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Brands — higher-order polymorphism in OCaml

Convenience types for working with 'defunctionalised' higher-kinded polymorphism à la 'Lightweight higher-kinded polymorphism', Jeremy Yallop and Leo White (2014).

STATUS: EXPERIMENTAL

Explanation

In OCaml, there is no first-class way to abstract over higher-kinded type operators without the use of functors:

type all_lists      = 'a list  (* OK! polymorphic over all element types of kind [—] *)
type int_containers = int 'f   (* FAIL! polymorphic over all container types of kind [— ⇒ —] *)

This library provides a mechanism to simulate such lightweight higher-kinded polymorphism:

  • define an encoding of type operator application ( app : — ⇒ — ⇒ —) in which each type operator corresponds to exactly one opaque type called the 'brand' of the operator;

  • provide injection and projection functions for type-safe conversion between the encoding (e.g. (int, list_brand) app) and the true representation (e.g. int list).

Since the encoding of application uses a simple type in place of a higher-kinded operator, it can be polymorphic over that operator. For example, we can write int 'f as (int, 'br) app where 'br ranges over the brands of the corresponding type operators 'f.

Related work

This method of achieving higher-kinded polymorphism in OCaml was first proposed by Jeremy Yallop and Leo White [Yal14]. This implementation is similar to the one that accompanies the paper (ocamllabs/higher), but differs in several regards:

  • Constructed brands are named br rather than t, to ease inclusion into existing modules.

  • Canonical brands for types defined in the OCaml standard library are provided.

  • The top-level module provides aliases for curried application (app2, app3 etc.).

There is also a Jane Street implementation (janestreet/higher_kinded) of the same ideas, with pre-provided brands for the types defined in (janestreet/base).

Installation

opam pin add --yes https://github.com/CraigFe/brands.git
opam install brands