Normal proofs and their grammar

M. Takahashi, Y. Akama, S. Hirokawa

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Citations (Scopus)


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
EditorsMasami Hagiya, John C. Mitchell
PublisherSpringer Verlag
Number of pages29
ISBN (Print)9783540578871
Publication statusPublished - 1994
Event2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994 - Sendai, Japan
Duration: 1994 Apr 191994 Apr 22

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


Conference2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994


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