Lambda the Ultimate

How OCaml type checker works -- or what polymorphism and garbage collection have in common

There is more to Hindley-Milner type inference than the Algorithm W. In 1988, Didier Rémy was looking to speed up the type inference in Caml and discovered an elegant method of type generalization. Not only it is fast, avoiding the scan of the type environment. It smoothly extends to catching of locally-declared types about to escape, to type-checking of universals and existentials, and to implementing MLF.

Alas, both the algorithm and its implementation in the OCaml type checker are little known and little documented. This page is to explain and popularize Rémy's algorithm, and to decipher a part of the OCaml type checker. The page also aims to preserve the history of Rémy's algorithm.

The attraction of the algorithm is its insight into type generalization as dependency tracking -- the same sort of tracking used in automated memory management such as regions and generational garbage collection. Generalization can be viewed as finding dominators in the type-annotated abstract syntax tree with edges for shared types. Fluet and Morrisett's type system for regions and MetaOCaml environment classifiers use the generalization of a type variable as a criterion of region containment. Uncannily, Rémy's algorithm views the region containment as a test if a type variable is generalizable.

As usual with Oleg, there's a lot going on here. Personally, I see parallels with "lambda with letrec" and "call-by-push-value," although making the connection with the latter takes some squinting through some of Levy's work other than his CBPV thesis. Study this to understand OCaml type inference and/or MLF, or for insights into region typing, or, as the title suggests, for suggestive analogies between polymorphism and garbage collection.