Polymorphic types : How to ?

Question

I'm reading this wiki about types in Caml , and I must admit I'm struggling to understand how polymorphic types are dealt with syntactically , so in general how can one define a polymorphic type ?

Answer 1

Polymorphism shows up in OCaml in many places. The polymorphic types discussed on that wiki are simply parameterized types. In some sense, they are type-level functions. To define a one-parameter type:

type 'a <name> = <definition using 'a>

For example

type 'a tagged = { value: 'a; tag: int }

In the <definition> part you use the type name ('a) as a formal parameter standing for whatever concrete type is supplied later.

After declaring the type (which declares value and tag as record fields), you can make values of the type:

# { value = "abc"; tag = 4 };;
- : string tagged = {value = "abc"; tag = 4}

The compiler infers that the type of this value is string tagged because the value field has type string.

Multiple parameter types are defined using parentheses to enclose the type parameters:

type ('a, 'b) name = <definition using 'a and 'b>

For example:

type ('a, 'b) paired = { first: 'a; second: 'b }

This defines the field names first and second, which you can then use to make values:

# { first = 1.5; second = [3] };;
- : (float, int list) paired = {first = 1.5; second = [3]}

To summarize, the syntax for making polymorphic (parameterized) types is the same as the syntax for making types, extended with the use of symbols like 'a for the type parameters.