Constraint Functional Logic Programming Research Articles

Applying CP(F D), CLP(F D) and CFLP(F D) to a Real-life Employee Timetabling Problem

This paper presents a case study based on a real-life Employee Timetabling Problem, formulating it and then making a com- parison of its modeling and solution with three different programming paradigms embedding Finite Domain constraint solving: Constraint Programming, Constraint Logic Programming and Constraint Functional Logic Programming. The analysis uses the systems Gecode, SICStus clpfd and TOY(F D) (with its two different versions relying on the Gecode and SICStus solvers, resp.) The modeling comparison via code examples points out the different abstraction levels the systems allow. The solving comparison uses different order-of-magnitude instances to perform a head-to-head comparison among the different systems.

A Theoretical Framework for the Higher-Order Cooperation of Numeric Constraint Domains

This paper presents a theoretical framework for the integration of the cooperative constraint solving of numeric constraint domains into higher-order functional and logic programming on λ-abstractions, using an instance of a generic Constraint Functional Logic Programming (CFLP) scheme over a so-called higher-order coordination domain. We provide this framework as a powerful computational model for the higher-order cooperation of algebraic constraint domains over real numbers and integers, which has been useful in practical applications involving the hybrid combination of its components, so that more declarative and efficient solutions can be promoted. Our proposal of computational model has been proved sound and complete with respect to the declarative semantics provided by the CFLP scheme, and enriched with new mechanisms for modeling the intended cooperation among the numeric domains and a novel higher-order constraint domain equipped with a sound and complete constraint solver for solving higher-order equations. We argue the applicability of our approach describing a prototype implementation on top of the constraint functional logic system TOY.

TOY: A System for Experimenting with Cooperation of Constraint Domains

This paper presents, from a user point-of-view, the mechanism of cooperation between constraint domains that is currently part of the system TOY, an implementation of a constraint functional logic programming scheme. This implementation follows a cooperative goal solving calculus based on lazy narrowing. It manages the invocation of solvers for each domain, and projection operations for converting constraints into mate domains via mediatorial constraints. We implemented the cooperation among Herbrand, real arithmetic (R), finite domain (FD) and set (S) domains. We provide two mediatorial constraints: The first one relates the numeric domains FD and R, and the second one relates FD and S.

A Logical Framework for Debugging in Declarative Constraint Programming

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.

On the cooperation of the constraint domains ℋ, ℛ, and ℱ in CFLP

AbstractThis paper presents a computational model for the cooperation of constraint domains and an implementation for a particular case of practical importance. The computational model supports declarative programming with lazy and possibly higher-order functions, predicates, and the cooperation of different constraint domains equipped with their respective solvers, relying on a so-called constraint functional logic programming (CFLP) scheme. The implementation has been developed on top of theCFLPsystem, supporting the cooperation of the three domains ℋ, ℛ, and ℱ, which supply equality and disequality constraints over symbolic terms, arithmetic constraints over the real numbers, and finite domain constraints over the integers, respectively. The computational model has been proved sound and complete w.r.t. the declarative semantics provided by theCFLPscheme, while the implemented system has been tested with a set of benchmarks and shown to behave quite efficiently in comparison to the closest related approach we are aware of.

Constraint functional logic programming over finite domains

AbstractIn this paper, we present our proposal to Constraint Functional Logic Programming over Finite Domains (CFLP($\fd$)) with a lazy functional logic programming language which seamlessly embodies finite domain ($\fd$) constraints. This proposal increases the expressiveness and power of constraint logic programming over finite domains (CLP($\fd$)) by combining functional and relational notation, curried expressions, higher-order functions, patterns, partial applications, non-determinism, lazy evaluation, logical variables, types, domain variables, constraint composition, and finite domain constraints. We describe the syntax of the language, its type discipline, and its declarative and operational semantics. We also describe\toy(fd)$, an implementation forCFLP($\fd$), and a comparison of our approach with respect toCLP($\fd$) from a programming point of view, showing the new features we introduce. And, finally, we show a performance analysis which demonstrates that our implementation is competitive with respect to existingCLP($\fd$) systems and that clearly outperforms the closer approach toCFLP($\fd$).

A Proposal for the Cooperation of Solvers in Constraint Functional Logic Programming

This paper presents a proposal for the cooperation of solvers in constraint functional logic programming, a quite expressive programming paradigm which combines functional, logic and constraint programming using constraint lazy narrowing as goal solving mechanism. Cooperation of solvers for different constraint domains can improve the efficiency of implementations since solvers can take advantage of other solvers' deductions. We restrict our attention to the cooperation of three solvers, dealing with syntactic equality and disequality constraints, real arithmetic constraints, and finite domain (FD) constraints, respectively. As cooperation mechanism, we consider to propagate to the real solver the constraints which have been submitted to the FD solver (and viceversa), imposing special communication constraints to ensure that both solvers will allow the same integer values for all the variables involved in the cooperation.

Programmed Search in a Timetabling Problem over Finite Domains

Labeling is crucial in the performance of solving timetabling problems with constraint programming. Traditionally, labeling strategies are based on static and dynamic information about variables and their domains, and selecting variables and values to assign. However, the size of combinatorial problems tractable by these techniques is limited. In this paper, we present a real problem solved with constraint programming using programmed search based on the knowledge about the solution structure as a starting point for classical propagation and labeling techniques to find a feasible solution. For those problems in which solutions are close to the seed because of its structure, propagation and labeling can reach a first solution within a small response time. We apply our approach to a real timetabling problem, and we tackle its implementation with two different languages, OPL and TOY, using the constraint programming paradigm over finite domains. While OPL is a commercial, algebraic, and specific-purpose constraint programming language, TOY is a prototype of a general-purpose constraint functional logic programming language. We present the specification of the problem, its implementation with both languages, and a comparative performance analysis.

A Fully Sound Goal Solving Calculus for the Cooperation of Solvers in the [formula omitted] Scheme

The CFLP scheme for Constraint Functional Logic Programming has instances CFLP(D) corresponding to different constraint domains D. In this paper, we propose an amalgamated sum construction for building coordination domains C, suitable to represent the cooperation among several constraint domains D1,…,Dn via a mediatorial domain M. Moreover, we present a cooperative goal solving calculus for CFLP(C), based on lazy narrowing, invocation of solvers for the different domains Di involved in the coordination domain C, and projection operations for converting Di constraints into Dj constraints with the aid of mediatorial constraints (so-called bridges) supplied by M. Under natural correctness assumptions for the projection operations, the cooperative goal solving calculus can be proved fully sound w.r.t. the declarative semantics of CFLP(C). As a relevant concrete instance of our proposal, we consider the cooperation between Herbrand, real arithmetic and finite domain constraints.

A new generic scheme for functional logic programming with constraints

In this paper we propose a new generic scheme CFLP?, intended as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain ?. As in the case of the well known CLP? scheme for Constraint Logic Programming, ? is assumed to provide domain specific data values and constraints. CFLP? programs are presented as sets of constrained rewrite rules that define the behavior of possibly higher order and/or non-deterministic lazy functions over ?. As a main novelty w.r.t. previous related work, we present a Constraint Rewriting Logic CRWL? which provides a declarative semantics for CFLP? programs. This logic relies on a new formalization of constraint domains and program interpretations, which allows a flexible combination of domain specific data values and user defined data constructors, as well as a functional view of constraints.

Constraint Functional Logic Programming Revisited

In this paper we propose a new generic scheme CFLP(D), intended as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain D. As in the case of the well known CLP(D) scheme for Constraint Logic Programming, D is assumed to provide domain specific data values and constraints. CFLP(D) programs are presented as sets of constrained rewrite rules that define the behaviour of possibly higher order and/or non-deterministic lazy functions over D. As the main novelty w.r.t. previous related work, we present a Constraint Rewriting Logic CRWL(D) which provides a declarative semantics for CFLP(D) programs. This logic relies on a new formalization of constraint domains and program interpretations, which allows a flexible combination of domain specific data values and user defined data constructors, as well as a functional view of constraints.

An open environment for cooperative equational solving

We describe a system called CFLP which aims at the integration of the best features of functional logic programming (FLP), cooperative constraint solving (CCS), and distributed computing. FLP provides support for defining one’s own abstractions over a constraint domain in an easy and comfortable way, whereas CCS is employed to solve systems of mixed constraints by iterating specialized constraint solving methods in accordance with a well defined strategy. The system is a distributed implementation of a cooperative constraint functional logic programming scheme that combines higher-order lazy narrowing with cooperative constraint solving. The model takes advantage of the existence of several constraint solving resources located in a distributed environment (e. g., a network of computers), which communicate asynchronously via message passing. To increase the openness of the system, we are redesigning CFLP based on CORBA. We discuss some design and implementation issues of the system.