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Technical Report: DCC-2001-9

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Intersection Types and the Linear Lambda-Calculus

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Mário Florido and Luís Damas^{}

DCC & LIACC
Universidade do Porto
Rua do Campo Alegre, 823 4150 Porto, Portugal
October 2001

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Abstract

In this paper we present a notion of expansion of a term in the lambda-calculus which transforms terms into linear terms. This transformation replaces each occurrence of a variable in the original term by a fresh variable taking into account non-trivial implications in the structure of the term caused by these simple replacements. We then prove that the class of terms which can be expanded is the same of terms typable in an Intersection Type System, i.e., the strongly normalizable terms.
This shows that there is a clear relation between Intersection Types, where a different type is given to different occurrences of the same variable, and linearization, where each occurrence of a shared variable is transformed into a new variable.

**Keywords:** Type systems; Lambda-calculus.