Proofs for Free - Parametricity for dependent types
Artikel i vetenskaplig tidskrift, 2012

Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems: for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic. Our proof gives a computationally meaningful way to interpret that assumption.


Corpus building

Lexicon extraction




Jean-Philippe Bernardy

Chalmers, Data- och informationsteknik, Programvaruteknik

Göteborgs universitet

Patrik Jansson

Chalmers, Data- och informationsteknik, Programvaruteknik

Göteborgs universitet

Ross Paterson

City University London

Journal of Functional Programming

0956-7968 (ISSN) 1469-7653 (eISSN)

Vol. 22 107-152


Informations- och kommunikationsteknik


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Datavetenskap (datalogi)