module StackExpr where

data Instr
  = Const Integer
  | Add
  | Sub
  | Mul
  | Neg
  | Abs
  | Sig
  deriving (Show)

newtype Program = P [Instr] deriving (Show)

instance Num Program where
  fromInteger i = P [Const i]
  P a + P b = P (b ++ a ++ [Add])
  P a - P b = P (b ++ a ++ [Sub])
  P a * P b = P (b ++ a ++ [Mul])
  negate (P a) = P (a ++ [Neg])
  abs (P a) = P (a ++ [Abs])
  signum (P a) = P (a ++ [Sig])

eval :: Program -> Integer
eval (P xs) = go [] xs
  where
    go (x:_) [] = x
    go xs (Const i:ys) = go (i:xs) ys
    go (a:b:xs) (Add:ys) = go ((a+b):xs) ys
    go (a:b:xs) (Mul:ys) = go ((a*b):xs) ys
    go (a:b:xs) (Sub:ys) = go ((a-b):xs) ys
    go (a:xs) (Neg:ys) = go ((negate a):xs) ys
    go (a:xs) (Abs:ys) = go ((abs a):xs) ys
    go (a:xs) (Sig:ys) = go ((signum a):xs) ys