Article

Fast and loose reasoning is morally correct

Authors:

Nils Anders Danielsson,

Patrik Jansson,

Jeremy GibbonsAuthors Info & Claims

POPL '06: Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 206 - 217

https://doi.org/10.1145/1111037.1111056

Published: 11 January 2006 Publication History

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.

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Index Terms

Fast and loose reasoning is morally correct
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

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Published In

cover image ACM Conferences

POPL '06: Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2006

432 pages

ISBN:1595930272

DOI:10.1145/1111037

General Chair:
Greg Morrisett
Harvard University, USA
,
Program Chair:
Simon Peyton Jones
Microsoft Research, UK

ACM SIGPLAN Notices Volume 41, Issue 1
Proceedings of the 2006 POPL Conference
January 2006
421 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1111320
Issue’s Table of Contents

Copyright © 2006 ACM.

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Published: 11 January 2006

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POPL06: The 33rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages 2006

January 11 - 13, 2006

South Carolina, Charleston, USA

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https://dl.acm.org/doi/10.1145/3661814.3662126
Xia YXiao XZhou JGao XPeng Q(2023)A Novel Multi-Domain Adaptation-Based Method for Blast Furnace Anomaly DetectionInternational Journal of Web Services Research10.4018/IJWSR.32675320:1(1-14)Online publication date: 24-Jul-2023
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Li YYin S(2023)User Cold Start Recommendation System Based on Hofstede Cultural TheoryInternational Journal of Web Services Research10.4018/IJWSR.32119920:1(1-17)Online publication date: 19-Apr-2023
https://dl.acm.org/doi/10.4018/IJWSR.321199
Xie XLiu JCao BPeng MKang GWen YFletcher K(2023)A Services Classification Method Based on Heterogeneous Information Networks and Generative Adversarial NetworksInternational Journal of Web Services Research10.4018/IJWSR.31996020:1(1-17)Online publication date: 17-Mar-2023
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