Compiling Monads ∗

Computational monads offer a powerful way to parameterize functional specifications, but they give rise to exceedingly tedious simplifications to instantiate this “monadic” interpreter. We report on the use of partial evaluation to achieve the following instantiations automatically. • We derive equivalent formulations of the monadic λ-interpreter, based on equivalent specifications of monads from algebra and category theory (join, clone, exp, and bind). This increases flexibility in formulating the parameterized interpreter. • We derive several well-known styled interpreters by instantiating the monadic interpreter with a particular monad (store, continuation, etc.). This illustrates the generality of the monadic interpreter. • We specialize the monadic interpreter with respect to a particular program, thereby compiling this program into a parameterized representation of its meaning (a.k.a. a monadic form). This makes it possible to reason about particular programs independently of their interpretation and also to measure the generality of the monadic interpreter. From a computational viewpoint, partial evaluation makes it possible for each of these instantiations to run significantly faster. In the spirit of the Scheme programming language, our Kleisli interpreter handles a fixed set of special forms. Therefore, the natural way to extend it is to add predefined functions in the initial environment, using Church encoding (call/cc instead of escape, etc.) if necessary. We study the consequences of this design. Equipping the exception monad with the usual operators forces us to adopt a new representation of arrows and therefore to modify the interpreter in a way reminiscent of call-by-name, even though the defined language is still call-by-value. Instantiating this new interpreter with the continuation monad yields the lesser-known continuation-passing style advocated by Reynolds. Finally, we relate the parameterization offered by monads with other ways of structuring a formal semantics, either for the purpose of flow analysis by abstract interpretation or for the purpose of semantics-directed compiling and compiler generation.