Motivation and History
While arrows were in use before being recognized as a distinct class, Hughes would publish their first definition in 2000. Until then, monads had proven sufficient for most problems requiring the combination of program logic in pure code. However, some useful libraries, such as the Fudgets library for graphical user interfaces and certain efficient parsers, defied rewriting in a monadic form.
The formal concept of arrows was developed to explain these exceptions to monadic code, and in the process, monads themselves turned out to be a subset of arrows. Since then, arrows have been an active area of research. Their underlying laws and operations have been refined several times, with recent formulations such as arrow calculus requiring only five laws.
In category theory, the Kleisli categories of all monads form a proper subset of Hughes arrows. While Freyd categories were believed to be equivalent to arrows for a time, it has since been proven that arrows are even more general. In fact, arrows are not merely equivalent, but directly equal to enriched Freyd categories.
Read more about this topic: Arrow (computer Science)
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