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.
CITATION STYLE
Phoa, W., & Fourman, M. (1992). A proposed categorical semantics for Pure ML. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 623 LNCS, pp. 533–544). Springer Verlag. https://doi.org/10.1007/3-540-55719-9_102
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