使用Map在递归表达式中进行记忆

Question

我正在计算一些形式为

的递归表达式

现在，假设我有一个索引列表 t，u，v ([t,u,v]::Int)为简单起见，我们可以将其表示为[[Int]]，并且我想计算每个索引[t,u,v]的 R 函数使用类似于以下代码的内容：

import qualified Data.Vector.Unboxed as U
import qualified Data.Map.Strict as M

data HermiteStateIntegral = HermiteStateIntegral {
               getmapI :: M.Map [Int] Double
              ,getkeyI :: [[Int]]
               } deriving Show

calcIntegrals :: [Double] ->[[Int]] -> Double -> Vector Double
calcIntegrals vs listIndex f0 = U.unfoldr (calcRecExpr vs) seedI
seedI     = HermiteStateIntegral mapI0 listIndex
mapI0     = M.insert [0,0,0] f0 M.empty

calcRecExpr :: [Double] -> HermiteStateIntegral -> Maybe (Double,HermiteStateIntegral)
calcRecExpr vs hs@(HermiteStateIntegral m is)= do
           i <- safeHead is -- safeHead :: [a] -> Maybe a
           -- if the value associated with the indexes t,u,v is not in the map
           -- calculate it using the recursive equations
           let Just (val,newMap) = (lookupM i m) `mplus` (fun vs i m)
               newSt = hs{getmapI = newMap,getkeyI = tail is}
           return (val,newSt)


 where lookupM :: Ord k => k -> M.Map k a -> Maybe (a , M.Map k a)
       lookupM k m = do 
          val <- M.lookup k m
          return (val,m)  

fun :: [Double] -> [Int] ->  M.Map [Int] Double -> Maybe (Double, M.Map [Int] Double)
fun vs i m = -- fun computes the value associated with some index [t,u,v]
             -- that is not in the Map, using the recursive equations. And   
             -- insert this value on the Map.

所以，我使用Map来明确存储 R 子表达式。如果我想计算例如索引[1,1,1]，Map将存储我可以使用的索引[0,1,1]，[0,0,1]，[0,0,0]未来的计算。

我的问题是：这是明确缓存 R 子表达式的有效实现吗？是否有更有效的方式来表达使用延迟评估的记忆？