Auto-memoization in Haskell by State monad

automemoization.hs

import Control.Monad.State
import qualified Data.Map as Map

recall :: Ord a => a -> State (Map.Map a r) (Maybe r)
recall n = do
  memory <- get
  return (Map.lookup n memory)

memorize :: Ord a => a -> r -> State (Map.Map a r) ()
memorize n result = do
  memory <- get
  put (Map.insert n result memory)

type MemorizedResult a r = State (Map.Map a r) r
type ClosedFunction a r = a -> MemorizedResult a r
type OpenFunction a r = ClosedFunction a r -> ClosedFunction a r

memoized :: Ord a => OpenFunction a r -> a -> r
memoized client arg = evalState (closeThroughMemory client arg) Map.empty

closeThroughMemory :: Ord a => OpenFunction a r -> ClosedFunction a r
closeThroughMemory client n = do
  recalled <- recall n
  case recalled of
    Just result -> return result
    Nothing -> do
      result <- client (closeThroughMemory client) n
      memorize n result
      return result


openFibonacci :: OpenFunction Int Integer
openFibonacci self n = do
  if n < 2
  then return (fromIntegral n)
  else do
    prev1 <- self (n - 1)
    prev2 <- self (n - 2)
    let result = prev1 + prev2
    return result

fibonacci :: Int -> Integer
fibonacci = memoized openFibonacci


main :: IO ()
main = do
  putStrLn "n = "
  n <- getLine
  let result = fibonacci (read n)
  putStrLn $ "fibonacci(" ++ n ++ ") = " ++ show result

$ ghc -O2 automemoization.hs 
$ time echo 10000 | ./automemoization 
n = 
fibonacci(10000) = 33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875

real    0m0.033s
user    0m0.029s
sys     0m0.006s

Beautiful!