Types of OCaml functions -

Types of OCaml functions -

i started learning functional programming (ocaml), don't understand 1 of import topic functional programming: types.

can explain me solution please?

have test week , can't reach resolution..

let f b c = (a b c) 0;; f: ('a -> int -> 'a) -> 'a -> int -> 'a

let f b c = (a b c) 0;;

your confusion involves types , type inference, i.e., when define function or binding, don't need give explicit types parameters, nor function/binding itself, ocaml figure out if definition of function/binding correct.

so, let's manual inferences ourselves. if human can do, compiler can do.

1.

let x = 1

1 integer, x must integer. don't need int x = 1 in other languages, right?

2.

let f x = 1

if there multiple variable names between let , =, must function definition, right? otherwise, won't create sense. in java language, makes no sense int x y = 1, right?

so f function , x must parameter. since righthand side of = integer, know f homecoming integer. x, don't know, x thought polymorphic type 'a.

so f: 'a -> int = <fun>.

3.

let f b c = (a b c) 0;;

f function, parameters a, b, c.

a must function, because on righthand side of =, function application.

a takes 2 arguments: (a b c) , 0. 0 integer, 2nd parameter of a must integer type.

look within (a b c), c 2nd arguement, c must integer.

we can't infer on b. b 'a.

since (a b c) can 1st argument of a, , (a b c) application on function a, homecoming type of a have same type of b 'a.

combine info above together, f: ('a -> int -> 'a) -> 'a -> int -> 'a.

if want larn formally, https://realworldocaml.org/ friend.

ocaml