last Z3_solver_check or Z3_solver_check_assumptions.
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.
unsigned Z3_API Z3_optimize_minimize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a minimization constraint.
Z3_stats Z3_API Z3_fixedpoint_get_statistics(Z3_context c, Z3_fixedpoint d)
Retrieve statistics information from the last call to Z3_fixedpoint_query.
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.
void Z3_API Z3_tactic_inc_ref(Z3_context c, Z3_tactic t)
Increment the reference counter of the given tactic.
Z3_parser_context Z3_API Z3_mk_parser_context(Z3_context c)
Create a parser context.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
void Z3_API Z3_solver_from_file(Z3_context c, Z3_solver s, Z3_string file_name)
load solver assertions from a file.
Z3_ast Z3_API Z3_mk_seq_last_index(Z3_context c, Z3_ast s, Z3_ast substr)
Return index of the last occurrence of substr in s. If s does not contain substr, then the value is -...
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
void Z3_API Z3_solver_propagate_eq(Z3_context c, Z3_solver s, Z3_eq_eh eq_eh)
register a callback on expression equalities.
Z3_ast Z3_API Z3_mk_string(Z3_context c, Z3_string s)
Create a string constant out of the string that is passed in The string may contain escape encoding f...
Z3_func_decl Z3_API Z3_mk_transitive_closure(Z3_context c, Z3_func_decl f)
create transitive closure of binary relation.
Z3_tactic Z3_API Z3_tactic_try_for(Z3_context c, Z3_tactic t, unsigned ms)
Return a tactic that applies t to a given goal for ms milliseconds. If t does not terminate in ms mil...
void Z3_API Z3_apply_result_dec_ref(Z3_context c, Z3_apply_result r)
Decrement the reference counter of the given Z3_apply_result object.
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_sort Z3_API Z3_mk_seq_sort(Z3_context c, Z3_sort s)
Create a sequence sort out of the sort for the elements.
unsigned Z3_API Z3_optimize_maximize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a maximization constraint.
Z3_ast_vector Z3_API Z3_solver_get_units(Z3_context c, Z3_solver s)
Return the set of units modulo model conversion.
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.
Z3_string Z3_API Z3_probe_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the probe with the given name.
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.
Z3_goal Z3_API Z3_apply_result_get_subgoal(Z3_context c, Z3_apply_result r, unsigned i)
Return one of the subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
Z3_probe Z3_API Z3_probe_le(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than or equal to the va...
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.
Z3_ast Z3_API Z3_mk_fpa_to_fp_float(Z3_context c, Z3_ast rm, Z3_ast t, Z3_sort s)
Conversion of a FloatingPoint term into another term of different FloatingPoint sort.
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_apply_result Z3_API Z3_tactic_apply(Z3_context c, Z3_tactic t, Z3_goal g)
Apply tactic t to the goal g.
Z3_ast Z3_API Z3_mk_fpa_round_nearest_ties_to_even(Z3_context c)
Create a numeral of RoundingMode sort which represents the NearestTiesToEven rounding mode.
void Z3_API Z3_solver_propagate_created(Z3_context c, Z3_solver s, Z3_created_eh created_eh)
register a callback when a new expression with a registered function is used by the solver The regist...
Z3_ast_vector Z3_API Z3_parser_context_from_string(Z3_context c, Z3_parser_context pc, Z3_string s)
Parse a string of SMTLIB2 commands. Return assertions.
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_stats Z3_API Z3_solver_get_statistics(Z3_context c, Z3_solver s)
Return statistics for the given solver.
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_string Z3_API Z3_fixedpoint_get_reason_unknown(Z3_context c, Z3_fixedpoint d)
Retrieve a string that describes the last status returned by Z3_fixedpoint_query.
Z3_func_decl Z3_API Z3_mk_linear_order(Z3_context c, Z3_sort a, unsigned id)
create a linear ordering relation over signature a. The relation is identified by the index id.
Z3_string Z3_API Z3_fixedpoint_get_help(Z3_context c, Z3_fixedpoint f)
Return a string describing all fixedpoint available parameters.
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_ast Z3_API Z3_mk_seq_in_re(Z3_context c, Z3_ast seq, Z3_ast re)
Check if seq is in the language generated by the regular expression re.
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_string Z3_API Z3_solver_to_dimacs_string(Z3_context c, Z3_solver s, bool include_names)
Convert a solver into a DIMACS formatted string.
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.
void Z3_API Z3_solver_propagate_decide(Z3_context c, Z3_solver s, Z3_decide_eh decide_eh)
register a callback when the solver decides to split on a registered expression. The callback may cha...
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_string Z3_API Z3_optimize_get_reason_unknown(Z3_context c, Z3_optimize d)
Retrieve a string that describes the last status returned by Z3_optimize_check.
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.
double Z3_API Z3_probe_apply(Z3_context c, Z3_probe p, Z3_goal g)
Execute the probe over the goal. The probe always produce a double value. "Boolean" probes return 0....
void Z3_API Z3_fixedpoint_assert(Z3_context c, Z3_fixedpoint d, Z3_ast axiom)
Assert a constraint to the fixedpoint context.
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).
void Z3_API Z3_solver_propagate_register(Z3_context c, Z3_solver s, Z3_ast e)
register an expression to propagate on with the solver. Only expressions of type Bool and type Bit-Ve...
Z3_ast Z3_API Z3_substitute_vars(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const to[])
Substitute the variables in a with the expressions in to. For every i smaller than num_exprs,...
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.
Z3_tactic Z3_API Z3_tactic_or_else(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that first applies t1 to a given goal, if it fails then returns the result of t2 appl...
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_sort Z3_API Z3_mk_fpa_sort(Z3_context c, unsigned ebits, unsigned sbits)
Create a FloatingPoint sort.
void Z3_API Z3_fixedpoint_set_params(Z3_context c, Z3_fixedpoint f, Z3_params p)
Set parameters on fixedpoint context.
void Z3_API Z3_optimize_from_string(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 string with assertions, soft constraints and optimization objectives....
Z3_string Z3_API Z3_fpa_get_numeral_significand_string(Z3_context c, Z3_ast t)
Return the significand value of a floating-point numeral as a string.
Z3_solver Z3_API Z3_solver_add_simplifier(Z3_context c, Z3_solver solver, Z3_simplifier simplifier)
Attach simplifier to a solver. The solver will use the simplifier for incremental pre-processing.
Z3_ast Z3_API Z3_fixedpoint_get_answer(Z3_context c, Z3_fixedpoint d)
Retrieve a formula that encodes satisfying answers to the query.
Z3_ast Z3_API Z3_mk_int_to_str(Z3_context c, Z3_ast s)
Integer to string conversion.
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_solver_propagate_fixed(Z3_context c, Z3_solver s, Z3_fixed_eh fixed_eh)
register a callback for when an expression is bound to a fixed value. The supported expression types ...
Z3_ast Z3_API Z3_fpa_get_numeral_sign_bv(Z3_context c, Z3_ast t)
Retrieves the sign of a floating-point literal as a bit-vector expression.
void Z3_API Z3_fixedpoint_register_relation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f)
Register relation as Fixedpoint defined. Fixedpoint defined relations have least-fixedpoint semantics...
Z3_ast Z3_API Z3_mk_char_is_digit(Z3_context c, Z3_ast ch)
Create a check if the character is a digit.
void Z3_API Z3_fixedpoint_add_cover(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred, Z3_ast property)
Add property about the predicate pred. Add a property of predicate pred at level. It gets pushed forw...
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_lbool Z3_API Z3_fixedpoint_query_relations(Z3_context c, Z3_fixedpoint d, unsigned num_relations, Z3_func_decl const relations[])
Pose multiple queries against the asserted rules.
Z3_string Z3_API Z3_apply_result_to_string(Z3_context c, Z3_apply_result r)
Convert the Z3_apply_result object returned by Z3_tactic_apply into a string.
Z3_string Z3_API Z3_solver_to_string(Z3_context c, Z3_solver s)
Convert a solver into a string.
void Z3_API Z3_optimize_register_model_eh(Z3_context c, Z3_optimize o, Z3_model m, void *ctx, Z3_model_eh model_eh)
register a model event handler for new models.
bool Z3_API Z3_fpa_is_numeral_normal(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is normal.
Z3_string Z3_API Z3_solver_get_reason_unknown(Z3_context c, Z3_solver s)
Return a brief justification for an "unknown" result (i.e., Z3_L_UNDEF) for the commands Z3_solver_ch...
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_tactic Z3_API Z3_tactic_repeat(Z3_context c, Z3_tactic t, unsigned max)
Return a tactic that keeps applying t until the goal is not modified anymore or the maximum number of...
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_lbool Z3_API Z3_optimize_check(Z3_context c, Z3_optimize o, unsigned num_assumptions, Z3_ast const assumptions[])
Check consistency and produce optimal values.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
Z3_ast Z3_API Z3_mk_fpa_round_toward_zero(Z3_context c)
Create a numeral of RoundingMode sort which represents the TowardZero rounding mode.
Z3_ast Z3_API Z3_mk_char_from_bv(Z3_context c, Z3_ast bv)
Create a character from a bit-vector (code point).
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_probe Z3_API Z3_probe_const(Z3_context x, double val)
Return a probe that always evaluates to val.
Z3_ast Z3_API Z3_mk_fpa_zero(Z3_context c, Z3_sort s, bool negative)
Create a floating-point zero of sort s.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
Z3_ast Z3_API Z3_mk_atmost(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
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.
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_tactic Z3_API Z3_tactic_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and t2 to every subgoal produced by t1.
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...
Z3_sort Z3_API Z3_mk_fpa_sort_double(Z3_context c)
Create the double-precision (64-bit) FloatingPoint sort.
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
bool Z3_API Z3_solver_next_split(Z3_context c, Z3_solver_callback cb, Z3_ast t, unsigned idx, Z3_lbool phase)
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.
Z3_ast Z3_API Z3_mk_string_to_code(Z3_context c, Z3_ast a)
String to code conversion.
Z3_sort Z3_API Z3_mk_string_sort(Z3_context c)
Create a sort for unicode strings.
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.
Z3_ast Z3_API Z3_mk_seq_nth(Z3_context c, Z3_ast s, Z3_ast index)
Retrieve from s the element positioned at position index. The function is under-specified if the inde...
bool Z3_API Z3_fpa_is_numeral_inf(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is a +oo or -oo.
Z3_ast Z3_API Z3_mk_seq_contains(Z3_context c, Z3_ast container, Z3_ast containee)
Check if container contains containee.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
bool Z3_API Z3_fpa_is_numeral_zero(Z3_context c, Z3_ast t)
Checks whether a given floating-point numeral is +zero or -zero.
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.
_coerce_char(ch, ctx=None)
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
SubSeq(s, offset, length)
get_default_fp_sort(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)
set_default_fp_sort(ebits, sbits, ctx=None)
IndexOf(s, substr, offset=None)
RecAddDefinition(f, args, body)
DeclareTypeVar(name, ctx=None)
RoundNearestTiesToEven(ctx=None)
_mk_fp_unary_pred(f, a, ctx)
FiniteDomainVal(val, sort, ctx=None)
PiecewiseLinearOrder(a, index)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
FPSort(ebits, sbits, ctx=None)
RoundTowardNegative(ctx=None)
SimpleSolver(ctx=None, logFile=None)
solve_using(s, *args, **keywords)
_coerce_expr_list(alist, ctx=None)
_mk_fp_bin(f, rm, a, b, ctx)
_pb_args_coeffs(args, default_ctx=None)
Repeat(t, max=4294967295, ctx=None)
RealVector(prefix, sz, ctx=None)
_solve_using_html(s, *args, **keywords)
RoundTowardZero(ctx=None)
parse_smt2_file(f, sorts={}, decls={}, ctx=None)
fpFP(sgn, exp, sig, ctx=None)
fpSignedToFP(rm, v, sort, ctx=None)
user_prop_fixed(ctx, cb, id, value)
SubString(s, offset, length)
fpFPToFP(rm, v, sort, ctx=None)
BitVecs(names, bv, ctx=None)
FPs(names, fpsort, ctx=None)
fpIsPositive(a, ctx=None)
SolverFor(logic, ctx=None, logFile=None)
user_prop_diseq(ctx, cb, x, y)
BoolVector(prefix, sz, ctx=None)
fpIsSubnormal(a, ctx=None)
user_prop_fresh(ctx, _new_ctx)
is_finite_domain_value(a)
fpBVToFP(v, sort, ctx=None)
fpToFPUnsigned(rm, x, s, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
_to_float_str(val, exp=0)
PropagateFunction(name, *sig)
fpUnsignedToFP(rm, v, sort, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
RoundTowardPositive(ctx=None)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
fpAdd(rm, a, b, ctx=None)
user_prop_pop(ctx, cb, num_scopes)
get_default_rounding_mode(ctx=None)
user_prop_decide(ctx, cb, t, idx, phase)
_and_then(t1, t2, ctx=None)
set_default_rounding_mode(rm, ctx=None)
fpRealToFP(rm, v, sort, ctx=None)
_mk_fp_bin_pred(f, a, b, ctx)
FreshReal(prefix="b", ctx=None)
fpIsNegative(a, ctx=None)
_reduce(func, sequence, initial)
fpDiv(rm, a, b, ctx=None)
probe_description(name, ctx=None)
BVAddNoOverflow(a, b, signed)
fpSub(rm, a, b, ctx=None)
ParAndThen(t1, t2, ctx=None)
fpMul(rm, a, b, ctx=None)
FreshBool(prefix="b", ctx=None)
FiniteDomainSort(name, sz, ctx=None)
AllChar(regex_sort, ctx=None)
user_prop_created(ctx, cb, id)
prove(claim, show=False, **keywords)
RoundNearestTiesToAway(ctx=None)
FPVal(sig, exp=None, fps=None, ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
fpToUBV(rm, x, s, ctx=None)
fpToFP(a1, a2=None, a3=None, ctx=None)
user_prop_eq(ctx, cb, x, y)
on_clause_eh(ctx, p, n, dep, clause)
tactic_description(name, ctx=None)
IntVector(prefix, sz, ctx=None)
RealVarVector(n, ctx=None)
fpToSBV(rm, x, s, ctx=None)
_probe_nary(f, args, ctx)
_mk_fp_bin_norm(f, a, b, ctx)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
CharIsDigit(ch, ctx=None)
_mk_fp_unary(f, rm, a, ctx)
fpFMA(rm, a, b, c, ctx=None)
_get_ctx2(a, b, ctx=None)
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
FP(name, fpsort, ctx=None)
_or_else(t1, t2, ctx=None)
_coerce_fp_expr_list(alist, ctx)
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
ParThen(t1, t2, ctx=None)
parse_smt2_string(s, sorts={}, decls={}, ctx=None)
_prove_html(claim, show=False, **keywords)
fpRoundToIntegral(rm, a, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
_mk_fp_tern(f, rm, a, b, c, ctx)
_solve_html(*args, **keywords)