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On the Almighty Wand

Abstract : We investigate decidability, complexity and expressive power issues for (first-order) separation logic with one record field (herein called SL) and its fragments. SL can specify properties about the memory heap of programs with singly-linked lists. Separation logic with two record fields is known to be un-decidable by reduction of finite satisfiability for classical predicate logic with one binary relation. Surprisingly, we show that second-order logic is as expressive as SL and as a by-product we get undecidability of SL. This is refined by showing that SL without the separating conjunction is as expressive as SL, whence undecidable too. As a consequence, in SL the separating implication (also known as the magic wand) can simulate the separating conjunction. By contrast, we establish that SL without the magic wand is decidable, and we prove a non-elementary complexity by reduction from satisfiability for the first-order theory over finite words. This result is extended with a bounded use of the magic wand that appears in Hoare-style rules. As a generalisation, it is shown that kSL, the separation logic over heaps with k ≥ 1 record fields, is equivalent to kSO, the second-order logic over heaps with k record fields.
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  • HAL Id : hal-01905158, version 1

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Rémi Brochenin, Stephane Demri, Etienne Lozes. On the Almighty Wand. Information and Computation, Elsevier, 2012. ⟨hal-01905158⟩

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