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TheUnbeliever

F# Ackermann Stack overflow

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So, I'm tinkering with a memoizing implementation of the Ackermann function using BigInt, and getting a stack overflow. I'm pretty sure I understand why - the closure for the memoization means that it's not able to 'true' tail recursion, so it can't be optimized out to a loop (and, yes, I've tested under Release mode with -O3). Can anyone see how to fix this, or even just comment on style?
#light

open System
open System.Collections.Generic

let memoize f = let cache = new Dictionary<_, _>()
                fun args -> if cache.ContainsKey(args)
                              then cache.[args]
                              else let r = f args
                                   cache.[args] <- r
                                   r

let rec _ack (m, n) = if m = 0I
                        then n + 1I
                        else if n = 0I
                               then ack (m - 1I, 1I)
                               else ack (m - 1I, ack (m, n - 1I))
                            
and ack = memoize _ack
                           
let main = Console.WriteLine(ack (4I, 1I))


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