Abstract. Monads are pervasive in functional programming. In order to reap the benefits of their abstraction power, combinator libraries for monads are necessary. Monad transformers provide the basis for such libraries, and are based on a design that has proved to be successful. In this article, we show that this design has a number of shortcomings and provide a new design that builds on the strengths of the traditional design, but addresses its problems. 1

Fusion is the process of improving the efficiency of modularly constructed programs by transforming them into monolithic equivalents. This paper defines a generalization of the standardbuild combinator which expresses uniform production of functorial contexts containing data of inductive types. It also proves correct a fusion rule which generalizes thefold/build andfold/buildp rules from the literature, and eliminates intermediate data structures of inductive types without disturbing the contexts in which they are situated. An important special case arises when this context is monadic. When it is, a second rule for fusing combinations of producers and consumers via monad operations, rather than via composition, is also available. We give examples illustrating both rules, and consider their coalgebraic duals as well.

We lay operational foundations for effect handlers. Introduced by Plotkin and Pretnar, effect handlers are a novel programming construct that generalises exception handlers, handling a range of computational effects, such as I/O, state, and nondeterminism. We propose a small-step structural operational semantics for a higher-order calculus of effect handlers, along with a sound type and effect system. We explore two alternative effect handler implementation techniques: free monads, and delimited continuations. Finally, we show that Filinski’s monadic reflection can be straightforwardly simulated by effect handlers. 1.