Recursion Is a Computational Eeect Recursion Is a Computational Eeect

In a recent paper, Launchbury, Lewis, and Cook observe that some Haskell applications could bene t from a combinator m x for expressing recursion over monadic types. We investigate three possible de nitions of m x and implement them in Haskell. Like traditional xpoint operators, there are two approaches to the de nition of m x: an unfolding one based on mathematical semantics, and an updating one based on operational semantics. The two de nitions are equivalent in pure calculi but have di erent behaviors when used within monads. The unfolding version can be easily de ned in Haskell if one restricts xpoints to function types. The updating version is much more challenging to dene in Haskell despite the fact that its de nition is straightforward in Scheme. After studying the Scheme de nition in detail, we mirror it in Haskell using the primitive unsafePerformIO. The resulting de nition of m x appears to work well but proves to be unsafe, in the sense that it breaks essential properties of the purely functional subset of Haskell. We conclude that the updating version of m x should be treated as a monadic e ect. This observation leads to a safe de nition based on monad transformers that pinpoints and exposes the subtleties of combining recursion with other e ects and puts them under the programmer's control to resolve as needed. The conclusion is that Haskell applications that need the functionality of m x can be written safely in any Haskell dialect that supports the multiparameter classes necessary for de ning monad transformers. No other extensions to standard Haskell are needed, although some syntactic abstractions and libraries can make the task of writing recursive monadic bindings much more convenient. Supported by National Science Foundation Grant number CCR-9733088. Work started at the University of Oregon.