Recursive Subtyping Revealed (2000) [27 citations — 3 self]
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author = {Vladimir Gapeyev and Michael Levin and Benjamin Pierce},
title = {Recursive Subtyping Revealed},
booktitle = {Journal of Functional Programming},
year = {2000},
pages = {2003}
}
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Abstract:
Algorithms for checking subtyping between recursive types lie at the core of many programming language implementations. But the fundamental theory of these algorithms and how they relate to simpler declarative specifications is not widely understood, due in part to the difficulty of the available introductions to the area. This tutorial paper offers an "end-to-end" introduction to recursive types and subtyping algorithms, from basic theory to efficient implementation, set in the unifying mathematical framework of coinduction. 1. INTRODUCTION Recursively defined types in programming languages and lambda-calculi come in two distinct varieties. Consider, for example, the type X described by the equation X = Nat!(Nat\ThetaX): An element of X is a function that maps a number to a pair consisting of a number and a function of the same form. This type is often written more concisely as X.Nat!(Nat\ThetaX). A variety of familiar recursive types such as lists and trees can be defined analogou...
