Freyd is Kleisli, for Arrows
نویسندگان
چکیده
Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (Eilenberg-Moore) algebras. Hence it makes sense to ask if there are analogous structures for Arrows. In this short note we shall take first steps in this direction, and identify for instance the Freyd category that is commonly associated with an Arrow as a Kleisli category.
منابع مشابه
Categorical semantics for arrows
Arrows are an extension of the well-established notion of a monad in functional programming languages. This article presents several examples and constructions, and develops denotational semantics of arrows as monoids in categories of bifunctors C×C→ C. Observing similarities to monads – which are monoids in categories of endofunctors C→ C – it then considers Eilenberg-Moore and Kleisli constru...
متن کاملWhat is a Categorical Model of Arrows?
We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow equivalent. In this paper, we show that the situation is more subtle. By considering Arrows wholly within the base category we derive two altern...
متن کاملArrows, like Monads, are Monoids
Monads are by now well-established as programming construct in functional languages. Recently, the notion of “Arrow” was introduced by Hughes as an extension, not with one, but with two type parameters. At first, these Arrows may look somewhat arbitrary. Here we show that they are categorically fairly civilised, by showing that they correspond to monoids in suitable subcategories of bifunctors ...
متن کاملGeneric models for computational effects
AFreyd-category is a subtle generalisation of the notion of a categorywith finite products. It is suitable formodelling environments in call-by-value programming languages, such as the computational -calculus, with computational effects.We develop the theory of Freyd-categorieswith that inmind.Wefirst show that any countable Lawvere theory, hence any signature of operationswith countable arity ...
متن کاملCorrect Looping Arrows from Cyclic Terms - Traced Categorical Interpretation in Haskell
Arrows involving a loop operator provide an interesting programming methodology for looping computation. On the other hand, Haskell can define cyclic data structures by recursive definitions. This paper shows that there exists a common principle underlying both cyclic data and cyclic computations of arrow programs. We examine three concrete examples of constructing looping arrows from a syntact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006