Haskell Quiz/Bytecode Compiler/Solution Michael Sloan

import Char(digitToInt)

data Tok = C Char | N Int | Op Char | App Tok Tok Tok | G {members :: [Tok]}

--Debugging porpoises
instance Show Tok where
    show (C ch) = ch : ""
    show (N i) = show i
    show (Op ch) = ch : ""
    show (App a o b) = '(' : (show a) ++ (show o) ++ (show b) ++ ")"
    show (G xs) = '[' : (concatMap (\x -> show x) xs) ++ "]"

parse xs = stripG $ prec '+' $ prec '-' $ prec '*' $ prec '/' $ prec '^' $ pToks $ parseNOp $ map (\ch -> C ch) xs

parseNOp [] = []
parseNOp ((N num):(C ch):inp) | ch `elem` "0123456789" = parseNOp (N (num * 10 + digitToInt ch) : inp)
parseNOp         ((C ch):inp) | ch `elem` "0123456789" = parseNOp (N (digitToInt ch) : inp)
parseNOp         ((C ch):inp) | ch `elem` "+-*/^%" = parseNOp (Op ch : inp)
parseNOp         ((C ch):inp) | ch `elem` " \t\r\n" = parseNOp inp
parseNOp (a:inp) = a : (parseNOp inp)

--Groups an array of tokens if it needs to be
g (x:xs) | null xs = x
g xs = G xs

--Returns parsed tokens/stream remainder
pToks = fst . parseG
pRem = snd . parseG

parseG []              = ([], [])
parseG [(G ts)]        = (ts, [])
parseG ((C '(') : inp) = (g (pToks inp) : (pToks $ pRem inp), []) 
parseG ((C ')') : inp) = ([], inp)
parseG (i:inp)         = (i : (pToks inp), pRem inp)

--Traverses groups, applies operators to their immediate arguments
prec mo [] = []
prec mo ((G xs):inp) = (g $ prec mo xs) : (prec mo inp)
prec mo (a:(Op o):b:inp) | o == mo = prec mo ((App (g $ prec mo [a]) (Op o) (g $ prec mo [b])) : inp)
prec mo ((App a o b):inp)          = (App (g $ prec mo [a]) o (g $ prec mo [b])) : (prec mo inp)
prec mo (x:inp) = x : (prec mo inp)

--Removes any vestigial grouping
stripG (App a o b) = App (stripG a) o (stripG b)
stripG (G (x:xs)) | null xs = error $ "error: " ++ show (x:xs) ++ " <- improper infix nesting here"
stripG (G (x:xs)) = stripG x
stripG x = x

--Converts to a byte format
bytes (C x) = error ("Invalid character: " ++ [x])
bytes (N n) = if abs n < 2^15 then 1 : toByteArray n 2 else 2 : toByteArray n 4
bytes (Op ch) = case ch of '+' -> [10]; '*' -> [11]; '^' -> [12]; '/' -> [14]; '%' -> [15]
bytes (App a o b) = (bytes a) ++ (bytes b) ++ (bytes o)
bytes x = error ("Error, invalid: " ++ show x)

toByteArray x n = map (\i -> (x `div` 2^(i*8)) `mod` 256 ) [(n-1),(n-2)..0]