This module provides a small set of functions for memoization. Whereas most memo combinators memoize based on equality, these do it based on whether the exact same argument has been passed to the function before (that is, is the same argument in memory).

• They only evaluate keys to WHNF.
• Relative to value-base memoization, this can be more suitable for recursive functions over graphs with cycles.
• These don't retain the keys they have seen so far, which allows mappings to be garbage collected if they will no longer be used. Finalizers are put in place to remove the corresponding entries from the memo table if this happens.
• Data.StableMemo.Weak provides an alternative set of combinators that also avoid retaining the results of the function, only reusing results if they have not yet been garbage collected.
• There is no type class constraint on the function's argument.

These will not work for arguments which happen to have the same value but are not the same heap object. This rules out many candidates for memoization, such as the most common example, the naive Fibonacci implementation whose domain is machine Ints; it can still be made to work for some domains, though, such as the lazy naturals.

data Nat = Succ Nat | Zero

fib :: Nat -> Integer
fib = memo fib'
  where fib' Zero                = 0
        fib' (Succ Zero)         = 1
        fib' (Succ n1@(Succ n2)) = fib n1 + fib n2

Below is an implementation of map that preserves sharing of the spine for cyclic lists. It should even be safe to use this on arbitrarily long, acyclic lists since as long as the garbage collector is chasing you, the size of the memo table should stay under control, too.

map :: (a -> b) -> [a] -> [b]
map f = go
  where go = memo map'
        map' []     = []
        map' (x:xs) = f x : go xs