Difference between revisions of "Sets"

From CVC4

Revision as of 09:50, 25 April 2018

As of July 2014 (CVC4 v1.4), we include support for theory of finite sets. The simplest way to get a sense of the syntax is to look at an example:

For reference, below is a short summary of the sorts, constants, functions and predicates.

	CVC language	SMTLIB language	C++ API
Logic string	Not needed	append "FS" for finite sets	append "FS" for finite sets
		`(set-logic QF_UFLIAFS)`	`smt.setLogic("QF_UFLIAFS");`
Sort	SET OF <Element Sort>	(Set <Element Sort>)	CVC4::ExprManager::mkSetType(CVC4::Type elementType)
	`X: SET OF INT;`	`(declare-fun X () (Set Int))`	`em.mkSetType( em.integerType() );`
Union	`X \| Y`	`(union X Y)`	`em.mkExpr(kind::UNION, X, Y);`
Intersection	`X & Y`	`(intersection X Y)`	`em.mkExpr(kind::INTERSECTION, X, Y);`
Set subtraction	`X – Y`	`(setminus X Y)`	`em.mkExpr(kind::SETMINUS, X, Y);`
Membership	`x IS_IN X`	`(member x X)`	`em.mkExpr(kind::MEMBER, x, X);`
Subset	`X <= Y`	`(subset X Y)`	`em.mkExpr(kind::SUBSET, X, Y);`
Empty set	{} :: <Type Ascription>	(as emptyset <Type Ascription>)	CVC4::EmptySet(CVC4::SetType setType)
	`{} :: SET OF INT`	`(as emptyset (Set Int))`	`em.mkConst(EmptySet(em.mkSetType(em.integerType())));`
Singleton set	`{1}`	`(singleton 1)`	`em.mkExpr(kind::SINGLETON, oneExpr);`
Cardinality	`CARD( X )`	`(card X)`	`em.mkExpr(kind::CARD, X);`
Insert/finite sets	`{1, 2, 3, 4}`	`(insert 1 2 3 (singleton 4))`	`em.mkExpr(kind::INSERT, c1, c2, c3, sgl4);`
Complement	`~ X`	`(complement X)`	`em.mkExpr(kind::COMPLEMENT, X);`
Universe set	UNIVERSE :: <Type Ascription>	(as univset <Type Ascription>)
	`UNIVERSE :: SET OF INT`	`(as univset (Set Int))`	`em.mkNullaryOperator(em.mkSetType(em.integerType()),kind::UNIVERSE_SET);`

Operator precedence for CVC language: & | – IS_IN <= =. For example, A - B | A & C <= D is read as ( A - ( B | (A & C) ) ) <= D.

Note: Currently, we only support encoding relational constraints in CVC4 native language. Support for SMT-LIB language is coming soon.

	CVC language	SMTLIB language	C++ API
Logic string	Not needed	`(set-logic QF_ALL)`	`smt.setLogic("QF_ALL");`
Tuple Sort	[<Sort_1>, ..., <Sort_n>]	(Tuple <Sort_1>, ..., <Sort_n>)	CVC4::ExprManager::mkTupleType(std::vector<CVC4::Type>& types)
	`X: [INT, INT];`	`(declare-fun X () (Tuple Int Int))`	`em.mkTupleType( em.integerType(), em.integerType() );`
Tuple constructor	`(X1, ..., Xn)`	`(mkTuple X1, ..., Xn)`	`DatatypeType t = em.mkTupleType(types);` `const Datatype& dt = t.getDatatype();` `Expr c = dt[0].getConstructor();` `em.mkExpr(kind::APPLY_CONSTRUCTOR, c, X1, ..., Xn);`
Relation Sort	SET OF [<Sort_1>, ..., <Sort_n>]	(Set (Tuple <Sort_1>, ..., <Sort_n>))	CVC4::ExprManager::mkSetType(CVC4::Type elementType)
	`X: SET OF [INT, INT];`	`(declare-fun X () (Set (Tuple Int Int)))`	`em.mkSetType( em.mkTupleType( em.integerType(), em.integerType() ) );`
Transpose	`TRANSPOSE(X)`	`(transpose X)`	`em.mkExpr(kind::TRANSPOSE, X);`
Transitive Closure	`TCLOSURE(X)`	`(tclosure X)`	`em.mkExpr(kind::TCLOSURE, X);`
Join	`X JOIN Y`	`(join X Y)`	`em.mkExpr(kind::JOIN, X);`
Product	`X PRODUCT Y`	`(product X Y)`	`em.mkExpr(kind::PRODUCT, X);`

@@ Line 125: / Line 125: @@
 | <code>(set-logic QF_'''ALL''')</code>
 | <code>smt.setLogic("QF_'''ALL'''");</code>
-|-
-| Relation Sort
-| SET OF [<Sort_1>, ..., <Sort_n>]
-| (Set (Tuple <Sort_1>, ..., <Sort_n>))
-| CVC4::ExprManager::mkSetType(CVC4::Type elementType)
-|-
-|
-| <code>X: '''SET OF [INT, INT]''';</code>
-| <code> (declare-fun X () '''(Set (Tuple Int Int))''') </code>
-| <code>em.mkSetType( em.mkTupleType( em.integerType(), em.integerType() ) );</code>
 |-
 | Tuple Sort
@@ Line 153: / Line 143: @@
 <code>Expr c = dt[0].getConstructor();</code><br>
 <code>em.mkExpr('''kind::APPLY_CONSTRUCTOR''', c, X1, ..., Xn);</code>
+|-
+| Relation Sort
+| SET OF [<Sort_1>, ..., <Sort_n>]
+| (Set (Tuple <Sort_1>, ..., <Sort_n>))
+| CVC4::ExprManager::mkSetType(CVC4::Type elementType)
+|-
+|
+| <code>X: '''SET OF [INT, INT]''';</code>
+| <code> (declare-fun X () '''(Set (Tuple Int Int))''') </code>
+| <code>em.mkSetType( em.mkTupleType( em.integerType(), em.integerType() ) );</code>
 |-
 | Transpose