count_change.fs

let memoize2 f =
        let cache = ref Map.empty
        fun a b ->
            match (!cache).TryFind (a,b) with
            | Some(cv) -> cv
            | None -> 
                let v = f a b
                cache := Map.add (a,b) v !cache
                v
 
let rec slowcc amount coins =
    match (amount, coins) with
    | (0,_) -> 1
    | (_,[]) -> 0
    | (amount,_) when amount < 0 -> 0
    | (_, hd :: tail) -> slowcc amount tail + slowcc (amount-hd) coins

let rec fastcc = memoize2 (fun amount coins ->
    match (amount, coins) with
    | (0,_) -> 1
    | (_,[]) -> 0
    | (amount,_) when amount < 0 -> 0
    | (_, hd :: tail) -> fastcc amount tail + fastcc (amount-hd) coins) 

You cannot do a when guard when both patterns do not bind the same variables.

That is true, that'll teach me to edit code without a compiler :-)