A Proposed Categorial Semantics for Pure ML

Wesley Phoa, Michael P. Fourman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

This paper outlines an approach to modelling the purely functional fragment of ML: it concentrates on the semantics of the Modules system. Our proposed semantics is set-theoretic: types and values are modelled by sets and functions in a topos, a categorical model of constructive set theory. Synthetic domain theory allows us to make sense of fixed points and recursive domains in a set-theoretic setting, while the notions of classifying topos and ‘generic’ structure provide a useful way of interpreting signatures, functors and sharing, as well as Extended ML specifications. We only give an informal account, concentrating on motivation and examples rather than giving a rigorous formal development—only elementary category theory is used.
Original languageEnglish
Title of host publicationAutomata, Languages and Programming
Subtitle of host publication19th International Colloquium, ICALP92, Vienna, Austria, July 13-17, 1992, Proceedings
PublisherSpringer-Verlag
Pages533-544
Number of pages12
Volume623
ISBN (Electronic)978-3-540-47278-0
ISBN (Print)978-3-540-55719-7
DOIs
Publication statusPublished - 1992

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