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module Helper where
import Control.Monad.State
import qualified Data.BitString as Bit
import qualified Data.ByteString as Byte
data Error = UndeclaredFunction String | DuplicateFunction String | InvalidIndex Int | FatalError String
instance Show Error where
show (UndeclaredFunction err) = "ERROR: undeclared function " <> show err
show (DuplicateFunction err) = "ERROR: duplicate function " <> show err
show (InvalidIndex err) = "ERROR: invalid index " <> show err
show (FatalError err) = show err
type Failable = Either Error
data Expression = Bruijn Int | Variable String | Abstraction Expression | Application Expression Expression
deriving (Ord, Eq)
data Instruction = Define String Expression [Instruction] | Evaluate Expression | Comment String | Import String String | Test Expression Expression
deriving (Show)
instance Show Expression where
show (Bruijn x ) = "\ESC[31m" <> show x <> "\ESC[0m"
show (Variable var) = "\ESC[35m" <> var <> "\ESC[0m"
show (Abstraction exp) = "\ESC[36m[\ESC[0m" <> show exp <> "\ESC[36m]\ESC[0m"
show (Application exp1 exp2) =
"\ESC[33m(\ESC[0m" <> show exp1 <> " " <> show exp2 <> "\ESC[33m)\ESC[0m"
type EnvDef = (String, Expression)
type Environment = [(EnvDef, [EnvDef])]
type Program = State Environment
---
listify :: [Expression] -> Expression
listify [] = Abstraction (Abstraction (Bruijn 0))
listify (fst : rst) =
Abstraction (Application (Application (Bruijn 0) fst) (listify rst))
encodeByte :: Bit.BitString -> Expression
encodeByte bits = listify (map encodeBit (Bit.toList bits))
where
encodeBit False = Abstraction (Abstraction (Bruijn 0))
encodeBit True = Abstraction (Abstraction (Bruijn 1))
encodeBytes :: Byte.ByteString -> Expression
encodeBytes bytes =
listify (map (encodeByte . Bit.from01List . (: [])) (Byte.unpack bytes))
encodeStdin :: IO Expression
encodeStdin = do
bytes <- Byte.getContents
pure $ encodeBytes bytes
---
likeTernary :: Expression -> Bool
likeTernary (Abstraction (Abstraction (Abstraction (Abstraction _)))) = True
likeTernary _ = False
-- Dec to Bal3 in Bruijn encoding: reversed application with 0=>0; 1=>1; T=>2; end=>3
-- e.g. 0=0=[[[[3]]]]; 2=1T=[[[[2 (0 3)]]]] -5=T11=[[[[0 (0 (2 3))]]]]
decimalToTernary :: Integer -> Expression
decimalToTernary n =
Abstraction $ Abstraction $ Abstraction $ Abstraction $ gen n
where
gen 0 = Bruijn 3
gen n = Application (Bruijn $ fromIntegral $ mod n 3) (gen $ div (n + 1) 3)
ternaryToDecimal :: Expression -> Integer
ternaryToDecimal exp = sum $ zipWith (*) (resolve exp) (iterate (* 3) 1)
where
multiplier (Bruijn 0) = 0
multiplier (Bruijn 1) = 1
multiplier (Bruijn 2) = (-1)
resolve' (Application x@(Bruijn _) (Bruijn 3)) = [multiplier x]
resolve' (Application fst@(Bruijn _) rst@(Application _ _)) =
(multiplier fst) : (resolve' rst)
resolve' _ = [0]
resolve (Abstraction (Abstraction (Abstraction (Abstraction n)))) =
resolve' n
resolve _ = [0]
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