The MSDN doc on Type Extensions states that "Before F# 3.1, the F# compiler didn't support the use of C#-style extension methods with a generic type variable, array type, tuple type, or an F# function type as the “this” parameter." (http://msdn.microsoft.com/en-us/library/dd233211.aspx) How can be a Type Extension used on F# function type? In what situations would such a feature be useful?
Here is how you can do it:
[<Extension>]
type FunctionExtension() =
[<Extension>]
static member inline Twice(f: 'a -> 'a, x: 'a) = f (f x)
// Example use
let increment x = x + 1
let y = increment.Twice 5 // val y : int = 7
Now for "In what situations would such a feature be useful?", I honestly don't know and I think it's probably a bad idea to ever do this. Calling methods on a function feels way too JavaScript-ey, not idiomatic at all in F#.