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the concept in computer science

In computer science, arrows or bolts are a type class used in programming to describe computations in a pure and declarative fashion. First proposed by computer scientist John Hughes as a generalization of monads, arrows provide a referentially transparent way of expressing relationships between logical steps in a computation. Unlike monads, arrows don't limit steps to having one and only one input. As a result, they have found use in functional reactive programming, point free programming, and parsers among other applications.

While arrows were in use before being recognized as a distinct class, it wasn't until 2000 that John Hughes first published research focusing on them. 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.

In category theory, the Kleisli categories of all monads form a proper subset of Hughes arrows. 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.

Like all type classes, arrows can be thought of as a set of qualities that can be applied to any data type. In the Haskell programming language, arrows allow functions (represented in Haskell by > symbol) to combine in a reified form. However, the actual term "arrow" may also come from the fact that some (but not all) arrows correspond to the morphisms (also known as "arrows" in category theory) of different Kleisli categories. As a relatively new concept, there is not a single, standard definition, but all formulations are logically equivalent, feature some required methods, and strictly obey certain mathematical laws.