A logic programming approach to the verification of functional-logic programs

Abstract

We address in this paper the question of how to verify program properties in modern functional logic languages, where it is allowed the presence of non-deterministic functions with call-time choice semantics. The main problem to face is that for such kind of programs equational reasoning is not valid. We develop some logical conceptual tools providing sound reasoning mechanisms for these programs, in particular for proving properties valid in the initial model of a program. We show how CRWL, a well known logical framework for functional logic programming, can be easily mapped into logic programming, and we use this mapping as a starting point of our work. We explore then how to prove properties of the resulting logic programming translation by means of different existing interactive proof assistants, and afterwards we give some proposals trying to overcome the limitations of the approach, specially with respect to its theoretical strength.

Multi-paradigm Declarative Languages

“…CRWL can be used as the logical foundation of functional logic languages with non-strict nondeterministic operations. It is a basis for the verification of functional logic programs [27] and has been extended in various directions, e.g., higher-order operations [37], algebraic types [17], polymorphic types [35], failure [68], constraints [67] etc. An account on CRWL and its applications can be found in [77].…”

Functional logic programming

“…The formal foundations of functional logic languages are also useful for the development of environments and tools for reasoning about programs. Developments in these areas include tools for program analysis [23], verification [16], partial evaluation [1], profiling [11], debugging [10], and testing [17].…”

A higher-order logical framework for the algorithmic debugging and verification of declarative programs

“…Typically, the proof of declarative properties is difficult to be done by automatic methods, and the help of an interactive proof assistant is very convenient. From the higher-order logical framework GHRC, our starting point is the successful approach considered in [7] for the verification of first-order declarative programs in the context of the CRWL logic. We follow this approach for the new case of higher-order defined functions by CPRS-programs because we think that this approach would be closer to the development of higher-order declarative programs in the Isabelle theorem prover [24,25], as we will argue below.…”