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Type-theory in color

Published: 25 September 2013 Publication History

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.

Supplementary Material

ZIP File (icfp006.pdf.zip)
Appendix B (proof details).

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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
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 25 September 2013

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Author Tags

  1. erasure
  2. parametricity
  3. type-theory

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ICFP'13
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ICFP'13: ACM SIGPLAN International Conference on Functional Programming
September 25 - 27, 2013
Massachusetts, Boston, USA

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ICFP '13 Paper Acceptance Rate 40 of 133 submissions, 30%;
Overall Acceptance Rate 333 of 1,064 submissions, 31%

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October 12 - 18, 2025
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  • (2018)Generic zero-cost reuse for dependent typesProceedings of the ACM on Programming Languages10.1145/32367992:ICFP(1-30)Online publication date: 30-Jul-2018
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