Automated Flaw Detection in Algebraic Specifications

Abstract

In interactive theorem proving practice a significant amount of time is spent on unsuccessful proof attempts of wrong conjectures. An automatic method that reveals them by generating finite counter examples would offer an extremely valuable support for a proof engineer by saving his time and effort. In practice, such counter examples tend to be small, so usually there is no need to search for big instances. Most definitions of functions or predicates on infinite structures do not preserve the semantics if a transition to arbitrary finite substructures is made. We propose constraints which guarantee a correct axiomatization on finite structures and present an approach which uses the Alloy Analyzer to generate finite instances of theories in the theorem prover KIV. It is evaluated on the library of basic data types as well as on some challenging case studies in KIV. The technique is implemented using the Kodkod constraint solver which is a successor of Alloy.

Model Finding for Recursive Functions in SMT

“…The approach finds sound (fragments of) models for formulas in the existential-bounded-universal frag-ment (i.e., formulas whose prenex normal forms contain no unbounded universal quantifiers ranging over datatypes). This idiom was refined by Dunets et al [18], who presented a translation scheme for primitive recursion. Their definedness guards play a similar role to the existential constraints generated by our translation A.…”

Extending Nunchaku to Dependent Type Theory

“…Finally, some theorem provers implement finite model finding on top of their proof calculus; this is the case for KIV [35], iProver [25], and CVC4 [38]. To make finite model finding more useful, techniques have been developed to search for partial fragments of infinite models [6,19,26,37,42].…”