M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of ISSAC'89.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....provers like Prolog [21] or Isabelle [25] In particular, he extended to the higher order case the decidability result of Knuth and Bendix about local confluence of first order term rewrite systems. 1 At the same time, after the works of Breazu Tannen [6] Breazu Tannen and Gallier [7] and Okada [24] on the combination of Church s simply typed calculus with first order term rewriting, Jouannaud and Okada introduced higher order algebraic specification languages [11, 12] to provide a computational model for typed functional languages extended with first order and higher order rewrite ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of ISSAC'89, ACM Press.

....on the term formation. It is of course important to provide a typed version of the calculus in order, in particular, to insure termination of the evaluation of well typed terms. When dealing with the combination of term rewriting and calculus, the rst such result was obtained in [GBT89] and [Oka89] One of the originalities of the calculus with respect to the previous approaches is that we consider only one calculus by opposition to the situation where the two frameworks of calculus and rewriting are combined. We are here in a di erent situation where rewriting (and not the ....

M. Okada. Strong normalizability for the combined system of the typed Lambda-calculus and an arbitrary convergent term rewrite system. In Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, Portland (Oregon), pages 357-363. ACM Press, July 1989. Report CRIN 89-R-220.

....tactics and tacticals. It is of course important to provide a typed version of the calculus in order, in particular, to insure termination of the evaluation of well typed terms. When dealing with the combination of term rewriting and calculus, the rst such result was obtained in [GBT89] and [Oka89] One of the originalities of the calculus with respect to the previous approaches is that we consider only one calculus by opposition to the situation where the two frameworks of calculus and rewriting are combined. We are here in a di erent situation where rewriting (and not the ....

M. Okada. Strong normalizability for the combined system of the typed Lambda-calculus and an arbitrary convergent term rewrite system. In Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, Portland (Oregon), pages 357-363. ACM Press, July 1989. Report CRIN 89-R-220.

....Investigation of the interaction between first order and higher order equational reasoning has emerged as an active line of research. The collective import of a recent series of papers, originating with [Bre88] and including (among others) Bar90] BG91a] BG91b] Dou92] JO91] and [Oka89], is that when various typed calculi are enriched by first order equational theories, the validity problem is well behaved, and furthermore that the respective computational approaches to verifying equations (fi reduction and term rewriting) interact in a modular fashion. This paper is ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent rewrite system. Proceedings, ISSAC 89, 1989.

....properties of its components, for example, combinations of manysorted rst order term rewriting systems and simply typed calculus are modular with respect to conAEuence and termination. These properties have been studied for a variety of combinations of term rewriting systems and calculi [6, 7, 8, 31, 1, 19, 10, 3, 2, 5]. Our aim is to show that a programming language based on a combination of calculus and term rewriting can be modeled in a uniform way using interaction nets. For this we will de ne a translation function that transforms an algebraic functional program into an interaction net program that ....

M. Okada. Strong normalizability for the combined systems of typed lambda calculus and an arbitrary convergent term rewrite system. In Proceedings of the 20th Int. Symp. on Symbolic and Algebraic Computation, Portland, 1989.

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M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of the 1989 Int. Symp. on Symbolic and Algebraic Computation, ACM Press.

....side recursive calls are structurally smaller than the left hand side call [12] His notion is very abstract, though, and relies on a well foundedness assumption which is satisfied in practice. Concurrently, following the pioneering works of Tannen [8] Tannen and Gallier [9,10] and Okada [40], the last two authors of the present paper proposed another solution, for a polymorphically typed calculus, based on pattern matching functional definitions following the so called General Schema [27,28] This work was then generalized so as to cover the full Calculus of Constructions [1 3] ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of the 1989 Int. Symp. on Symbolic and Algebraic Computation, ACM Press.

....is the strong normalization property of inductive data type systems, in case of a simple type discipline. 1 Introduction The recent years have seen a proliferation of formalisms for programming and proof development. The present paper is a contribution towards their unification in the lines of [6, 17]. Our goal is to argue in favor of a language which borrows from algebraic languages like OBJ their structuring mechanisms as well as functional definitions by pattern matching, from functional programming the possibility of defining functions by recursion, and from type theory the Curry Howard ....

Mitsuhiro Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of the 20th Int. Symp. on Symbolic and Algebraic Computation, Portland, Oregon, 1989. 15

....by pattern matching, provided all righthand side recursive calls are structurally smaller than the lefthand side call [12] His notion is very abstract, though, and relies on a well foundedness assumption which is satisfied in practice. Concurrently, following the pioneering work of Tannen [7, 8, 39, 9], the last two authors of the present paper proposed another solution, for a polymorphically typed calculus, based on pattern matching functional definitions following the so called General Schema [26, 27] This work was then generalized so as to cover the full Calculus of Constructions [1, 2, ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In G. H. Gonnet, editor, Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, pages 357--363. ACM Press, July 1989.

....work further by combining it with the work of Barbanera and his coauthors. Breazu Tannen was the first to advocate for combining (simply typed) calculus with (firstorder) algebraic rewriting [8] This work had a strong influence, and developed into a whole area to which many contributed (e.g. [10, 24, 1, 2, 7]) Since the present paper is by no means a survey of this subfield, we do not intend to give a full account of the literature on the subject. A partial account can be found in [22, 3] The present development was also influenced by the Coq group s view that inductive types play an important role ....

....we have function symbols defined by rewrite rules, to prove the main lemma for strong normalization, we need to prove that the application of a function symbol to computable arguments yield a computable term. The case of the first order function symbols has first been treated in [9, 10] and in [24] independently. We will not restate it here and refer the reader to [22] Before to give the proof for the higher order function symbols, we need to prove that an accessible subterm of a computable term is also computable. Lemma 21 (Compatibility of accessibility with computability) Assume that a ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In G. H. Gonnet, editor, Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, pages 357--363. ACM Press, July 1989.

.... R[fi T 0 Gamma M : T 0 Since the pioneer work by Breazu Tannen in 1988 [5] on the confluence of the combination of the simply typed calculus with first order algebraic rewriting, soon followed, as for the strong normalization, by Breazu Tannen and Gallier [6] and, independently, by Okada [21], this question has been very active. We started our program at the beginning of the decade, by developing the notion of abstract data type system [18] in which the user defined computations could be described by using rewrite rules belonging to the so called General Schema, a generalization of ....

M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In G. H. Gonnet, editor, Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, pages 357--363. ACM Press, July 1989.

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M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of ISSAC'89.

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Okada, M.: Strong Normalizability for the Combined System of the Typed Lambda Calculus and an Arbitrary Convergent Term Rewrite System, Proceedings of the 1989 International Symposium on Symbolic and Algebraic Computation, ACM Press.

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M. Okada. Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system. In Proc. of the 1989 Int. Symp. on Symbolic and Algebraic Computation, , ACM Press. C. Paulin-Mohring. Extracting F#'s programs from proofs in the Calculus of Constructions. In Proc. of the 16th ACM Symp. on Principles of Programming Languages, 1989.

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