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-- This code partly uses algorithms (drip/abstract) created by John Tromp.
-- Since they did not license their code (afaik), I assume it's okay to reuse it.
module Transpile
( transpileSKI
, transpileJottary
) where
import Term
import Utils
data SKI = S | K | I | AppSKI SKI SKI | IdxSKI Int
deriving (Eq, Ord)
instance Show SKI where
showsPrec _ S = showString "s"
showsPrec _ K = showString "k"
showsPrec _ I = showString "i"
showsPrec _ (AppSKI x y) =
showString "(" . shows x . showString " " . shows y . showString ")"
showsPrec _ (IdxSKI i) = shows i
drip :: SKI -> SKI
drip i@(AppSKI (AppSKI S K) _) = i
drip ( IdxSKI 0 ) = invalid
drip ( IdxSKI i ) = IdxSKI (i - 1)
drip ( AppSKI x y ) = AppSKI (drip x) (drip y)
drip x = x
abstract :: SKI -> SKI
abstract (AppSKI sk@(AppSKI S K) _) = sk
abstract e = if freeIn (== 0) e then occabstract e else AppSKI K (drip e) where
freeIn _ (AppSKI (AppSKI S K) _) = False
freeIn fv (AppSKI x y) = freeIn fv x || freeIn fv y
freeIn fv (IdxSKI i ) = fv i
freeIn _ _ = False
isConst = not . freeIn (const True)
occabstract (IdxSKI 0) = I
occabstract (AppSKI m (IdxSKI 0)) | not (freeIn (== 0) m) = drip m
occabstract (AppSKI (AppSKI l m) l') | l == l' =
occabstract (AppSKI (AppSKI (AppSKI (AppSKI S S) K) l) m)
occabstract (AppSKI m (AppSKI n l)) | isConst m && isConst n =
occabstract (AppSKI (AppSKI (AppSKI S (abstract m)) n) l)
occabstract (AppSKI (AppSKI m n) l) | isConst m && isConst l =
occabstract (AppSKI (AppSKI (AppSKI S m) (abstract l)) n)
occabstract (AppSKI (AppSKI m l) (AppSKI n l'))
| l == l' && isConst m && isConst n = occabstract
(AppSKI (AppSKI (AppSKI S m) n) l)
occabstract (AppSKI e1 e2) = AppSKI (AppSKI S (abstract e1)) (abstract e2)
occabstract _ = invalid
transpileSKI :: Term -> SKI
transpileSKI (Idx i ) = IdxSKI i
transpileSKI (App m n) = AppSKI (transpileSKI m) (transpileSKI n)
transpileSKI (Abs m ) = abstract (transpileSKI m)
fromBinary :: [Bool] -> Int
fromBinary (x : xs) = fromEnum x + 2 * fromBinary xs
fromBinary [] = 0
jottarify :: SKI -> Int
jottarify s = fromBinary (reverse $ True : go s) - 1
where
go S = [True, True, True, True, True, False, False, False]
go K = [True, True, True, False, False]
go I = go $ AppSKI (AppSKI S K) K
go (AppSKI a b) = True : (go a ++ go b)
go _ = invalid
transpileJottary :: SKI -> String
transpileJottary s = replicate (jottarify s) '1'
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