Difference between unit type and 'a in ocaml

Question

What's the difference between unit -> unit and 'a -> 'a in OCaml?

For example:

# let f g a = if (g a > a) then a ;;
val f : (unit -> unit) -> unit -> unit = <fun>

# let f g a = if (g a > a ) then a else a;;
val f : ('a -> 'a) -> 'a -> 'a = <fun>

Why does the first one give unit -> unit and the second 'a -> 'a?

Answer 1

Note that in OCaml, if is an expression: it returns a value.

The key to understand your problem is that

if condition then a

is equivalent to

if condition then a else ()

The typing rules for if are the following:

• the condition should have type bool
• both branches should have the same type
• the whole if expression has the same type as the branches

In other words, in if cond then a, a should have type unit.

Answer 2

unit is the type used when nothing is return by a function (basically, functions who are printing things)

'a is a neutral type. It is a placeholder for any type.