A functional correspondence between monadic evaluators and abstract machines for languages with computational effects

  • Authors:

  • Mads Sig Ager;Olivier Danvy;Jan Midtgaard

  • Affiliations:

  • BRICS, Department of Computer Science, University of Aarhus, Aarhus N, Denmark;BRICS, Department of Computer Science, University of Aarhus, Aarhus N, Denmark;BRICS, Department of Computer Science, University of Aarhus, Aarhus N, Denmark

  • Venue:
  • Theoretical Computer Science - Applied semantics: Selected topics
  • Year:
  • 2005

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Abstract

We extend our correspondence between evaluators and abstract machines from the pure setting of the λ-calculus to the impure setting of the computational λ-calculus. We show how to derive new abstract machines from monadic evaluators for the computational λ-calculus. Starting from (1) a generic evaluator parameterized by a monad and (2) a monad specifying a computational effect, we inline the components of the monad in the generic evaluator to obtain an evaluator written in a style that is specific to this computational effect. We then derive the corresponding abstract machine by closure-converting, CPS-transforming, and defunctionalizing this specific evaluator. We illustrate the construction with the identity monad, obtaining the CEK machine, and with a lifted state monad, obtaining a variant of the CEK machine with error and state.In addition, we characterize the tail-recursive stack inspection presented by Clements and Felleisen as a lifted state monad. This enables us to combine this stack-inspection monad with other monads and to construct abstract machines for languages with properly tail-recursive stack inspection and other computational effects. The construction scales to other monads--including one more properly dedicated to stack inspection than the lifted state monad--and other monadic evaluators.