Evaluation strategies for monadic computations

Abstract

Monads have become a powerful tool for structuring effectful computations in functional programming, because they make the order of effects explicit. When translating pure code to a monadic version, we need to specify evaluation order explicitly. Two standard translations give call-by-value and call-by-name semantics. The resulting programs have different structure and types, which makes revisiting the choice difficult. In this paper, we translate pure code to monadic using an additional operation malias that abstracts out the evaluation strategy. The malias operation is based on computational comonads; we use a categorical framework to specify the laws that are required to hold about the operation. For any monad, we show implementations of malias that give call-by-value and call-by-name semantics. Although we do not give call-by-need semantics for all monads, we show how to turn certain monads into an extended monad with call-by-need semantics, which partly answers an open question. Moreover, using our unified translation, it is possible to change the evaluation strategy of functional code translated to the monadic form without changing its structure or types.