Better pattern for caching results

Question

I'm running a number of times now into a similar pattern which is error-prone (typos can skip some caching) and simply doesn't look nice to me. Is there a better way of writing something like this?

sum_with_cache' result cache ((p1,p2,p3,p4):partitions) = let (cache_p1, sol1) = count_noncrossing' cache p1 (cache_p2, sol2) = count_noncrossing' cache_p1 p2 (cache_p3, sol3) = count_noncrossing' cache_p2 p3 (cache_p4, sol4) = count_noncrossing' cache_p3 p4 in sum_with_cache' (result+(sol1*sol2*sol3*sol4)) cache_p4 partitions

So basically N operations which can update the cache?

I could write also something like:

process_with_cache' res cache _ [] = (cache, res) process_with_cache' res cache f (x:xs) = let (new_cache, r) = f cache x in process_with_cache' (r:res) new_cache f xs process_with_cache = process_with_cache' []

But that doesn't look really clean either. Is there a nicer way of writing this code?

If you want to maintain an implicit state between function calls, look at Control.Monad.State. — Koterpillar
– Koterpillar, Commented Mar 17, 2013 at 2:13
Are you trying to build a memo table? haskell.org/haskellwiki/Memoization — Don Stewart
– Don Stewart, Commented Mar 17, 2013 at 11:29

ertes · Accepted Answer · 2013-03-17 03:24:06Z

Another similar pattern is when you request a series of named random numbers:

let (x, rng') = random rng'' (y, rng) = random rng' in (x^2 + y^2, rng)

This is exactly when using a state monad is the right way to go:

import Control.Monad.State

For all random number generators of type (RandomGen g) => g there is a state monad State g, which threads the state implicitly:

do x <- state random y <- state random return (x^2 + y^2)

The state function simply takes a function of type s -> (a, s) and turns it into a computation of type State s a, in this case:

state :: (RandomGen g) => (g -> (a, g)) -> State g a

You can run a State computation by using runState, evalState or execState:

runState (liftA2 (\x y -> x^2 + y^2) (state random) (state random)) (mkStdGen 0)

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