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Pure Type Systems with Corecursion on Streams: From Finite to Infinitary Normalisation

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conference contribution
posted on 28.10.2013, 15:24 by Paula Severi, Fer-Jan de Vries
In this paper, we use types for ensuring that programs involving streams are well-behaved.We extend pure type systems with a type constructor for streams, a modal operator next and a fixed point operator for expressing corecursion. This extension is called Pure Type Systems with Corecursion (CoPTS). The typed lambda calculus for reactive programs defined by Krishnaswami and Benton can be obtained as a CoPTS. CoPTSs allow us to study a wide range of typed lambda calculi extended with corecursion using only one framework. In particular, we study this extension for the calculus of constructions which is the underlying formal language of Coq. We use the machinery of infinitary rewriting and formalise the idea of well-behaved programs using the concept of infinitary normalisation. The set of finite and infinite terms is defined as a metric completion. We establish a precise connection between the modal operator (• A) and the metric at a syntactic level by relating a variable of type (• A) with the depth of all its occurrences in a term. This syntactic connection between the modal operator and the depth is the key to the proofs of infinitary weak and strong normalisation.

History

Citation

Severi, P.; de Vries, F. ‘Pure Type Systems with Corecursion on Streams: From Finite to Infinitary Normalisation’ in ICFP '12 - Proceedings of the 17th ACM SIGPLAN international conference on Functional programming (© 2012 AMC), pp. 141-152

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Source

The 17th ACM SIGPLAN International Conference on Functional Programming (ICFP 2012), Copenhagen, Denmark

Version

AM (Accepted Manuscript)

Published in

Severi

Publisher

Association for Computing Machinery (ACM)

isbn

978-1-4503-1054-3

Copyright date

2012

Available date

28/10/2013

Publisher version

http://dl.acm.org/citation.cfm?doid=2364527.2364550 http://icfpconference.org/icfp2012/

Temporal coverage: start date

10/09/2012

Temporal coverage: end date

12/09/2012

Language

en