Higher-Order Separation Logic in Isabelle/HOLCF

We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF. The assertion language is modeled in such a way that one may use any theory defined in Isabelle/HOLCF to construct assertions, e.g., primitive recursion, least or greatest fixed points etc. The higher-order logic ensures that we can show non-trivial algorithms correct without having to extend the semantics of the language as was done previously in verifications based on first-order separation logic [2,20]. We provide non-trivial examples to support this claim and to show how the higher-order logic natural assertions in specifications. To support abstract reasoning we have implemented rules for tation hiding and data abstraction as seen in [1]. The logic is represented as lemmas for reasoning about the denotational semantics of the programming language. This follows the definitional approach common in HOL theorem provers, i.e., the soundness of our mod...

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Carsten Varming, Lars Birkedal
• Keywords: ENTCS 2008, First-order Imperative Language, First-order Separation Logic, Separation Logic