In mathematics, a fixed-point operator is a function that takes a function as input and returns a fixed point of that function. A fixed point of a function is a point that the function maps to itself.
The Y combinator is a well-known fixed-point operator. In functional programming, the Y combinator is used to define recursive functions.
In F#, the Y combinator can be implemented as follows:
let rec y f = f (y f)
This function takes a function f as input and returns a fixed point of f.
To use the Y combinator, we can define a recursive function as follows:
let rec factorial n =
if n <= 1 then 1
else n * factorial (n-1)
This function is not directly recursive, but it can be made recursive by using the Y combinator:
let factorial = y (fun f n ->
if n <= 1 then 1
else n * f (n-1))
The Y combinator can be used to define other recursive functions, such as the Fibonacci function:
let fibonacci = y (fun f n ->
if n <= 2 then 1
else f (n-1) + f (n-2))
