CVC4 supports a syntax for separation logic as an extension of the *.smt2 language.
Given a (decidable) base theory T, CVC4 has a decision procedure for quantifier-free formulas, where "Loc" and "Data" are any sort belonging to T. A formula is one from the following grammar:
F : L | (emp t u) | (pto t u) | (sep F1 ... Fn) | (wand F1 F2) | ~F1 | F1 op ... op Fn
where "op" is any classical Boolean connective, t and u are terms built from symbols in the signature of T of sort Loc and Data respectively, and L is a T-literal. The operator "emp" denotes the empty heap constraint, the operator "pto" denotes the points-to predicate, the operator "sep" denotes separation start and is variadic, and the operator "wand" denote magic wand.
A satisfiability relation is defined for formulas , where I is an interpretation, and h is a heap. The semantics of separation logic operators are as follows:
|L||Iff||L, if L is a T-literal|
|(sep )||Iff||there exist heaps s.t. and|
|(wand )||Iff||for all heaps if and then|
where denotes the disjoint union of heaps and denotes that heaps h' and h are disjoint, and is a distinguished variable of sort Loc. All classical Boolean connectives are interpreted as expected. Note that the arguments of "emp" are used to denote the type of the heap and have no meaning otherwise.
Separation logic in CVC4 requires the "all supported" logic:
The syntax for the operators of separation logic is summarized in the following table:
|CVC language||SMTLIB language||C++ API|
The following input on heaps Int -> Int is unsatisfiable:
(set-logic QF_ALL_SUPPORTED) (set-info :status unsat) (declare-const x Int) (declare-const a Int) (declare-const b Int) (assert (and (pto x a) (pto x b))) (assert (not (= a b))) (check-sat)
The following input on heaps U -> Int is satisfiable. Notice that the formula (not (emp x 0)) is satisfied by heaps U -> Int (the types of x and 0 respectively) whose domain is non-empty.
(set-logic QF_ALL_SUPPORTED) (set-info :status unsat) (declare-sort U 0) (declare-const x U) (declare-const a Int) (assert (and (not (_ emp Int U)) (pto x a)) (check-sat)
The following input on heaps Int -> Node is satisfiable, where Node denotes a user-defined inductive datatype:
(set-logic QF_ALL_SUPPORTED) (set-info :status sat) (declare-const x Int) (declare-const y Int) (declare-const z Int) (declare-datatypes () ((Node (node (data Int) (left Int) (right Int))))) (assert (pto x (node 0 y z))) (check-sat)
Given a separation logic input, the sorts Loc and Data are inferred by CVC4, and must be consistent across all predicates occurring in an input. CVC4 does not accept an input such as:
(set-logic QF_ALL_SUPPORTED) (declare-sort U 0) (declare-const x U) (assert (and (pto x 0) (pto 1 2)))
since the sorts of the first arguments of the points-to predicates do not agree.