Lightweight Monadic Programming in ML

Many useful programming constructions can be expressed as monads. Examples include probabilistic modeling, functional reactive programming, parsing, and information flow tracking, not to mention effectful functionality like state and I/O. In this paper, we present a type-based rewriting algorithm to make programming with arbitrary monads as easy as using ML's built-in support for state and I/O. Developers write programs using monadic values of type *M t* as if they were of type *t*, and our algorithm inserts the necessary binds, units, and monad-to-monad morphisms so that the program type checks. Our algorithm, based on Jones' qualified types, produces principal types. But principal types are sometimes problematic: the program's semantics could depend on the choice of instantiation when more than one instantiation is valid. In such situations we are able to simplify the types to remove any ambiguity but without adversely affecting typability; thus we can accept strictly more programs. Moreover, we have proved that this simplification is *efficient* (linear in the number of constraints) and *coherent*: while our algorithm induces a particular rewriting, all related rewritings will have the same semantics. We have implemented our approach for a core functional language and applied it successfully to simple examples from the domains listed above, which are used as illustrations throughout the paper.

This is an intriguing paper, with an implementation in about 2,000 lines of OCaml. I'm especially interested in its application to probabilistic computing, yielding a result related to Kiselyov and Shan's Hansei effort, but without requiring delimited continuations (not that there's anything wrong with delimited continuations). On a theoretical level, it's nice to see such a compelling example of what can be done once types are freed from the shackle of "describing how bits are laid out in memory" (another such compelling example, IMHO, is type-directed partial evaluation, but that's literally another story).

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