A Logical Framework for Debugging in Declarative Constraint Programming

Abstract

We present a logical and semantic framework for diagnosing wrong computed answers in CFLP(D), a newly proposed generic scheme for lazy Constraint Functional Logic Programming which can be instantiated by any constraint domain D given as parameter, and supports a powerful combination of functional and constraint logic programming over D. Our approach extends and combines declarative debugging techniques previously developed for less expressive programming paradigms, namely the CLP(D) scheme and lazy functional logic languages. Debugging starts with the observation of a wrong computed answer which the user regards as incorrect w.r.t. an intended model that provides a declarative description of the program's semantics. Debugging proceeds by exploring an abridged proof tree that provides a purely declarative view of the computation, so that the user does not need to understand the complex underlying operational mechanisms. Debugging ends with the detection of a function rule in the program that is incorrect w.r.t. the intended model. We prove the logical correctness of the debugging method for any sound CFLP(D)-system whose computed answers are logical consequences of the program, and we describe a practical tool which implements the debugging method for the domain of arithmetic constraints over the real numbers.