Fold-Unfold Transformations on State Monadic Interpreters

Abstract

In this paper we advocate the use of fold-unfold transformations for mastering the complexity of abstract machines intended for real implementations. The idea is to express the abstract machine as an interpreter in a purely functional language. The initial interpreter should be ‘obviously correct’ (but might be inefficient — we don’t care at this point). Fold-unfold transformations are then used to remove inefficiencies in the interpreter/abstract machine. We illustrate this by deriving (the equivalent of) the ε-scheme of the G-machine from (the equivalent of) the composition of C and the EVAL instruction. This is first done on a call-by-name (tree reduction) interpreter. To model sharing and the graph manipulation that goes on in a real graph reduction implementation, we use state monads. We do the same transformation of the state monadic interpreter. It is much less straightforward to transform the state monadic interpreter, as we have to lean heavily on the laws of the state monad. In return the state monadic interpreter can be said to better model a real implementation.