Principal type-schemes of BCI-lambda-terms

Sachio Hirokawa

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

5 Citations (Scopus)


A BCI-λ-term is a λ-term in which each variable occurs exactly once. It represents a proof figure for implicational formula provable in linear logic. A principal type-scheme is a most general type to the term with respect to substitution. The notion of “relevance relation” is introduced for type-variables in a type. Intuitively an occurrence of a type-variable b is relevant to other occurrence of some type-variable c in a type α, when b is essentially concerned with the deduction of c in α. This relation defines a directed graph G(α) for type-variables in the type. We prove that a type a is a principal type-scheme of BCI-λ-term iff (a), (b) and (c) holds: (a) Each variable occurring in α occurs exactly twice and the occurrences have opposite sign. (b) G(α) is a tree and the right-most type variable in α is its root. (c) For any subtype γ of α, each type variable in γ is relevant to the right-most type variable in γ. A type-schemes of some BCI-λ-term is minimal iff it is not a non-trivial substitution instance of other type-scheme of BCI-λ-term. We prove that the set of BCI-minimal types coincides with the set of principal type-schemes of BCI-λ-terms in βη-normal form.

Original languageEnglish
Title of host publicationTheoretical Aspects of Computer Software - International Conference TACS 1991, Proceedings
EditorsAlbert R. Meyer, Takayasu Ito
PublisherSpringer Verlag
Number of pages18
ISBN (Print)9783540544159
Publication statusPublished - 1991
Externally publishedYes
Event1st International Conference on Theoretical Aspects of Computer Software, TACS 1991 - Sendai, Japan
Duration: Sept 24 1991Sept 27 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume526 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other1st International Conference on Theoretical Aspects of Computer Software, TACS 1991

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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