A new notation for arrows

The categorical notion of monad, used by Moggi to structure denotational de scriptions, has proved to be a powerful tool for structuring combinator lib raries. Moreover, the monadic programming style provides a convenient synta x for many kinds of computation, so that each library defines a new sublang uage. Recently, several workers have proposed a generalization of monads, called variously "arrows" or Freyd-categories. The extra generality promises to in crease the power, expressiveness and efficiency of the embedded approach, b ut does not mesh as well with the native abstraction and application. Defin itions are typically given in a point-free style, which is useful for provi ng general properties, but can be awkward for programming specific instance s. In this paper we define a simple extension to the functional language Haske ll that makes these new notions of computation more convenient to use. Our language is similar to the monadic style, and has similar reasoning propert ies. Moreover, it is extensible, in the sense that new combining forms can be defined as expressions in the host language.