Normal proofs and their grammar

M. Takahashi, Y. Akama, Sachio Hirokawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

First we give a grammatical (or equational) description of the set {M normal form │ Γ ⊢ M : A} for a given basis Γ and a given type A in the simple type system, and give some applications of the description. Then we extend the idea to systems in λ-cube and more generally to normalizing pure type systems. The attempt resulted in derived (or ‘macro’) rules the totality of which is sound and complete for type assignments of normal terms. A feature of the derived rules is that they reflect the syntactic structure of legal terms in normal form, and thus they may give us more global view than the original definition of the systems.

Original languageEnglish
Title of host publicationTheoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings
EditorsJohn C. Mitchell, Masami Hagiya
PublisherSpringer Verlag
Pages465-493
Number of pages29
ISBN (Print)9783540578871
Publication statusPublished - Jan 1 1994
Event2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994 - Sendai, Japan
Duration: Apr 19 1994Apr 22 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume789 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994
CountryJapan
CitySendai
Period4/19/944/22/94

Fingerprint

Syntactics
Type Systems
Grammar
Normal Form
Macros
Acoustic waves
Term
Regular hexahedron
Assignment
Syntax
Sound

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Takahashi, M., Akama, Y., & Hirokawa, S. (1994). Normal proofs and their grammar. In J. C. Mitchell, & M. Hagiya (Eds.), Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings (pp. 465-493). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 789 LNCS). Springer Verlag.

Normal proofs and their grammar. / Takahashi, M.; Akama, Y.; Hirokawa, Sachio.

Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings. ed. / John C. Mitchell; Masami Hagiya. Springer Verlag, 1994. p. 465-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 789 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Takahashi, M, Akama, Y & Hirokawa, S 1994, Normal proofs and their grammar. in JC Mitchell & M Hagiya (eds), Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 789 LNCS, Springer Verlag, pp. 465-493, 2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994, Sendai, Japan, 4/19/94.
Takahashi M, Akama Y, Hirokawa S. Normal proofs and their grammar. In Mitchell JC, Hagiya M, editors, Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings. Springer Verlag. 1994. p. 465-493. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Takahashi, M. ; Akama, Y. ; Hirokawa, Sachio. / Normal proofs and their grammar. Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings. editor / John C. Mitchell ; Masami Hagiya. Springer Verlag, 1994. pp. 465-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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