Constraint Logic Programming and Mu-Calculus

A wide range of problems such as static program analysis and symbolic verii-cation induces the need for an evaluation mechanism of xed point, and thus, a certain form of quantiication over relations. Many specialized tools (MVL 7], MEC 1], .. .) exist, mainly based upon the mu-calculus formalism 9]. On the one hand, while generally ooering good performances, these tools use their own syntaxes, and are restricted to particular applications. On the other hand, Constraint Logic Programming languages are easy to use, give compact source code, provide friendly development platforms with lots of useful libraries, but often suuer from poor performances and lack of features such as second order quantiication and explicit manipulation of relations. The purpose of the work described in this paper is to take the best of the two approaches, more precisely, to integrate a solver of xed point equations, based on the-calculus, into a well known and open Prolog environment : SICStus Prolog. This work originate in the Toupie 10] project. Toupie is a constraint language designed on an extension of-calculus over symbolic nite domain, which provide full universal and existential quantiication and allow the deenition of relations as xed point of equations. We will rst describe the module which has been implemented, then give some results obtained for groundness analysis of logic programs and nally propose promising extensions to this work. 2 The module We chose to implement this solver of xed point equations as a SICStus Prolog module. The SICStus Prolog environment provides a lot of libraries (terms, AVL trees,. ..). Especially, it has a boolean constraints solver 4], coded as a module, and using the ordered binary decision diagram (OBBD) 2, 3] data structure. Techniques of representation of boolean relations and formulas of-calculus using BDDs (and their extensions) have proved to be eecient 6, 10]. It was thus convenient for us to use the BDD primitive of the boolean constraint solver in order to represent our formulas.