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Why are there no function headers in OCaml?

Some programming languages, especially C, have header files with function declarations. These headers come before the code and are required for situations with mutual recursion. When function headers are placed in the header file, they also help link situations where multiple C files are compiled together.

My understanding of function headers in a C file is that they help with compilation, because they determine the function input if it is called before it is defined. If this is not so, I would be happy if I were corrected and better informed, but this is my understanding.

So I don’t understand why other languages ​​- in this case I highlight OCaml - do not have function headers. There are modules with signatures in OCaml, but the signature does not allow your function instances to be mutually recursive, even if specified. To have mutual recursion in OCaml, you need to use either the "and" keyword or define one function locally inside another function (as far as I know).

(* version 1 *)
let rec firstfun = function
  | 0 -> 1
  | x -> secondfun (x - 1)
and secondfun = function
  | 0 -> 1
  | x -> firstfun x

(* version 2 *)
let rec firstfun = function
  | 0 -> 1
  | x -> 
       let rec secondfun = function
         |0 -> 1
         | x -> firstfun x in
       secondfun (x - 1)

So why is that so? Is this related to polymorphism? Is there a compilation bottleneck that I am not considering?

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(* version 1 *)
let rec firstfun = function 0 -> 1
  | x -> secondfun (x - 1)
and secondfun = function 0 -> 1
  | x -> firstfun x

, , ( , First_module ):

module First_module = struct
  let rec firstfun secondfun = function 0 -> 1
    | x -> secondfun (x - 1)
end

module Second_module = struct
  let rec secondfun = function 0 -> 1
    | x -> First_module.firstfun secondfun x
end

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EDIT:

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module rec All : sig
  val firstfun : int -> int
  val secondfun : int -> int
end = struct

  let firstfun = function 0 -> 1
    | x -> All.secondfun (x - 1)

  let secondfun = function 0 -> 1
    | x -> All.firstfun x

end

include All

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 (* many lines *)
 .....
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 ....
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 ....

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