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**1 - 3**of**3**### Imagining CLP(Λ,≡αβ)

, 1995

"... . We study under which conditions the domain of -terms () and the equality theory of the -calculus (j fffi ) form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom j, and the formula language must depart from Horn clause ..."

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. We study under which conditions the domain of -terms () and the equality theory of the -calculus (j fffi ) form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom j, and the formula language must depart from Horn clauses and accept universal quantifications and implications in goals. In short, CLP(, j fffi ) must be close to Prolog. 1 Introduction Logic programming is a programming paradigm in which programs are logical formulas, and executing them amounts to search for a proof. The most famous practical incarnation of logic programming is Prolog, which is based on Horn formulas [31]. The formalism of Horn programs is computationally complete [1, 49], but one has often tried to augment it to gain more flexibility and expressivity. One of these attempts is the paradigm of constraint logic programming [11, 27, 10, 50]. It amounts to replacing unification of first-order terms, considered as a procedure for s...

### I R I S a

, 1994

"... : We study under which conditions the domain of -terms () and the equality theory of the -calculus (j fffi ) form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom j, and the formula language must depart from Horn clause ..."

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: We study under which conditions the domain of -terms () and the equality theory of the -calculus (j fffi ) form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom j, and the formula language must depart from Horn clauses and accept universal quantifications and implications in goals. In short, CLP(, j fffi ) must be close to Prolog. Key-words: CLP, -Calculus, Prolog (R'esum'e : tsvp) ridoux@irisa.fr Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universite de Rennes 1 -- Insa de Rennes et en Automatique -- unite de recherche de Rennes Imaginons CLP(,j fffi ) R'esum'e : Nous 'etudions sous quelles conditions le domaine des -termes () et la th'eorie de l"egalit'e du -calcul (j fffi ) forment une base utilisable pour un langage de programmation logique par contrainte (CLP). Les conditions sont que la th'eorie de l"egalit'e doit aussi contenir l'axio...

### The Compilation of λProlog and its Execution with MALI

, 1993

"... We present a compiled implementation of λProlog that uses the abstract memory MALI for representing the execution state. λProlog is a logic programming language allowing a more general clause form than Standard Prolog's (namely hereditary Harrop formulas instead of Horn formulas) and using simply ty ..."

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We present a compiled implementation of λProlog that uses the abstract memory MALI for representing the execution state. λProlog is a logic programming language allowing a more general clause form than Standard Prolog's (namely hereditary Harrop formulas instead of Horn formulas) and using simply typed λ-terms as a term domain instead of first order terms. The augmented clause form causes the program (a set of clauses) and the signature (a set of constants) to be changeable in a very disciplined way. The new term domain has a semi-decidable and infinitary unification theory, and it introduces the need for a fi-reduction operation at run-time. MALI is an abstract memory that is suitable for storing the search-state of depth-first search processes. Its main feature is its efficient memory management. We have used an original λProlog-to-C translation along which predicates are transformed into functions operating on continuations for handling failure and success in unifications, and change...