On generic context lemmas for lambda calculi with sharing

  • This paper proves several generic variants of context lemmas and thus contributes to improving the tools to develop observational semantics that is based on a reduction semantics for a language. The context lemmas are provided for may- as well as two variants of mustconvergence and a wide class of extended lambda calculi, which satisfy certain abstract conditions. The calculi must have a form of node sharing, e.g. plain beta reduction is not permitted. There are two variants, weakly sharing calculi, where the beta-reduction is only permitted for arguments that are variables, and strongly sharing calculi, which roughly correspond to call-by-need calculi, where beta-reduction is completely replaced by a sharing variant. The calculi must obey three abstract assumptions, which are in general easily recognizable given the syntax and the reduction rules. The generic context lemmas have as instances several context lemmas already proved in the literature for specific lambda calculi with sharing. The scope of the generic context lemmas comprises not only call-by-need calculi, but also call-by-value calculi with a form of built-in sharing. Investigations in other, new variants of extended lambda-calculi with sharing, where the language or the reduction rules and/or strategy varies, will be simplified by our result, since specific context lemmas are immediately derivable from the generic context lemma, provided our abstract conditions are met.

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Author:Manfred Schmidt-SchaußORCiDGND, David SabelORCiDGND
Parent Title (German):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 27
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (27)
Publisher:Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
Place of publication:Frankfurt [am Main]
Document Type:Working Paper
Date of Publication (online):2007/01/06
Date of first Publication:2007/01/06
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2007/02/28
Tag:context lemma; functional programming languages; lambda calculus; observational semantics
Issue:Version: 6. Januar 2007
Page Number:17
Last Page:17
HeBIS-PPN:291844286 (rev. version)
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht