Intersection Types for Unboundedness Problems

Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for describing quantitative properties of simply typed lambda-t...

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Bibliographic Details
Main Author: Paweł Parys
Format: Article
Language:English
Published: Open Publishing Association 2019-04-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1904.10105v1
Description
Summary:Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for describing quantitative properties of simply typed lambda-terms. We present two type systems. The first allows to estimate (by appropriately defined value of a derivation) the number of appearances of a fixed constant 'a' in the beta-normal form of a considered lambda-term. The second type system is more complicated, and allows to estimate the maximal number of appearances of the constant 'a' on a single branch.
ISSN:2075-2180