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Formalising FinFuns -- generating code for functions as data from Isabelle/HOL (2009)
| Venue: | OF LECTURE NOTES IN COMPUTER SCIENCE |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Lochbihler09formalisingfinfuns,
author = {Andreas Lochbihler},
title = {Formalising FinFuns -- generating code for functions as data from Isabelle/HOL},
booktitle = {OF LECTURE NOTES IN COMPUTER SCIENCE},
year = {2009},
pages = {310--326},
publisher = {Springer}
}
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Abstract
FinFuns are total functions that are constant except for a finite set of points, i.e. a generalisation of finite maps. We formalise them in Isabelle/HOL and present how to safely set up Isabelle’s code genera-tor such that operations like equality testing and quantification on FinFuns become executable. On the code output level, FinFuns are explicitly represented by constant functions and pointwise updates, similarly to associative lists. Inside the logic, they behave like ordinary functions with extensionality. Via the update/constant pattern, a recursion combinator and an induction rule for FinFuns allow for defining and reasoning about operators on FinFuns that directly become executable. We apply the approach to an executable formalisation of sets and use it for the semantics for a subset of concurrent Java.
Keyphrases
isabelle hol equality testing fi-nite set as-sociative list isabelle code genera-tor induction rule total function executable formalisation code output level fin-funs become finite map recursion combinator finfuns allow update constant pattern concurrent java pointwise update constant function ordinary function
