H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... root are the unification grammar formalisms FUG [14] and LFG [13] developed for applications in computational linguistics (see [8] for a more recent paper in this area) Another, independent root is Ait Kaci s term calculus [1, 2] which is the basis of several constraint programming languages [3, 4, 5]. Smolka [20] gives a unified logical view of most earlier feature formalisms and studies an expressive feature constraint logic. Feature trees appeared only recently with the work on FT [7, 6] To our knowledge the notion of an arity constraint is new. Carpenter s [8] extensional types are ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

....attempts at doing functional (lazy) evaluating in logic programming, and to work on combining functional relational programming into one framework. An survey of this research area is given in [11] GCLA itself [5,15] is of course one example of a programming system which combines the two styles. [1] classify this kind of research into four main trends: an embedding approach; a syntactic approach; an algebraic approach and a higher order logic approach. Our method should then probably be classified as an example of the syntactic approach, that is we take a program written in some syntax and ....

H. Ait-Kaci, R. Nasr, Integrating Logic and Functional Programming, Lisp and Symbolic Computation, 2 pp 51-89, 1989.

....meets the original specification F . Elsewhere [Pin] we exploit the idea of using definitions to control the applications of the cut rule to give a proof theoretic semantics to integrate logic and functional programming by defining names for deliverables. The language LeFun, as presented in [AKN89], is a programming language that integrates logic and functional programming. In this language a program is a list of logical formulae together with a list of definitions. A definition in LeFun has the form name = def term, thus leaving out the specification the term satisfies as well as a ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

....normally calls answer substitution in logic programming. Although proof search is carried out in a sequent calculus that allows cut elimination a search for a proof does not involve uses of the cut rule or anything corresponding to our definition mechanism. The language LeFun, as presented in [AKN89], is a programming language that integrates logic and functional programming. In this language a program is a list of logical formulae together with a list of definitions of simple type, where a definition is used only to expand out a defined constant. 6 Conclusions Open Problems We have ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

....functional logic languages, mathematical specification, evolving algebras. 1 Introduction Many investigations during the last years have been devoted to the combination of the functional and logic programming paradigms (for surveys on different approaches and proposals, see e.g. DL86] BL86] AN89] The interest of such an integration has been well motivated by several researchers and is presently quite widely accepted. One of the possible approaches to logic functional programming builds so called functional logic languages [Red85, Red87] which are syntactically very similar to ....

H. A it Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

....entailment simplification. One origin of FT is Ait Kaci s term calculus [1] which is at the heart of the programming language LOGIN [3] and further extended in the language LIFE [5] with functions over feature structures thanks to a generalization of the concept of residuation of Le Fun [4]. Other precursors of FT are the feature descriptions found in so called unification grammars [13, 12] developed for natural language processing, and also the formalisms of Mukai [17, 18] These early feature structure formalism were presented in a nonlogical form. Major steps in the process of ....

....constructor constraints; for instance, the constructor constraint x : A(y; z) can be expressed equivalently as Ax xf1; 2g x1y x2z, if we assume that A is a sort and the numbers 1; 2 are features. Second, it seems attractive to extend FT such that it can accommodate a sort lattice as used in [1, 3, 4, 5, 23]. One possibility to do this is to assume a partial order on sorts and replace sort constraints Ax with quasi sort constraints [A]x whose declarative semantics is given as [A]x j BA Bx: Given the assumption that the sort ordering has greatest lower bounds if lower bounds exist, it seems that ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

.... root are the unification grammar formalisms FUG [21] and LFG [20] developed for applications in computational linguistics (see [11] for a more recent paper in this area) Another, independent root is Ait Kaci s term calculus [1, 2] which is the basis of several constraint programming languages [4, 5, 6]. Smolka [29] gives a unified logical view of most earlier feature formalisms and studies an expressive feature constraint logic. Feature trees appeared only recently with the work on FT [9, 7] To our knowledge the notion of an arity constraint is new. Carpenter s [11] extensional types are ....

.... The resulting constraint system CFT is a conservative extension of both Prolog II s rational tree system [12, 13] and the feature tree system FT [9, 7] Thus CFT brings together the work on classical tree constraints (e.g. 17, 12, 13, 23, 26] and the work on feature descriptions (e.g. [21, 20, 1, 2, 4, 5, 6, 29, 9, 7, 11]) two lines of research that seemed to be rather far apart in the past. The declarative semantics of CFT was specified both algebraicly (the feature tree structure T ) and logically (the first order theory CFT given by five axiom schemes) For the constraint problems considered in the paper the ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

....entailment simplification. One origin of FT is Ait Kaci s term calculus [1] which is at the heart of the programming language LOGIN [3] and further extended in the language LIFE [5] with functions over feature structures thanks to a generalization of the concept of residuation of Le Fun [4]. Other precursors of FT are the feature descriptions found in so called unification grammars [13, 12] developed for natural language processing, and also the formalisms of Mukai [17, 18] These early feature structure formalism were presented in a nonlogical form. Major steps in the process of ....

....constraints; for instance, the constructor constraint x : A(y; z) can be expressed equivalently as Ax xf1; 2g x1y x2z, if we assume that A is a sort and the numbers 1; 2 are features. Second, it seems attractive to extend FT such that it can accommodate a sort lattice as used in [1, 3, 4, 5, 23]. One possibility to do this is to assume a partial order on sorts and replace sort constraints Ax with quasi sort constraints [A]x whose declarative semantics is given as [A]x j BA Bx: Given the assumption that the sort ordering has greatest lower bounds if lower bounds exist, it seems that ....

H. Ait-Kaci and R. Nasr. Integrating logic and functional programming. Lisp and Symbolic Computation, 2:51--89, 1989.

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