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# kinds -*- sh -*-
#
# For documentation on this file format, please refer to
# src/theory/builtin/kinds.
#
theory THEORY_SETS \
::CVC4::theory::sets::TheorySets \
"theory/sets/theory_sets.h"
typechecker "theory/sets/theory_sets_type_rules.h"
rewriter ::CVC4::theory::sets::TheorySetsRewriter \
"theory/sets/theory_sets_rewriter.h"
properties parametric
properties check propagate presolve
# constants
constant EMPTYSET \
::CVC4::EmptySet \
::CVC4::EmptySetHashFunction \
"expr/emptyset.h" \
"the empty set constant; payload is an instance of the CVC4::EmptySet class"
# the type
operator SET_TYPE 1 "set type, takes as parameter the type of the elements"
cardinality SET_TYPE \
"::CVC4::theory::sets::SetsProperties::computeCardinality(%TYPE%)" \
"theory/sets/theory_sets_type_rules.h"
well-founded SET_TYPE \
"::CVC4::theory::sets::SetsProperties::isWellFounded(%TYPE%)" \
"::CVC4::theory::sets::SetsProperties::mkGroundTerm(%TYPE%)" \
"theory/sets/theory_sets_type_rules.h"
enumerator SET_TYPE \
"::CVC4::theory::sets::SetEnumerator" \
"theory/sets/theory_sets_type_enumerator.h"
# operators
operator UNION 2 "set union"
operator INTERSECTION 2 "set intersection"
operator SETMINUS 2 "set subtraction"
operator SUBSET 2 "subset predicate; first parameter a subset of second"
operator MEMBER 2 "set membership predicate; first parameter a member of second"
operator SINGLETON 1 "the set of the single element given as a parameter"
operator INSERT 2: "set obtained by inserting elements (first N-1 parameters) into a set (the last parameter)"
operator CARD 1 "set cardinality operator"
operator COMPLEMENT 1 "set COMPLEMENT (with respect to finite universe)"
nullaryoperator UNIVERSE_SET "(finite) universe set, all set variables must be interpreted as subsets of it."
# A set comprehension is specified by:
# (1) a bound variable list x1 ... xn,
# (2) a predicate P[x1...xn], and
# (3) a term t[x1...xn].
# A comprehension C with the above form has members given by the following
# semantics:
# forall y. ( exists x1...xn. P[x1...xn] ^ t[x1...xn] = y ) <=> (member y C)
# where y ranges over the element type of the (set) type of the comprehension.
# Notice that since all sets must be interpreted as finite, this means that
# CVC4 will not be able to construct a model for any set comprehension such
# that there are infinitely many y that satisfy the left hand side of the
# equivalence above. The same limitation occurs more generally when combining
# finite sets with quantified formulas.
operator COMPREHENSION 3 "set comprehension specified by a bound variable list, a predicate, and a term."
operator JOIN 2 "set join"
operator PRODUCT 2 "set cartesian product"
operator TRANSPOSE 1 "set transpose"
operator TCLOSURE 1 "set transitive closure"
operator JOIN_IMAGE 2 "set join image"
operator IDEN 1 "set identity"
typerule UNION ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
typerule INTERSECTION ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
typerule SETMINUS ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
typerule SUBSET ::CVC4::theory::sets::SubsetTypeRule
typerule MEMBER ::CVC4::theory::sets::MemberTypeRule
typerule SINGLETON ::CVC4::theory::sets::SingletonTypeRule
typerule EMPTYSET ::CVC4::theory::sets::EmptySetTypeRule
typerule INSERT ::CVC4::theory::sets::InsertTypeRule
typerule CARD ::CVC4::theory::sets::CardTypeRule
typerule COMPLEMENT ::CVC4::theory::sets::ComplementTypeRule
typerule UNIVERSE_SET ::CVC4::theory::sets::UniverseSetTypeRule
typerule COMPREHENSION ::CVC4::theory::sets::ComprehensionTypeRule
typerule JOIN ::CVC4::theory::sets::RelBinaryOperatorTypeRule
typerule PRODUCT ::CVC4::theory::sets::RelBinaryOperatorTypeRule
typerule TRANSPOSE ::CVC4::theory::sets::RelTransposeTypeRule
typerule TCLOSURE ::CVC4::theory::sets::RelTransClosureTypeRule
typerule JOIN_IMAGE ::CVC4::theory::sets::JoinImageTypeRule
typerule IDEN ::CVC4::theory::sets::RelIdenTypeRule
construle UNION ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
construle INTERSECTION ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
construle SETMINUS ::CVC4::theory::sets::SetsBinaryOperatorTypeRule
construle SINGLETON ::CVC4::theory::sets::SingletonTypeRule
construle INSERT ::CVC4::theory::sets::InsertTypeRule
construle CARD ::CVC4::theory::sets::CardTypeRule
construle COMPLEMENT ::CVC4::theory::sets::ComplementTypeRule
construle JOIN ::CVC4::theory::sets::RelBinaryOperatorTypeRule
construle PRODUCT ::CVC4::theory::sets::RelBinaryOperatorTypeRule
construle TRANSPOSE ::CVC4::theory::sets::RelTransposeTypeRule
construle TCLOSURE ::CVC4::theory::sets::RelTransClosureTypeRule
construle JOIN_IMAGE ::CVC4::theory::sets::JoinImageTypeRule
construle IDEN ::CVC4::theory::sets::RelIdenTypeRule
endtheory
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