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A unified treatment of syntax with binders

Part of: JFP Research Articles

Published online by Cambridge University Press:  15 August 2012

NICOLAS POUILLARD  and
FRANÇOIS POTTIER
NICOLAS POUILLARD
Affiliation:
INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay, Cedex, France (e-mail: [email protected], [email protected])
FRANÇOIS POTTIER
Affiliation:
INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay, Cedex, France (e-mail: [email protected], [email protected])
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Abstract

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Atoms 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.

Type
Articles
Information
Journal of Functional Programming , Volume 22 , Special Issue 4-5: ICFP 2010 , September 2012 , pp. 614 - 704
Copyright
Copyright © Cambridge University Press 2012

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