# 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