F# Understanding Recursion Function

Question

I am trying to understand why a recursion function is behaving the way it is.

let rec fact = function 
   |0 -> 1
   |n -> n * fact(n-1);;

When i execute:

fact 4;;

it responds:

val it : int = 24

which is ofcourse Is correct since 1*2*3*4 = 24

What i don't get is this piece of code:

|n -> n * fact(n-1);;

I don't get why It doesn't calculate:

4 -> 4 * (4-1)
4 -> 4 * 3
4 -> 12

My guess Is I am misunderstanding the definition of n

can someone do the honor and enlighten me?

Answer 1

That would be true if the definition were n -> n * (n - 1) but it is making a recursive call to fact so it is:

4 * fact(4 - 1)
=> 4 * fact(3)
=> 4 * (3 * fact(2))
=> 4 * (3 * (2 * fact(1)))
=> 4 * (3 * (2 * (1 * fact(0))))
=> 4 * (3 * (2 * (1 * 1)))
=> 4 * (3 * (2 * 1))
=> 4 * (3 * 2)
=> 4 * 6
=> 24