$\{log\}$ (read ‘setlog’) was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, $\{log\}$ is a constraint satisfiability solver implementing decision procedures for several fragments of set theory. Hence, $\{log\}$ can be used as a declarative, set, logic programming language and as an automated theorem prover for set theory. Over time $\{log\}$ has been extended with some components integrated to the satisfiability solver thus providing a formal verification environment. In this paper we make a comprehensive presentation of this environment which includes a language for the description of state machines based on set theory, an interactive environment for the execution of functional scenarios over state machines, a generator of verification conditions for state machines, automated verification of state machines, and test case generation. State machines are both, programs and specifications; exactly the same code works as a program and as its specification. In this way, with a few additions, a CLP language turned into a seamlessly integrated programming and automated proof system.

This technical note shows how we have combined prescriptive type checking and constraint solving to increase automation during software verification. We do so by defining a type system and implementing a typechecker for $\{log\}$ (read ‘setlog’), a Constraint Logic Programming language and satisfiability solver based on set theory. The constraint solver is proved to be safe w.r.t. the type system. Two industrial-strength case studies are presented where this combination is used with very good results.

Formal reasoning about finite sets and cardinality is important for many applications, including software verification, where very often one needs to reason about the size of a given data structure. The Constraint Logic Programming tool $$\{ log\} $$ provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, although it does not provide cardinality constraints. In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into $$\{ log\} $$. The proposed solver is proved to be a decision procedure for its formulas. Besides, the new CLP instance is implemented as part of the $$\{ log\} $$ tool. In turn, the implementation uses Howe and King’s Prolog SAT solver and Prolog’s CLP(Q) library, as an integer linear programming solver. The empirical evaluation of this implementation based on +250 real verification conditions shows that it can be useful in practice.

Under consideration in Theory and Practice of Logic Programming (TPLP)

Partial functions are common abstractions in formal specification notations such as Z, B and Alloy. Conversely, executable programming languages usually provide little or no support for them. In this paper we propose to add partial functions as a primitive feature to a Constraint Logic Programming (CLP) language, namely {log}. Although partial functions could be programmed on top of {log}, providing them as first-class citizens adds valuable flexibility and generality to the form of set-theoretic formulas that the language can safely deal with. In particular, the paper shows how the {log} constraint solver is naturally extended in order to accommodate for the new primitive constraints dealing with partial functions. Efficiency of the new version is empirically assessed by running a number of non-trivial set-theoretical goals involving partial functions, obtained from specifications written in Z.