Let us describe the seen language with a LL(1) grammar, and let us make use of the lack of backtracking, lack of look-ahead, when deciding which parser approach to use.
Some notes about the used parser library: I shall use the didactical approach read in paper Monadic Parser Combinators (written by Graham Hutton and Erik Meier). The optimalisations described in the paper are avoided here. Of course, we can make optimalisations, or choose sophisticated parser libraries (Parsec, arrow parsers). A pro for this simpler parser: it may be easier to augment it with other monad transformers. But, I think, the task does not require such ability. So the real pro for it is that it looks more didactical for me. Of couse, it may be inefficient at many other tasks, but I hope, the LL(1) grammar will not raise huge problems.
module Decode (clP) where import Parser (Parser, item) import CL (CL, k, s, apply) import CLExt ((>>@)) import PreludeExt (bool) clP :: Parser Bool CL clP = item >>= bool applicationP baseP applicationP :: Parser Bool CL applicationP = clP >>@ clP baseP :: Parser Bool CL baseP = item >>= bool k s kP, sP :: Parser Bool CL kP = return k sP = return s
Combinatory logic term modules
module CL (CL, k, s, apply) where import Tree (Tree (Leaf, Branch)) import BaseSymbol (BaseSymbol, kay, ess) type CL = Tree BaseSymbol k, s :: CL k = Leaf kay s = Leaf ess apply :: CL -> CL -> CL apply = Branch
module CLExt ((>>@)) where import CL (CL, apply) import Control.Monad (Monad, liftM2) (>>@) :: Monad m => m CL -> m CL -> m CL (>>@) = liftM2 apply
module BaseSymbol (BaseSymbol, kay, ess) where data BaseSymbol = K | S kay, ess :: BaseSymbol kay = K ess = S
module Tree (Tree (Leaf, Branch)) where data Tree a = Leaf a | Branch (Tree a) (Tree a)
module Parser (Parser, runParser, item) where import Control.Monad.State (StateT, runStateT, get, put) type Parser token a = StateT [token]  a runParser :: Parser token a -> [token] -> [(a, [token])] runParser = runStateT item :: Parser token token item = do token : tokens <- get put tokens return token
module PreludeExt (bool) where bool :: a -> a -> Bool -> a bool thenC elseC t = if t then thenC else elseC