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arXiv · 1907.07591

Defining Functions on Equivalence Classes

Lawrence C. Paulson
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Abstract

A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are \emph{equivalence classes}: sets of equivalent concrete values. Simple techniques are presented for defining and reasoning about quotient constructions, based on a general lemma library concerning functions that operate on equivalence classes. The techniques are applied to a definition of the integers from the natural numbers, and then to the definition of a recursive datatype satisfying equational constraints.

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Lawrence C. Paulson. 2019-07-17. Defining Functions on Equivalence Classes. https://doi.org/10.1145/1183278.1183280

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