Functional and Constraint Logic Programming

Abstract

Dpto. Sistemas Informáticos y Programación, UCM, Madrid IntroductionStarting at a seminal paper published by J. Jaffar and J.L. Lassez in 1987 [JL87], Constraint Logic Programming (CLP) has developed as a powerful programming paradigm which supports a clean combination of logic (in the form of Horn clauses) and domain-specific methods for constraint satisfaction, simplification and optimization. The well established mathematical foundations of logic programming [Llo87, Apt90] have been succesfully extended to CLP [JMMS96]. Simultaneously, practical applications of CLP have arisen in many fields. Good introductions to the theory, implementation issues and programming applications of CLP languages can be found in [JM94,MS98]. On the other hand, the combination of logic programming with other declarative programming paradigms (especially functional programming) has been widely investigated during the last decade, leading to useful insights for the design of more expressive declarative languages. The first attempt to combine functional and logic languages was done by J.A. Robinson and E.E. Sibert when proposing the language LOGLISP [RS82]. Some other early proposals for the design of functional + logic languages are described in [De86]. A more recent survey of the operational principles and implementation techniques used for the integration of functions into logic programming can be found in [Han94b].Declarative programming, in the wide sense, should provide a logical semantics for programs. Nevertheless, many of the early proposals for the integration of functional and logic programming had no clear logical basis. Among the logically well-founded approaches, most proposals (as e.g. [JLM84, GM87, Höl89]) have suggested to use equational logic. This allows to represent programs as sets of oriented equations, also known as rewrite rules, whose computational use can rely on a well established theory [DJ90,Klo92,BN98]. Goals (also called queries) for a functional logic program can be represented as systems of equations, and narrowing (a natural combination of rewriting and unification, originally proposed as a theorem proving tool [Sla74, Lan75, Fay79, Hul80]) can be used as a goal solving mechanism.

Multi-paradigm Declarative Languages

“…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].…”

“…Thus, typical applications of constraint logic programming can be covered and combined with features of lazy higherorder programming [10,19,30,31,67,70,77]. As an example demonstrating the compactness obtained by combining constraint programming with higher-order features, consider a solver for SuDoku puzzles 6 with finite domain constraints.…”

“…[7] contains a good survey on more recent evaluation strategies and classes of functional logic programs. [77] is more specialized but reviews the efforts to integrate constraints into functional logic languages.…”

Rewriting and Call-Time Choice: The HO Case

“…Finally, we are not inventing HO FLP, but only contributing to some aspects of its foundation. Then it is not our aim here convincing of the practical interest of HO FLP: other documents [16,26,7,4] contain enough evidences of that. Proofs of the results have been omitted, but can be found at http://gpd.sip.ucm.es/fraguas/papers/flops08long.pdf.…”

“…To the best of our knowledge, the only works where such combination has been addressed as to explain consistently the behavior of the program above are those related to HOCRWL [7,8], an extension to HO of CRWL 2 [11], a semantic framework specifically devised for FLP with call-time choice semantics for non-determinism (see [26] for a survey of CRWL and its extensions). HOCRWL provides logic and model-theoretic semantics, based on an intensional view of functions, where different descriptions -in the form of HO-patterns-of the same extensional function are distinguished as different data.…”