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We analyze three proof strategies commonly used in deductive verification of deterministic sequential programs formalized with operational semantics. The strategies are (i) stepwise invariants, (ii) clock functions, and (iii) inductive assertions. We show how to formalize the strategies in the...
We present a complete mechanized proof of the result in homological algebra known as basic perturbation lemma. The proof has been carried out in the proof assistant Isabelle, more concretely, in the implementation of higher-order logic (HOL) available in the system. We report on the difficulties...
Traditionally, a conditional rewrite rule directs replacement of one term by another term that is provably equal to it, perhaps under some hypotheses. This paper generalizes the notion of rewrite rule to permit the connecting relation to be merely an equivalence relation. We then extend the...
This article describes the formal verification of a compilation algorithm that transforms parallel moves (parallel assignments between variables) into a semantically-equivalent sequence of elementary moves. Two different specifications of the algorithm are given: an inductive specification and a...
This paper describes a formalisation of the lambda-calculus in a HOL-based theorem prover using nominal techniques. Central to the formalisation is an inductive set that is bijective with the alpha-equated lambda-terms. Unlike de-Bruijn indices, however, this inductive set includes names and...
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