Relational analysis of algebraic datatypes

Abstract

We present a technique that enables the use of finite model finding to check the satisfiability of certain formulas whose intended models are infinite. Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. As a result, when a formula belongs to this class, we can use existing finite model finding tools to check whether the formula holds in the desired infinite model.

Automated Flaw Detection in Algebraic Specifications

“…Based on this notion we show soundness of the method for specifications of free data types with compatible operation definitions. We extend results by Kuncak and Jackson [20] who give an approach of utilizing model finding for the analysis of term algebras, where the language is restricted to selectors only. Dunets et al [10] was the first step toward extending the language with arbitrary functions which however was restricted to a very special class of definitions of recursive functions on freely generated data types only.…”

“…the constant nil and the function cons : elem × list → list for lists. Here we refer to the work of Kuncak and Jackson [20]. We adopt their ideas to generate structures in Alloy which correspond to term algebras.…”

“…Kuncak and Jackson [20] proved that a finite structure M constructed with Alloy for τ fin (SP) is isomorphic to some finite subterm-closed substructure A 0 of A where A |= SP. This result applies for specifications of free data types with the language restricted to constructors and selectors only (F = (C s ) s∈S , P = ∅, Ax = ∅).…”

“…This result applies for specifications of free data types with the language restricted to constructors and selectors only (F = (C s ) s∈S , P = ∅, Ax = ∅). Further, they established a finite satisfiability result by proving that for a specific class of For this purpose a notion of bounded quantification is introduced, see [20]. Roughly, if a witness (a finite structure M) for an EBU formula is found, we can pick the same witness in the infinite model A.…”

“…We will give a positive answer below for a class of formulas with universal and bounded existential quantification similar to [20]. The answer has the precondition, that function (7)), is not in M list .…”