Chaitin's construction/Parser
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.
Decoding module
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
CL
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
CL extension
module CLExt ((>>@)) where
import CL (CL, apply)
import Control.Monad (Monad, liftM2)
(>>@) :: Monad m => m CL -> m CL -> m CL
(>>@) = liftM2 apply
Base symbol
module BaseSymbol (BaseSymbol, kay, ess) where
data BaseSymbol = K | S
kay, ess :: BaseSymbol
kay = K
ess = S
Utility modules
Binary tree
module Tree (Tree (Leaf, Branch)) where
data Tree a = Leaf a | Branch (Tree a) (Tree a)
Parser
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
Prelude extension
module PreludeExt (bool) where
bool :: a -> a -> Bool -> a
bool thenC elseC t = if t then thenC else elseC