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Type-theory in color

Published:25 September 2013Publication History
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Abstract

Dependent type-theory aims to become the standard way to formalize mathematics at the same time as displacing traditional platforms for high-assurance programming. However, current implementations of type theory are still lacking, in the sense that some obvious truths require explicit proofs, making type-theory awkward to use for many applications, both in formalization and programming. In particular, notions of erasure are poorly supported.

In this paper we propose an extension of type-theory with colored terms, color erasure and interpretation of colored types as predicates. The result is a more powerful type-theory: some definitions and proofs may be omitted as they become trivial, it becomes easier to program with precise types, and some parametricity results can be internalized.

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      • Published in

        cover image ACM SIGPLAN Notices
        ACM SIGPLAN Notices  Volume 48, Issue 9
        ICFP '13
        September 2013
        457 pages
        ISSN:0362-1340
        EISSN:1558-1160
        DOI:10.1145/2544174
        Issue’s Table of Contents
        • cover image ACM Conferences
          ICFP '13: Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
          September 2013
          484 pages
          ISBN:9781450323260
          DOI:10.1145/2500365

        Copyright © 2013 ACM

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        New York, NY, United States

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        • Published: 25 September 2013

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