Article

Step-Indexed syntactic logical relations for recursive and quantified types

Author:

Amal AhmedAuthors Info & Claims

ESOP'06: Proceedings of the 15th European conference on Programming Languages and Systems

Pages 69 - 83

https://doi.org/10.1007/11693024_6

Published: 27 March 2006 Publication History

Abstract

We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a λ-calculus with recursive types and impredicative universal and existential types. Our development builds on the step-indexed PER model of recursive types presented by Appel and McAllester. We have discovered that a direct proof of transitivity of that model does not go through, leaving the “PER” status of the model in question. We show how to extend the Appel-McAllester model to obtain a logical relation that we can prove is transitive, as well as sound and complete with respect to contextual equivalence. We then augment this model to support relational reasoning in the presence of quantified types.

Step-indexed relations are indexed not just by types, but also by the number of steps available for future evaluation. This stratification is essential for handling various circularities, from recursive functions, to recursive types, to impredicative polymorphism. The resulting construction is more elementary than existing logical relations which require complex machinery such as domain theory, admissibility, syntactic minimal invariance, and ⊤⊤-closure.

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cover image Guide Proceedings

ESOP'06: Proceedings of the 15th European conference on Programming Languages and Systems

March 2006

342 pages

ISBN:354033095X

Editor:
Peter Sestoft
IT University of Copenhagen, Denmark

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 27 March 2006

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Gierczak OMenon LDimoulas CAhmed A(2024)Gradually Typed Languages Should Be Vigilant!Proceedings of the ACM on Programming Languages10.1145/36498428:OOPSLA1(864-892)Online publication date: 29-Apr-2024
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