Towards a categorical semantics of type classes

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Abstract

This is an exercise in the description of programming languages as indexed categories. Type classes have been introduced into functional programming languages to provide a uniform framework for ‘overloading’. We establish a correspondence between type classes and comprehension schemata in categories. Coherence results allow us to describe subclasses and implicit conversions between types.

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Hilken, B. P., & Rydeheard, D. E. (1991). Towards a categorical semantics of type classes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 520 LNCS, pp. 191–201). Springer Verlag. https://doi.org/10.1007/3-540-54345-7_62

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