13 Module Type Syntax and Semantics

Syntax

module type ModuleTypeName = sig
    specifications...
end

• Name doesn't need to be capitalized, but usually is.
• Specifications include anything...

Semantics

If you give a module a type:

module Mod : Sig = struct ... end

The type checker ensures

1. Signature matching: everything specified in Sig must be defined in Mod with correct types
2. Encapsulation: only what is specified in Sig can be accessed outside Mod. The module is sealed.

Signature matching

• Every name specified in Sig must be defined in Mod
• The types in Mod must be the same as in Sig, or more general, for example:

module type IntFun = sig
	val f : int -> int
end

module type IntFun = sig val f : int -> int end

We can implement this module with a function of type int -> int.

module SuccFun : IntFun = struct
	let f x = x + 1
end

module SuccFun : IntFun

We can also implement this module with a more general type:

module IdFun : IntFun = struct
	let f x = x
end

module IdFun : IntFun

Here, the function f has type 'a -> 'a. You will never get a type error for a more general type.

IdFun.f "hello"

File "[4]", line 1, characters 8-15:
1 | IdFun.f "hello"
            ^^^^^^^
Error: This expression has type string but an expression was expected of type
         int

Note that we can't use any other type here, as the module is sealed.