Constructive Data Refinement in Typed Lambda Calculus (2000)
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@MISC{Honsell00constructivedata,
author = {Furio Honsell and John Longley and Donald Sannella and Andrzej Tarlecki},
title = {Constructive Data Refinement in Typed Lambda Calculus},
year = {2000}
}
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Abstract
. A new treatment of data refinement in typed lambda calculus is proposed, based on pre-logical relations [HS99] rather than logical relations as in [Ten94], and incorporating a constructive element. Constructive data refinement is shown to have desirable properties, and a substantial example of refinement is presented. 1 Introduction Various treatments of data refinement in the context of typed lambda calculus, beginning with Tennent's in [Ten94], have used logical relations to formalize the intuitive notion of refinement. This work has its roots in [Hoa72], which proposes that the correctness of a concrete version of an abstract program be verified using an invariant on the domain of concrete values together with a function mapping concrete values (that satisfy the invariant) to abstract values. In algebraic terms, what is required is a homomorphism from a subalgebra of the concrete algebra to the abstract algebra. A strictly more general method is to take a homomorphic relatio...
