Nameless, painless

Pouillard, Nicolas

doi:10.1145/2034574.2034817

Cited by 6 publications

(7 citation statements)

References 12 publications

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“…By providing an automatic second step, we hope to spare language designers the effort to adapt Reynolds' (1983) abstraction theorem for new type systems in an ad-hoc way. Indeed, Pouillard (2011) has derived correctness properties of a library for names and binders by following our method.…”

Section: Future Workmentioning

confidence: 99%

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Bernardy¹,

Jansson²,

Paterson³

2012

J. Funct. Prog.

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link: R O S S P A T E R S O NCity University, London, UK (e-mail:)ross@soi.city.ac.uk) AbstractReynolds' abstraction theorem (Reynolds, J. C. (1983) Types, abstraction and parametric polymorphism, Inf. Process. 83(1), 513-523) 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 (PTSs): 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.

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Section: Future Workmentioning

confidence: 99%

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Bernardy¹,

Jansson²,

Paterson³

2012

J. Funct. Prog.

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“…For example, Pouillard [25] describes the following representation for terms, using the AGDA [21] proof assistant:…”

Section: Introductionmentioning

confidence: 99%

A Computational Interpretation of Parametricity

Bernardy

Moulin

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

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Reynolds' abstraction theorem has recently been extended to lambda-calculi with dependent types. In this paper, we show how this theorem can be internalized. More precisely, we describe an extension of Pure Type Systems with a special parametricity rule (with computational content), and prove fundamental properties such as Church-Rosser's and strong normalization. All instances of the abstraction theorem can be both expressed and proved in the calculus itself. Moreover, one can apply parametricity to the parametricity rule: parametricity is itself parametric.

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“…Our previous papers This paper combines and extends two conference papers (Pouillard & Pottier, 2010;Pouillard, 2011a). Here is a summary of the differences between these papers and the present work and of the path that we have followed.…”

Section: Systemsmentioning

confidence: 86%

A unified treatment of syntax with binders

Pouillard¹,

Pottier²

2012

J. Funct. Prog.

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International audienceAtoms and de Bruijn indices are two well-known representation techniques for data structures that involve names and binders. However, using either technique, it is all too easy to make a programming error that causes one name to be used where another was intended. We propose an abstract interface to names and binders that rules out many of these errors. This interface is implemented as a library in Agda. It allows defining and manipulating term representations in nominal style and in de Bruijn style. The programmer is not forced to choose between these styles: on the contrary, the library allows using both styles in the same program, if desired. Whereas indexing the types of names and terms with a natural number is a well-known technique to better control the use of de Bruijn indices, we index types with worlds. Worlds are at the same time more precise and more abstract than natural numbers. Via logical relations and parametricity, we are able to demonstrate in what sense our library is safe, and to obtain theorems for free about world-polymorphic functions. For instance, we prove that a world-polymorphic term transformation function must commute with any renaming of the free variables. The proof is entirely carried out in Agda

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Nameless, painless

Cited by 6 publications

References 12 publications

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A Computational Interpretation of Parametricity

A unified treatment of syntax with binders

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