Proof-relevant parametricity

Ghani, Neil and Nordvall Forsberg, Fredrik and Orsanigo, Federico; Lindley, Sam and McBride, Conor and Trinder, Phil and Sannella, Don, eds. (2016) Proof-relevant parametricity. In: A List of Successes That Can Change the World. Lecture Notes in Computer Science . Springer-Verlag, Switzerland, pp. 109-131. ISBN 9783319309354 (https://doi.org/10.1007/978-3-319-30936-1_6)

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Abstract

Parametricity is one of the foundational principles which underpin our understanding of modern programming languages. Roughly speaking, parametricity expresses the hidden invariants that programs satisfy by formalising the intuition that programs map related inputs to related outputs. Traditionally parametricity is formulated with proofirrelevant relations but programming in Type Theory requires an extension to proof-relevant relations. But then one might ask: can our proofs that polymorphic functions are parametric be parametric themselves? This paper shows how this can be done and, excitingly, our answer requires a trip into the world of higher dimensional parametricity.

ORCID iDs

Ghani, Neil ORCID logoORCID: https://orcid.org/0000-0002-3988-2560, Nordvall Forsberg, Fredrik ORCID logoORCID: https://orcid.org/0000-0001-6157-9288 and Orsanigo, Federico; Lindley, Sam, McBride, Conor, Trinder, Phil and Sannella, Don
  • Item type:Book Section
    ID code:64286
    Dates:
    Date
    Event
    25 March 2016
    Published
    5 December 2015
    Accepted
    Notes:This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science. The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-30936-1_6
    Keywords:computer science, computers, higher-dimensional, parametricity, polymorphic functions, relevant relations, type theory, artificial intelligence, Electronic computers. Computer science, Computer Science(all), Theoretical Computer Science
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:06 Jun 2018 15:31
    Last modified:11 Dec 2021 01:14
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64286
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