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Extending PPTL for Verifying Heap Evolution Properties
In this paper, we integrate separation logic with Propositional Projection
Temporal Logic (PPTL) to obtain a two-dimensional logic, namely
PPTL^{\tiny\mbox{SL}}. The spatial dimension is realized by a decidable
fragment of separation logic which can be used to describe linked lists, and
the temporal dimension is expressed by PPTL. We show that PPTL and
PPTL^{\tiny\mbox{SL}} are closely related in their syntax structures. That
is, for any PPTL^{\tiny\mbox{SL}} formula in a restricted form, there exists
an "isomorphic" PPTL formula. The "isomorphic" PPTL formulas can be obtained by
first an equisatisfiable translation and then an isomorphic mapping. As a
result, existing theory of PPTL, such as decision procedure for satisfiability
and model checking algorithm, can be reused for PPTL^{\tiny\mbox{SL}}