We extend our correspondence between evaluators and abstract machines from the pure setting of the lambda-calculus to the impure setting of the computational lambda-calculus. We show how to derive new abstract machines from monadic evaluators for the computational lambda-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 first with the identity monad, obtaining the CEK machine, and then with a lifting monad, a state monad, and with a lifted state monad, obtaining variants of the CEK machine with error handling, state and a combination of error handling 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.
Theoretical Computer Science, 2005, Vol 342, Issue 1, p. 149-172
λ-calculus; Interpreters; Abstract machines; Closure conversion; calculusTransformation into continuation-passing style (CPS); Defunctionalization; Monads; Effects; Proper tail recursion; Stack inspection ms