Parametricity and dependent types

Author:

Bernardy Jean-Philippe1,Jansson Patrik1,Paterson Ross2

Affiliation:

1. Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

2. City University, London, United Kingdom

Abstract

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 (in second order predicate logic) about inhabitants of the type. We obtain a similar result for a single lambda calculus (a pure type system), in which terms, types and their relations are expressed. Working within a single system dispenses with the need for an interpretation layer, allowing for an unusually simple presentation. While the unification puts some constraints on the type system (which we spell out), the result applies to many interesting cases, including dependently-typed ones.

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design,Software

Reference34 articles.

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2. }}J.-P. Bernardy. A proof of the abstraction theorem for pure type systems (unary case). http://www.cse.chalmers.se/~bernardy/ParDep/html/Theorem.html 2010. }}J.-P. Bernardy. A proof of the abstraction theorem for pure type systems (unary case). http://www.cse.chalmers.se/~bernardy/ParDep/html/Theorem.html 2010.

3. Testing Polymorphic Properties

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