The abstract: We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure context-dependent computation. In particular, we develop a generic comonadic interpreter of languages for context-dependent computation and instantiate it for stream-based computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and context-dependent computation. If you've ever wondered about dataflow or comonads, this paper is a good read. It begins with short reviews of monads, arrows, and comonads and includes an implementation. One feature that stood out is the idea of a higher-order dataflow language.
Comonads are an abstraction from category theory dualing many qualities of Monads. They are conceptually much simpler than arrows but seem to offer a solution to some problems not easily solved by monads. The ideas presented here are not novel except for the comonadic combinators for a nicer syntax. Typeclass Combinators Reader State Stream Writer Links