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

Limitations of the monad stacks get in the way of developing highly modular programs with effects. This pearl demonstrates that Functional Programming’s abstractions are up to the challenge. Of course, abstraction must be followed by clever instantiation: Huet’s zipper for the monad stack makes components jump through unanticipated hoops.

The worker/wrapper transformation is a general technique for improving the performance of recursive programs by changing their types. The previous formalisation (Gill & Hutton, 2009) was based upon a simple fixed point semantics of recursion. In this article we develop a more structured approach, based upon initial algebra semantics. In particular, we show how the worker/wrapper transformation can be applied to programs defined using the structured pattern of recursion captured by fold operators, and illustrate our new technique with a number of examples.

The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting monad. A complication of this approach is that the operations associated to the pre-existing monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system F ω. Here, we recast and extend those results in a category-theoretic setting. We abstract and generalize from monads to monoids (in a monoidal category), and from monad transformers to monoid transformers. The generalization brings more simplicity and clarity, and opens the way for lifting of operations with applicability beyond monads. Key words: Monad, Monoid, Monoidal Category

Limitations of monad stacks get in the way of developing highly modular programs with effects. This pearl demonstrates that Functional Programming’s abstraction tools are up to the challenge. Of course, abstraction must be followed by clever instantiation: Huet’s zipper for the monad stack makes components jump through unanticipated hoops. Categories and Subject Descriptors D.1.1 [Programming Techniques]: