gistfile1.txt

{-# LANGUAGE LambdaCase #-}

module Main where

import Data.Traversable
import System.Environment
import Data.Foldable

data A
  = N
  | Add A A
  | Sub A A
  | Mul A A
  | Div A A
  | Pow A A

pretty :: Double -> A -> String
pretty n a =
  let f = \case
        N       -> show n
        Add x y -> "(" ++ f x ++ "+" ++ f y ++ ")"
        Sub x y -> "(" ++ f x ++ "-" ++ f y ++ ")"
        Mul x y -> "(" ++ f x ++ "*" ++ f y ++ ")"
        Div x y -> "(" ++ f x ++ "/" ++ f y ++ ")"
        Pow x y -> "(" ++ f x ++ "^" ++ f y ++ ")"
  in  f a ++ " = " ++ show (eval n a)

eval :: Double -> A -> Double
eval n = \case
  N -> n
  Add x y -> eval n x + eval n y
  Sub x y -> eval n x - eval n y
  Mul x y -> eval n x * eval n y
  Div x y -> eval n x / eval n y
  Pow x y -> eval n x ** eval n y

trees :: Int -> [A]
trees 1 = [N]
trees n =
  [ op l r
  | s  <- [0 .. pred n]
  , l  <- trees s
  , r  <- trees (n - s)
  , op <- [Add, Sub, Mul, Div, Pow]
  ]

main = do
  [n] <- fmap read <$> getArgs
  let t = 6
  traverse_ (putStrLn . pretty n) . filter (((==) t) . eval n) $ trees 4