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Abstract: We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suitable logical relation. This allows us to introduce new types and operations of any order on those types, and to impose equations between terms of any order. Implementations are required to respect... (Update)
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BibTeX entry: (Update)
@inproceedings{ power00logical,
author = "John Power and Edmund Robinson",
title = "Logical Relations and Data Abstraction",
booktitle = "{CSL}",
pages = "497--511",
year = "2000",
url = "citeseer.ist.psu.edu/498498.html" }
Citations (may not include all citations):359 Introduction to higher order categorical logic (context) - Lambek, Scott - 1986
291 Computational Lambda-calculus and Monads - Moggi - 1989
229 Foundations for programming languages (context) - Mitchell - 1996
25 An Axiomatic Approach to Binary Logical Relations with Appli.. - Kinoshita, O'Hearn et al. - 1997
23 An axiomatisation of computationally adequate domain-theoret.. - Fiore, Plotkin - 1994
13 Lax logical relations - Plotkin, Power et al. - 2000
12 Correctness of data representations in ALGOL-like languages (context) - Tennent - 1994
11 abstraction and parametric polymorphism (context) - Ma, Reynolds
3 available as ECS-LFCS (context) - Hermida, Fibrations - 1993
2 A new characterisation of lambda denability (context) - Jung, Tiuryn - 1993
2 A Characterisation of Lambda Denability in Categorical Model.. (context) - Alimohamed - 1995
2 Flum and Rodriguez-Artalejo (context) - Honsell, Sannella - 1999
2 Lecture Notes in Computer Science (context) - Found, Lang - 1991
1 Information Processing 83 Mason (context) - Reynolds - 1983
1 Handbook of Theoretical Computer Science em B (context) - Mitchell - 1990
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