Fast and Loose Reasoning is Morally Correct

Fast and Loose Reasoning is Morally Correct
Nils Anders Danielsson, John Hughes, Patrik Jansson and Jeremy Gibbons
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages (POPL 2006). © ACM, 2006. This is a minor revision of the work published in POPL'06, http://doi.acm.org/10.1145/1111037.1111056. Accompanying technical report. [pdf]

Abstract

Functional programmers often reason about programs as if they were written in a total language, expecting the results to carry over to non-total (partial) languages. We justify such reasoning.

Two languages are defined, one total and one partial, with identical syntax. The semantics of the partial language includes partial and infinite values, and all types are lifted, including the function spaces. A partial equivalence relation (PER) is then defined, the domain of which is the total subset of the partial language. For types not containing function spaces the PER relates equal values, and functions are related if they map related values to related values.

It is proved that if two closed terms have the same semantics in the total language, then they have related semantics in the partial language. It is also shown that the PER gives rise to a bicartesian closed category which can be used to reason about values in the domain of the relation.

(Note that this is a minor revision of the published paper. A small error has been fixed, see Section 11.)

Nils Anders Danielsson
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