DouKaku?

import Numeric

data Item a b = Value a | Op (a->a->a) b [Char]

cat a b = a*10+b

ops :: [Item Double Integer]
ops = [Op cat 2 "", Op (+) 0 "+", Op (-) 0 "-", Op (*) 1 "*", Op (/) 1 "/"]
 
opparse [] _ vs = reverse vs
opparse (op:ops) (i:is) vs = opparse ops is $ push op (Value i) vs

push op@(Op o p _) v (op'@(Op o' p' _):vs)
  | (p <= p') = (op:v:op':vs)
  | otherwise = (op':push op v vs)
push op v vs = op:v:vs

calc [a] [] = a
calc ns ((Value a):vs) = calc (a:ns) vs
calc (a:b:ns) ((Op op _ _):vs) = calc ((op b a):ns) vs
calc _ _ = error "invalid stack state"

showFormula ops = "1" ++ rec [2..] ops where
   rec _ [] = ""
   rec (i:is) ((Op _ _ n):ops) = n ++ (showInt . round) i (rec is ops)

genops 0 = [[]]
genops n = [o:os | o <- map (ops!!) [0..4], os <- genops (n-1)]

komachi n = [ops | ops <- genops n, test 100 ops] where
   test sum ops = abs (sum - (calc [] $ opparse ops [2..] [Value 1])) <= 1.0e-10

main = putStr $ unlines $ map showFormula $ komachi 8