# Chaitin's construction/Parser

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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)

(>>@) :: 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
``` module PreludeExt (bool) where