@inproceedings{39f414701a2e491ab00a3bbead0b32b1,
title = "Principal type-schemes of BCI-lambda-terms",
abstract = "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.",
author = "Sachio Hirokawa",
year = "1991",
month = jan,
day = "1",
doi = "10.1007/3-540-54415-1_68",
language = "English",
isbn = "9783540544159",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "633--650",
editor = "Meyer, {Albert R.} and Takayasu Ito",
booktitle = "Theoretical Aspects of Computer Software - International Conference TACS 1991, Proceedings",
address = "Germany",
note = "1st International Conference on Theoretical Aspects of Computer Software, TACS 1991 ; Conference date: 24-09-1991 Through 27-09-1991",
}