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Notions of category theory in functional programming Gammon, Shauna C. A.

Abstract

We present a detailed examination of applications of category theory to functional programming languages, with a primary focus on monads in Haskell. First, we explore E. Moggi's work in categorical semantics, which provides the theoretical foundation for employing monads in functional languages. In particular, we examine his use of Kleisli triples to model notions of computation. We then study P. Wadler's implementation of Moggi's ideas as a means to mimic side-effects in the purely functional language Haskell. We explicitly demonstrate the connections between Kleisli triples, categorytheoretic monads, and Haskell monads. It is our principal aim to provide a coherent translation between the abstracted concept of monads that exists in category theory, and the formulation of monads as type-constructors that is implemented in Haskell.

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