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Verified heap theorem prover by paramodulation. in preparation (2011)
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@MISC{Stewart11verifiedheap,
author = {Gordon Stewart and Lennart Beringer},
title = {Verified heap theorem prover by paramodulation. in preparation},
year = {2011}
}
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Abstract
We present VeriStar, a verified theorem prover for a decidable subset of separation logic. Together with VeriSmall [2], a proved-sound Smallfoot-style program analysis for C minor, VeriStar demonstrates that fully machine-checked static analyses equipped with efficient theorem provers are now within the reach of formal methods. As a pair, VeriStar and VeriSmall represent the first application of the Verified Software Toolchain [3], a tightly integrated collection of machine-verified program logics and compilers giving foundational correctness guarantees. VeriStar is (1) purely functional, (2) machine-checked, (3) endto-end, (4) efficient and (5) modular. By purely functional, we mean it is implemented in Gallina, the pure functional programming language embedded in the Coq theorem prover. By machine-checked, we mean it has a proof in Coq that when the prover says “valid”, the checked entailment holds in a proved-sound separation logic for C minor. By end-to-end, we mean that when the static analysis+theorem prover says a C minor program is safe, the program will be compiled to a semantically equivalent assembly program that runs on real hardware. By efficient, we mean that the prover implements a state-of-the-art algorithm for deciding heap entailments and uses highly tuned verified functional data structures. By modular, we mean that VeriStar can be retrofitted to other static analyses as a plug-compatible entailment checker and its soundness proof can easily be ported to other separation logics.
Keyphrases
verified heap theorem prover separation logic pure functional programming language efficient theorem provers formal method present veristar foundational correctness guarantee verified software toolchain static analysis theorem prover equivalent assembly program real hardware minor program heap entailment plug-compatible entailment checker first application verified functional data structure verified theorem prover state-of-the-art algorithm soundness proof checked entailment proved-sound separation logic proved-sound smallfoot-style program analysis machine-checked static analysis coq theorem prover decidable subset machine-verified program logic static analysis
