Polyadic approximations, fibrations and intersection types

Starting from an exact correspondence between linear approximations and non-idempotent intersection types, we develop a general framework for building systems of intersection types characterizing normalization properties. We show how this construction, which uses in a fundamental way Melliès and Zei...

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Bibliographic Details
Published in:	Proceedings of ACM on programming languages Vol. 2; no. POPL; pp. 1 - 28
Main Authors:	Mazza, Damiano, Pellissier, Luc, Vial, Pierre
Format:	Journal Article
Language:	English
Published:	ACM 01.01.2018
Subjects:	Computer Science Logic in Computer Science CCS Concepts Linear logic Linear logic, intersection types, type systems, multicategories CCS Concepts: Theory of computation → Type structures Linear logic Linear logic, intersection types, type systems, multicategories Theory of computation → Type structures
ISSN:	2475-1421, 2475-1421
Online Access:	Get full text
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Summary:	Starting from an exact correspondence between linear approximations and non-idempotent intersection types, we develop a general framework for building systems of intersection types characterizing normalization properties. We show how this construction, which uses in a fundamental way Melliès and Zeilberger's ``type systems as functors'' viewpoint, allows us to recover equivalent versions of every well known intersection type system (including Coppo and Dezani's original system, as well as its non-idempotent variants independently introduced by Gardner and de Carvalho). We also show how new systems of intersection types may be built almost automatically in this way.
ISSN:	2475-1421 2475-1421
DOI:	10.1145/3158094