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-- MIT License, Copyright (c) 2022 Marvin Borner
module Conversion where
import qualified Data.BitString as Bit
import qualified Data.ByteString.Lazy as Byte
import qualified Data.ByteString.Lazy.Char8 as C
import Data.Char ( chr )
import GHC.Real ( denominator
, numerator
)
import Numeric ( showFFloatAlt )
import Helper
listify :: [Expression] -> Expression
listify [] = Abstraction (Abstraction (Bruijn 0))
listify (e : es) =
Abstraction (Application (Application (Bruijn 0) e) (listify es))
binarify :: [Expression] -> Expression
binarify = foldr Application (Bruijn 2)
encodeByte :: [Bool] -> Expression
encodeByte bits = Abstraction $ Abstraction $ Abstraction $ binarify
(map encodeBit bits)
where
encodeBit False = Bruijn 0
encodeBit True = Bruijn 1
-- TODO: There must be a better way to do this :D
encodeBytes :: Byte.ByteString -> Expression
encodeBytes bytes = listify $ map
(encodeByte . Bit.toList . Bit.bitStringLazy . Byte.pack . (: []))
(Byte.unpack bytes)
stringToExpression :: String -> Expression
stringToExpression = encodeBytes . C.pack
charToExpression :: Char -> Expression
charToExpression ch = encodeByte $ Bit.toList $ Bit.bitStringLazy $ C.pack [ch]
encodeStdin :: IO Expression
encodeStdin = encodeBytes <$> Byte.getContents
unlistify :: Expression -> Maybe [Expression]
unlistify (Abstraction (Abstraction (Bruijn 0))) = Just []
unlistify (Abstraction (Application (Application (Bruijn 0) e) es)) =
(:) <$> Just e <*> unlistify es
unlistify _ = Nothing
unpairify :: Expression -> Maybe [Expression]
unpairify (Abstraction (Application (Application (Bruijn 0) e1) e2)) =
Just (e1 : [e2])
unpairify _ = Nothing
decodeByte :: Expression -> Maybe [Bool]
decodeByte (Abstraction (Abstraction (Abstraction es))) = decodeByte es
decodeByte (Application (Bruijn 0) es) = (:) <$> Just False <*> decodeByte es
decodeByte (Application (Bruijn 1) es) = (:) <$> Just True <*> decodeByte es
decodeByte (Bruijn 2 ) = Just []
decodeByte _ = Nothing
decodeStdout :: Expression -> Maybe String
decodeStdout e = do
u <- unlistify e
pure $ C.unpack $ Byte.concat $ map
(\m -> case decodeByte m of
Just b -> Bit.realizeBitStringLazy $ Bit.fromList b
Nothing -> Byte.empty
)
u
---
floatToRational :: Rational -> Expression
floatToRational f = Abstraction
(Application (Application (Bruijn 0) (decimalToTernary p))
(decimalToTernary $ q - 1)
)
where
p = numerator f
q = denominator f
floatToReal :: Rational -> Expression
floatToReal = Abstraction . floatToRational
floatToComplex :: Rational -> Rational -> Expression
floatToComplex r i = Abstraction $ Abstraction $ Application
(Application (Bruijn 0) (Application (floatToReal r) (Bruijn 1)))
(Application (floatToReal i) (Bruijn 1))
-- 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 (1 3)]]]] -5=T11=[[[[1 (1 (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)
-- Decimal to binary encoding
decimalToBinary :: Integer -> Expression
decimalToBinary n | n < 0 = decimalToBinary 0
| otherwise = Abstraction $ Abstraction $ Abstraction $ gen n
where
gen 0 = Bruijn 2
gen n' = Application (Bruijn $ fromIntegral $ mod n' 2) (gen $ div n' 2)
-- Decimal to unary (church) encoding
decimalToUnary :: Integer -> Expression
decimalToUnary n | n < 0 = decimalToUnary 0
| otherwise = Abstraction $ Abstraction $ gen n
where
gen 0 = Bruijn 0
gen n' = Application (Bruijn 1) (gen (n' - 1))
-- Decimal to de Bruijn encoding
decimalToDeBruijn :: Integer -> Expression
decimalToDeBruijn n | n < 0 = decimalToDeBruijn 0
| otherwise = gen n
where
gen 0 = Abstraction $ Bruijn $ fromInteger n
gen n' = Abstraction $ gen (n' - 1)
unaryToDecimal :: Expression -> Maybe String
unaryToDecimal e = (<> "u") . show <$> unaryToDecimal' e
unaryToDecimal' :: Expression -> Maybe Integer
unaryToDecimal' e = do
res <- resolve e
return (sum res :: Integer)
where
multiplier (Bruijn 1) = Just 1
multiplier _ = Nothing
resolve' (Bruijn 0) = Just []
resolve' (Application x@(Bruijn _) (Bruijn 0)) =
(:) <$> multiplier x <*> Just []
resolve' (Application x@(Bruijn _) xs@(Application _ _)) =
(:) <$> multiplier x <*> resolve' xs
resolve' _ = Nothing
resolve (Abstraction (Abstraction n)) = resolve' n
resolve _ = Nothing
binaryToChar :: Expression -> Maybe String
binaryToChar e = show <$> binaryToChar' e
binaryToChar' :: Expression -> Maybe Char
binaryToChar' e = do
n <- binaryToDecimal e
if n > 31 && n < 127 || n == 10 then Just $ chr $ fromIntegral n else Nothing
binaryToString :: Expression -> Maybe String
binaryToString e = (<> "b") . show <$> binaryToDecimal e
binaryToDecimal :: Expression -> Maybe Integer
binaryToDecimal e = do
res <- resolve e
return (sum $ zipWith (*) res (iterate (* 2) 1) :: Integer)
where
multiplier (Bruijn 0) = Just 0
multiplier (Bruijn 1) = Just 1
multiplier _ = Nothing
resolve' (Bruijn 2) = Just []
resolve' (Application x@(Bruijn _) (Bruijn 2)) =
(:) <$> multiplier x <*> Just []
resolve' (Application x@(Bruijn _) xs@(Application _ _)) =
(:) <$> multiplier x <*> resolve' xs
resolve' _ = Nothing
resolve (Abstraction (Abstraction (Abstraction n))) = resolve' n
resolve _ = Nothing
ternaryToString :: Expression -> Maybe String
ternaryToString e = (<> "t") . show <$> ternaryToDecimal e
ternaryToDecimal :: Expression -> Maybe Integer
ternaryToDecimal e = do
res <- resolve e
return (sum $ zipWith (*) res (iterate (* 3) 1) :: Integer)
where
multiplier (Bruijn 0) = Just 0
multiplier (Bruijn 1) = Just 1
multiplier (Bruijn 2) = Just (-1)
multiplier _ = Nothing
resolve' (Bruijn 3) = Just []
resolve' (Application x@(Bruijn _) (Bruijn 3)) =
(:) <$> multiplier x <*> Just []
resolve' (Application x@(Bruijn _) xs@(Application _ _)) =
(:) <$> multiplier x <*> resolve' xs
resolve' _ = Nothing
resolve (Abstraction (Abstraction (Abstraction (Abstraction n)))) =
resolve' n
resolve _ = Nothing
rationalToString :: Expression -> Maybe String
rationalToString (Abstraction (Application (Application (Bruijn 0) a) b)) = do
n <- ternaryToDecimal a
d <- ternaryToDecimal b
Just
$ show n
<> "/"
<> show (d + 1)
<> " (approx. "
<> showFFloatAlt (Just 8)
(fromIntegral n / fromIntegral (d + 1) :: Double)
""
<> ")"
rationalToString _ = Nothing
realToString :: Expression -> Maybe String
realToString (Abstraction e) = rationalToString e
realToString _ = Nothing
complexToString :: Expression -> Maybe String
complexToString (Abstraction (Abstraction (Application (Application (Bruijn 0) (Abstraction (Application (Application (Bruijn 0) lr) rr))) (Abstraction (Application (Application (Bruijn 0) li) ri)))))
= do
nlr <- ternaryToDecimal lr
drr <- ternaryToDecimal rr
nli <- ternaryToDecimal li
dri <- ternaryToDecimal ri
Just
$ show nlr
<> "/"
<> show (drr + 1)
<> " + "
<> show nli
<> "/"
<> show (dri + 1)
<> "i"
<> " (approx. "
<> showFFloatAlt (Just 8)
(fromIntegral nlr / fromIntegral (drr + 1) :: Double)
""
<> "+"
<> showFFloatAlt (Just 8)
(fromIntegral nli / fromIntegral (dri + 1) :: Double)
""
<> "i)"
complexToString _ = Nothing
|
