I'm not sure if there's a simpler way to do this, but one approach would be to create a memoizing y-combinator:
let memoY f =
let cache = Dictionary<_,_>()
let rec fn x =
match cache.TryGetValue(x) with
| true,y -> y
| _ -> let v = f fn x
cache.Add(x,v)
v
fn
Then, you can use this combinator in lieu of "let rec", with the first argument representing the function to call recursively:
let tailRecFact =
let factHelper fact (x, res) =
printfn "%i,%i" x res
if x = 0 then res
else fact (x-1, x*res)
let memoized = memoY factHelper
fun x -> memoized (x,1)
EDIT
As Mitya pointed out, memoY doesn't preserve the tail recursive properties of the memoee. Here's a revised combinator which uses exceptions and mutable state to memoize any recursive function without overflowing the stack (even if the original function is not itself tail recursive!):
let memoY f =
let cache = Dictionary<_,_>()
fun x ->
let l = ResizeArray([x])
while l.Count <> 0 do
let v = l.[l.Count - 1]
if cache.ContainsKey(v) then l.RemoveAt(l.Count - 1)
else
try
cache.[v] <- f (fun x ->
if cache.ContainsKey(x) then cache.[x]
else
l.Add(x)
failwith "Need to recurse") v
with _ -> ()
cache.[x]
Unfortunately, the machinery which is inserted into each recursive call is somewhat heavy, so performance on un-memoized inputs requiring deep recursion can be a bit slow. However, compared to some other solutions, this has the benefit that it requires fairly minimal changes to the natural expression of recursive functions:
let fib = memoY (fun fib n ->
printfn "%i" n;
if n <= 1 then n
else (fib (n-1)) + (fib (n-2)))
let _ = fib 5000
EDIT
I'll expand a bit on how this compares to other solutions. This technique takes advantage of the fact that exceptions provide a side channel: a function of type 'a -> 'b doesn't actually need to return a value of type 'b, but can instead exit via an exception. We wouldn't need to use exceptions if the return type explicitly contained an additional value indicating failure. Of course, we could use the 'b option as the return type of the function for this purpose. This would lead to the following memoizing combinator:
let memoO f =
let cache = Dictionary<_,_>()
fun x ->
let l = ResizeArray([x])
while l.Count <> 0 do
let v = l.[l.Count - 1]
if cache.ContainsKey v then l.RemoveAt(l.Count - 1)
else
match f(fun x -> if cache.ContainsKey x then Some(cache.[x]) else l.Add(x); None) v with
| Some(r) -> cache.[v] <- r;
| None -> ()
cache.[x]
Previously, our memoization process looked like:
fun fib n ->
printfn "%i" n;
if n <= 1 then n
else (fib (n-1)) + (fib (n-2))
|> memoY
Now, we need to incorporate the fact that fib should return an int option instead of an int. Given a suitable workflow for option types, this could be written as follows:
fun fib n -> option {
printfn "%i" n
if n <= 1 then return n
else
let! x = fib (n-1)
let! y = fib (n-2)
return x + y
} |> memoO
However, if we're willing to change the return type of the first parameter (from int to int option in this case), we may as well go all the way and just use continuations in the return type instead, as in Brian's solution. Here's a variation on his definitions:
let memoC f =
let cache = Dictionary<_,_>()
let rec fn n k =
match cache.TryGetValue(n) with
| true, r -> k r
| _ ->
f fn n (fun r ->
cache.Add(n,r)
k r)
fun n -> fn n id
And again, if we have a suitable computation expression for building CPS functions, we can define our recursive function like this:
fun fib n -> cps {
printfn "%i" n
if n <= 1 then return n
else
let! x = fib (n-1)
let! y = fib (n-2)
return x + y
} |> memoC
This is exactly the same as what Brian has done, but I find the syntax here is easier to follow. To make this work, all we need are the following two definitions:
type CpsBuilder() =
member this.Return x k = k x
member this.Bind(m,f) k = m (fun a -> f a k)
let cps = CpsBuilder()