C.B. Jay, Long fij Normal Forms and Confluence, Tech. Rep. ECS-LFCS91 -183 (and its revised version).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....idea of using expansion rules seems to have passed unnoticed for a long time, even if the so called j long normal forms were well known and used in the study of higher order unification problems [Hue76] only in these last years there has been a renewed interest in expansion rules. In recent work [Jay92], still motivated by category theoretic investigation, Jay explores a simply typed 1 See [Bar84] p. 403 409 for a short history and references. 2 This is the Unit type in languages like ML. 3 The same idea is present in [Min77] 3 calculus with just T and a natural number type N as base ....

....recent related works are [Dou93] who provides another proof of confluence and strong normalization, and [Aka93] where an interesting divide and conquer approach is proposed to prove the same properties. 2. 1 Our work The present paper is inspired by all the previous works, but especially by [Jay92] and [PV87] We use expansion rules to provide a confluent rewriting system for the typed calculus with not only products and terminal object, but also sums and recursion. This result is derived from the confluence of a restricted system where recursion is bounded (recursive calls of infinite ....

C. B. Jay. Long fij normal forms and confluence (and its revised version). Technical Report ECS-LFCS-91-183, LFCS, University of Edimburgh, 1992.

.... literature[13] Expansion of a value to reflect its type has been used by Danvy, Malmkjaer and Palsberg to perform binding time improvements[11] The technique of using expansion reduction systems to reach normal forms is well known in the rewriting community, especially the use of eta expansion[17]. Recent work has used such techniques to construct the inverse of the evaluation functional[2] and to demonstrate that every term (in a combinator form) of system F has a normal form[1] In the latter work, a constructive proof is used to extract an ML program remarkably similar to the ....

C. B. Jay. Long fij normal forms and confluence (revised). Technical Report ECS-LFCS-91-183, Department of Computer Science, University of Edinburgh, June 1992. revised version available at http://theory.doc.ic.ac.uk/tfm/papers/JayCB/longbetaeta. dvi.Z.

.... exp;0 , the system with labelled fixed point constants and no algebraic rules, is confluent and strongly normalizing, either by adapting the logical relations proof discussed previously, or by modifying the proof for a similar system (with iteration instead of labelled fix reduction) given by Jay [27], which is based on Girard s candidats de reducibilit e. The normal forms in this strongly normalizing system are known as long normal forms; for example, the long normal form of a variable f : ae oe Theta , where oe and are base types, is lnf (f) j x: ae: h 1 (fx) 2 (fx)i. Using long ....

C.B. Jay. Long fij normal forms and confluence. Technical Report ECS-LFCS-91-183, Laboratory for Foundations of Computer Science, Department of Computer Science, University of Edinburgh, October 1991.

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C.B. Jay, Long fij Normal Forms and Confluence, Tech. Rep. ECS-LFCS91 -183 (and its revised version).

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C.B. Jay, Long fij normal forms and confluence (revised) preprint.

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C. B. Jay. Long fij normal forms and confluence (and its revised version). Technical Report ECS-LFCS-91-183, LFCS, University of Edimburgh, 1992.

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