Conference Paper

An Equational Calculus for Alloy.

DOI: 10.1007/978-3-540-30482-1_19 In proceeding of: Formal Methods and Software Engineering, 6th International Conference on Formal Engineering Methods, ICFEM 2004, Seattle, WA, USA, November 8-12, 2004, Proceedings
Source: DBLP

ABSTRACT In this paper we show that, by translating Alloy formulas to formulas in the language of fork algebras, we obtain a complete, equa- tional, and purely relational calculus for Alloy.

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    ABSTRACT: Alloy is an increasingly popular lightweight specification language based on relational logic. Alloy models can be automatically verified within a bounded scope using off-the-shelf SAT solvers. Since false assertions can usually be disproved using small counter-examples, this approach suffices for most applications. Unfortunately, it can sometimes lead to a false sense of security, and in critical applications a more traditional unbounded proof may be required. The automatic theorem prover Prover9 has been shown to be particularly effective for proving theorems of relation algebras [7], a quantifier-free (or point-free) axiomatization of a fragment of relational logic. In this paper we propose a translation from Alloy specifications to fork algebras (an extension of relation algebras with the same expressive power as relational logic) which enables their unbounded verification in Prover9. This translation covers not only logic assertions, but also the structural aspects (namely type declarations), and was successfully implemented and applied to several examples.
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    ABSTRACT: Refactorings are usually proposed in an ad hoc way because it is difficult to prove that they are sound with respect to a formal semantics, not guaranteeing the absence of type errors or semantic changes. Consequently, developers using refactoring tools must rely on compilation and tests to ensure type-correctness and semantics preservation, respectively, which may not be satisfactory to critical software development. In this paper, we formalize a static semantics for Alloy, which is a formal object-oriented modeling language, and encode it in Prototype Verification System (PVS). The static semantics' formalization can be useful for specifying and proving that transformations in general (not only refactorings) do not introduce type errors, for instance, as we show here.
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