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The title is the question, simple.
The identity function fun x -> x has the type 'a -> 'a.
Are there any other functions with the same type 'a -> 'a?
I can't think of another.
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Similarly, OCaml functions do not have to have names; they may be anonymous. For example, here is an anonymous function that increments its input: fun x -> x + 1 . Here, fun is a keyword indicating an anonymous function, x is the argument, and -> separates the argument from the body.
The operator is usually called type arrow where T1 -> T2 represents functions from type T1 to type T2 . For instance, the type of + is int -> (int -> int) because it takes two integers and returns another one.
Using Operator as Function Operators, such as + * etc, can be considered as functions of 2 parameters. They can be used as a function in ocaml. A function call has the form f arg1 arg2 with function named f , while operator such as + is used in the form arg1 + arg2 .
ML-derived languages like OCaml are "mostly pure". They allow side-effects through things like references and arrays, but by and large most of the code you'll write will be pure functional because they encourage this thinking.
No.
fun x -> print_endline "foo"; x;;
(failwith "bang" : 'a -> 'a);;
(fun x -> failwith "bang" : 'a -> 'a);;
(fun x -> List.hd [] : 'a -> 'a);;
let rec f (x : 'a) : 'a = f x;;
let counter = ref 0;;
(fun x -> incr counter; x);;
The identity function is the only inhabitant of 'a -> 'a in total programming language with no side-effects whatsoever, including nontermination. Neither OCaml nor Haskell qualify, but some languages used as proof assistants (where this totality is important) do, in particular Coq (which has the impredicative polymorphism used to formulate this type).
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