Should I use a Monad or a Comonad ?
نویسنده
چکیده
The category theoretic structures of monads and comonads can be used as an abstraction mechanism for simplifying both language semantics and programs. Monads have been used to structure impure computations, whilst comonads have been used to structure context-dependent computations. Interestingly, the class of computations structured by monads and the class of computations structured by comonads are not mutually exclusive. This paper formalises and explores the conditions under which a monad and a comonad can both structure the same notion of computation: when a comonad is left adjoint to a monad. Furthermore, we examine situations where a particular monad/comonad model of computation is deficient in capturing the essence of a computational pattern and provide a technique for calculating an alternative monad or comonad structure which fully captures the essence of the computation. Included is some discussion on how to choose between a monad or comonad structure in the case where either can be used to capture a particular notion of computation.
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