Proofs for Free - Parametricity for dependent types
Journal article, 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.

Lexicon extraction

Shahmukhi

Morphology

Corpus building

Punjabi

Author

Jean-Philippe Bernardy

Chalmers, Computer Science and Engineering (Chalmers), Software Technology (Chalmers)

University of Gothenburg

Patrik Jansson

Chalmers, Computer Science and Engineering (Chalmers), Software Technology (Chalmers)

University of Gothenburg

Ross Paterson

City University

Journal of Functional Programming

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

Vol. 22 2 107-152

Areas of Advance

Information and Communication Technology

Roots

Basic sciences

Subject Categories

Computer Science

DOI

10.1017/S0956796812000056