Automatic memoizing in functional programming languages

Question

I always thought that Haskell would do some sort of automatic intelligent memoizing. E.g., the naive Fibonacci implementation

fib 0 = 0
fib 1 = 1
fib n = fib         


        

Answer 1

I said in a comment that your requirements sounded like garbage collection. I thought this because you are interested in managing a limited pool of memory, purging it once in a while so that it doesn't go over.

Now that I think about it, it's more like a virtual memory page replacement algorithm. You can read that Wikipedia page for various approaches used to solve that kind of problem, such as "not recently used", "aging", "clock", "second chance", etc.

However, memoization isn't often done by restricting the results retained; the required mutation for the above-mentioned algorithms is generally un-haskellish. Don't let that discourage you, though. You have interesting ideas that could be valuable additions to the exploration of memoization possibilities in Haskell performed thusfar.

Sometimes a particular memoization problem lends itself well to limited memory. For example, aligning two gene sequences can be done with Dynamic Programming (see Wikipedia's Dynamic Programming # Sequence alignment) with a 2-dimensional memoization table. But since the DP solution for a given cell only depends on the results from the preceding row, you can start from the bottom and discard rows that are more than 1 away from the current row. Fibonacci numbers are the same: you only need the previous two numbers in the sequence in order to compute the next. You can discard anything earlier if all you are interested in is the n^th number.

Most memoizations are for the sake of speeding up recursive algorithms where there are shared subproblems. Many such problems do not have an easy way of sequencing the evaluations in order to throw away the results you no longer need. At that point, you're just guessing, using heuristics (like frequency of use) to determine who gets how much access to the limited resource.