OCaml polymorphism example other than template function?

Question

I am trying to understand for myself, which form of polymorhism does OCaml language have.

I was provided by an example

let id x = x

Isn't this example equivalent to C++ template function

template<class A> A id(A x) { return x; }

If so then my question is: are there any other forms of polymorphism in OCaml? This notion is called "generic algorithm" in the world of imperative languages, not "polymorphism".

sepp2k · Accepted Answer · 2013-01-21 15:14:13Z

There are basically three language features that are sometimes called polymorphism:

Parametric polymorphism (i.e. "generics")
Subtype polymorphism, this is the ability of a subtype of a type to offer a more specific version of an operation than the supertype, i.e. the ability to override methods (and the ability of the the runtime system to call the correct implementation of a method based on the runtime type of an object). In OO languages this is often simply referred to as "polymorphism".
So-called ad-hoc polymorphism, i.e. the ability to overload functions/methods.

As you already discovered, OCaml has parametric polymorphism. It also has subtype polymorphism. It does not have ad-hoc polymorphism.

Since in your title you've asked for examples, here's an example of subtype polymorphism in OCaml:

class c = object
    method m x = x+1
end

class d = object
    inherit c
    method m x = x+2
end

let main = 
    let o:c = new d in
    print_int (o#m 2)

This will print 4.

+1 Now that I see it, this is the answer I think should have been written for a previous question by the OP.
OCaml doesn't have subtyping polymorphism, as it actually enforces to explicitly upcast values in the places where their supertype is requested. Though, of course, OCaml has the notion of subtype and typing rules that checks whether an upcasting operation is valid. The example, that OP provides, is an example of the row polymorphism, that is a completely different beast, read the following for more details stackoverflow.com/questions/48092739/…

Jack · Accepted Answer · 2013-01-21 14:37:59Z

This kind of polymorphism is called generic programming but the theoretical concept behind it is called parametric polymorphism.

The two examples you provided indeed show parametric polymorphism but OCaml is supported by a strong inferring type checker instead that the one provided by C++ (which is a solution more pragmatic and with more caveats) so the real difference is that in C++ the code is duplicated for every type you use it in your code while in OCaml it is resolved by type checker by verifying that a substitution of implicit type variables through unification does exist.

Everything can be polymorphic in OCaml just because nothing is usually annotated with types so in practice if something can be used as an argument to any function then it is implicitly allowed.

You can for example have type variables to define polymorphic methods:

let swap ((x : 'a), (y : 'b)) : 'b * 'a = (y, x)

so that this will work whatever type 'a o 'b is.

Another powerful polymorphic feature of OCaml are functors (which are not the common C++ functors) but are modules parametrized by other modules. The concept sounds scarier that it is but they indeed represent an higher order of polymorphic behavior for OCaml code.

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