Representing monads

  • Authors:

  • Andrzej Filinski

  • Affiliations:

  • School of Computer Science, Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 1994

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Abstract

We show that any monad whose unit and extension operations are expressible as purely functional terms can be embedded in a call-by-value language with “composable continuations”. As part of the development, we extend Meyer and Wand's characterization of the relationship between continuation-passing and direct style to one for continuation-passing vs. general “monadic” style. We further show that the composable-continuations construct can itself be represented using ordinary, non-composable first-class continuations and a single piece of state. Thus, in the presence of two specific computational effects - storage and escapes - any expressible monadic structure (e.g., nondeterminism as represented by the list monad) can be added as a purely definitional extension, without requiring a reinterpretation of the whole language. The paper includes an implementation of the construction (in Standard ML with some New Jersey extensions) and several examples.