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. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1

Unfolds generate data structures, and folds consume them.

Abstract. We propose a novel, comonadic approach to dataflow (stream-based) 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 contextdependent 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. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1

Accumulations are recursive functions widely used in the context of functional programming. They maintain intermediate results in additional parameters, called accumulators, that may be used in later stages of computing. In a former work [Par02] a generic recursion operator named afold was presented. Afold makes it possible to write accumulations defined by structural recursion for a wide spectrum of datatypes (lists, trees, etc.). Also, a number of algebraic laws were provided that served as a formal tool for reasoning about programs with accumulations. In this work, we present an extension to afold that allows a greater flexibility in the kind of accumulations that may be represented. This extension, in essence, provides the expressive power to allow accumulations to have more than one recursive call in each subterm, with different accumulator values —something that was not previously possible. The extension is conservative, in the sense that we obtain similar algebraic laws for the extended operator. We also present a case study that illustrates the use of the algebraic laws in a calculational setting and a technique for the improvement of fused programs