-----------------------------------------------------------------------------
-- |
-- Module : Data.Spine
-- Copyright : (c) 2010 University of Minho
-- License : BSD3
--
-- Maintainer : hpacheco@di.uminho.pt
-- Stability : experimental
-- Portability : non-portable
--
-- Pointless Rewrite:
-- automatic transformation system for point-free programs
--
-- Representation of spines for generic programming a la SYB revolutions.
--
-----------------------------------------------------------------------------
module Data.Spine where
import Data.Type
import Data.Monoid hiding (Any)
import Generics.Pointless.Functors
import Generics.Pointless.Combinators
-- * A spine representation for data values à la SYB revolutions
data Typed a = Type a :| a
data Spine a where
As :: a -> Con -> Spine a
Ap :: Spine (a -> b) -> Typed a -> Spine b
data Fixity = Prefix | Infix deriving Eq
data Con = Con {name :: String, fixity :: Fixity}
scon n = Con {name = show n, fixity = Prefix}
pcon s = Con {name = s, fixity = Prefix}
icon s = Con {name = s, fixity = Infix}
-- | Converting from a spine to a value
fromSpine :: Spine a -> a
fromSpine (c `As` _) = c
fromSpine (Ap f (_ :| a)) = (fromSpine f) a
-- | Converting from a value to a spine
toSpine :: Type a -> a -> Spine a
toSpine Any x = x `As` (pcon "Any")
toSpine (Id a) x = x `As` (pcon "Id")
toSpine Int n = n `As` (scon n)
toSpine Bool n = n `As` (scon n)
toSpine Char n = n `As` (scon n)
toSpine One x = x `As` (pcon "(_L::One)")
toSpine (Either a _) (Left x) = Left `As` (pcon "Left")
`Ap` (a :| x)
toSpine (Either _ b) (Right y) = Right `As` (pcon "Right")
`Ap` (b :| y)
toSpine (Prod a b) (x,y) = (,) `As` (icon ",")
`Ap` (a :| x)
`Ap` (b :| y)
toSpine (Fun a b) f = f `As` (pcon "Fun")
toSpine (Lns c a) l = l `As` (pcon "Lns")
toSpine (a@(Data s fctr)) v = inn `As` (pcon $ "innT" ++ s)
`Ap` ((rep fctr a) :| out v)
toSpine Dynamic (Dyn t x) = Dyn t `As` (pcon "Dyn")
`Ap` (t :| x)
toSpine TP x = x `As` (pcon "TP")
toSpine (TU a) x = x `As` (pcon "TQ")
toSpine (Pf _) HOLE = HOLE `As` (pcon "_L")
toSpine (Pf _) TOP = TOP `As` (pcon "T")
toSpine (Pf (Fun _ _)) (FUN s f) = (FUN s f) `As` (pcon s)
toSpine (Pf (Fun a c)) (CONV e@(Left _) f) = CONV e `As` (pcon "lconv")
`Ap` (Pf (Fun c a) :| f)
toSpine (Pf (Fun a c)) (CONV e@(Right _) f) = CONV e `As` (pcon "rconv")
`Ap` (Pf (Fun c a) :| f)
toSpine (Pf (Lns a c)) (CONV_LNS e@(Left _) f) = CONV_LNS e `As` (pcon "lconv")
`Ap` (Pf (Lns c a) :| f)
toSpine (Pf (Lns a c)) (CONV_LNS e@(Right _) f) = CONV_LNS e `As` (pcon "rconv")
`Ap` (Pf (Lns c a) :| f)
toSpine (Pf (Lns c a)) (LNS s l) = (LNS s l) `As` (pcon s)
toSpine (Pf (Fun c a)) (COMPF fctr b f g) = (COMPF fctr b) `As` (pcon $ "compf " ++ show fctr)
`Ap` (Pf (Fun (rep fctr b) a) :| f)
`Ap` (Pf (Fun c (rep fctr b)) :| g)
toSpine (Pf (Lns c a)) (COMPF_LNS fctr b f g) = (COMPF_LNS fctr b) `As` (pcon $ "compf_lns " ++ show fctr)
`Ap` (Pf (Lns (rep fctr b) a) :| f)
`Ap` (Pf (Lns c (rep fctr b)) :| g)
toSpine (Pf (Fun a b)) (PROTECT f) = PROTECT `As` (pcon "protect")
`Ap` (Pf (Fun a b) :| f)
toSpine (Pf (Lns a b)) (PROTECT_LNS f) = PROTECT_LNS `As` (pcon "protect_lns")
`Ap` (Pf (Lns a b) :| f)
toSpine (Pf _) (VAR s) = VAR s `As` (pcon s)
toSpine (Pf (Fun a b)) (PNT vb) = PNT vb `As` (pcon $ showL ["pnt",gshow b vb])
toSpine (Pf (Fun _ _)) BANG = BANG `As` (pcon "bang")
toSpine (Pf (Fun a c)) (COMP b f g) = COMP b `As` (icon ".")
`Ap` (Pf (Fun b c) :| f)
`Ap` (Pf (Fun a b) :| g)
toSpine (Pf (Fun _ _)) FST = FST `As` (pcon "fst")
toSpine (Pf (Fun _ _)) SND = SND `As` (pcon "snd")
toSpine (Pf (Fun a (Prod b c))) (SPLIT f g) = SPLIT `As` (icon "/\\")
`Ap` (Pf (Fun a b) :| f)
`Ap` (Pf (Fun a c) :| g)
toSpine (Pf (Fun (Prod a b) (Prod c d))) (PROD f g) = PROD `As` (icon "><")
`Ap` (Pf (Fun a c) :| f)
`Ap` (Pf (Fun b d) :| g)
toSpine (Pf (Fun _ _)) INL = INL `As` (pcon "inl")
toSpine (Pf (Fun _ _)) INR = INR `As` (pcon "inr")
toSpine (Pf (Fun (Either a b) c)) (EITHER f g) = EITHER `As` (icon "\\/")
`Ap` (Pf (Fun a c) :| f)
`Ap` (Pf (Fun b c) :| g)
toSpine (Pf (Fun (Either a b) (Either c d))) (SUM f g) = SUM `As` (icon "-|-")
`Ap` (Pf (Fun a c) :| f)
`Ap` (Pf (Fun b d) :| g)
toSpine (Pf func) ZERO = aux func
where aux :: Monoid y => Type (x -> y) -> Spine (Pf (x -> y))
aux t@(Fun _ (Data "List" fctr)) = ZERO `As` pcon "nil"
aux (Fun _ Int) = ZERO `As` pcon "const 0"
aux _ = ZERO `As` pcon "mempty"
toSpine (Pf func) PLUS = aux func
where aux :: Monoid a => Type ((a,a) -> a) -> Spine (Pf ((a,a) -> a))
aux (Fun _ (Data "List" fctr)) = PLUS `As` pcon "(++)"
aux (Fun _ Int) = PLUS `As` pcon "(uncurry (+))"
aux _ = PLUS `As` pcon "mappend"
toSpine (Pf (Fun _ _)) ID = ID `As` (pcon "id")
toSpine (Pf (Fun _ _)) SWAP = SWAP `As` (pcon "swap")
toSpine (Pf (Fun _ _)) COSWAP = COSWAP `As` (pcon "coswap")
toSpine (Pf (Fun _ _)) DISTL = DISTL `As` (pcon "distl")
toSpine (Pf (Fun _ _)) UNDISTL = UNDISTL `As` (pcon "undistl")
toSpine (Pf (Fun _ _)) DISTR = DISTR `As` (pcon "distr")
toSpine (Pf (Fun _ _)) UNDISTR = UNDISTR `As` (pcon "undistr")
toSpine (Pf (Fun _ _)) ASSOCL = ASSOCL `As` (pcon "assocl")
toSpine (Pf (Fun _ _)) ASSOCR = ASSOCR `As` (pcon "assocr")
toSpine (Pf (Fun _ _)) COASSOCL = COASSOCL `As` (pcon "coassocl")
toSpine (Pf (Fun _ _)) COASSOCR = COASSOCR `As` (pcon "coassocr")
toSpine (Pf (Fun _ a@(Data s _))) INN = INN `As` (pcon $ "inn" ++ s)
toSpine (Pf (Fun a@(Data s _) _)) OUT = OUT `As` (pcon $ "out" ++ s)
toSpine (Pf (Fun _ _)) (FMAP fctr (Fun a c) f) = FMAP fctr (Fun a c) `As` (pcon $ "fmap")
`Ap` (Pf (Fun a c) :| f)
toSpine (Pf (Fun _ _)) (FZIP fctr t f) = FZIP fctr t `As` (pcon $ "fzip")
`Ap` (Pf t :| f)
toSpine (Pf (Fun a b@(Data s fctr))) (ANA f) = ANA `As` (pcon $ "ana" ++ s)
`Ap` (Pf (Fun a (rep fctr a)) :| f)
toSpine (Pf (Fun a@(Data s fctr) b)) (CATA f) = CATA `As` (pcon $ "cata" ++ s)
`Ap` (Pf (Fun (rep fctr b) b) :| f)
toSpine (Pf func) (PARA f) = aux func f
where aux :: Type (a -> c) -> Pf (F a (c,a) -> c) -> Spine (Pf (a -> c))
aux (Fun a@(Data _ fctr) c) f = (PARA `As` pcon ("para")) `Ap` (Pf (Fun (rep fctr (Prod c a)) c) :| f)
toSpine (Pf (Fun c a)) (GET l) = GET `As` (pcon "get")
`Ap` (Pf (Lns c a) :| l)
toSpine (Pf (Fun (Prod a c) _)) (PUT l) = PUT `As` (pcon "put")
`Ap` (Pf (Lns c a) :| l)
toSpine (Pf (Fun a c)) (CREATE l) = CREATE `As` (pcon "create")
`Ap` (Pf (Lns c a) :| l)
toSpine (Pf (Lns c a)) (COMP_LNS b f g) = (COMP_LNS b) `As` (icon ".<")
`Ap` (Pf (Lns b a) :| f)
`Ap` (Pf (Lns c b) :| g)
toSpine (Pf (Lns (Prod a b) _)) (FST_LNS f) = FST_LNS `As` (pcon "fst_lns")
`Ap` (Pf (Fun a b) :| f)
toSpine (Pf (Lns (Prod a b) _)) (SND_LNS f) = SND_LNS `As` (pcon "snd_lns")
`Ap` (Pf (Fun b a) :| f)
toSpine (Pf (Lns (Prod c d) (Prod a b))) (PROD_LNS f g) = PROD_LNS `As` (icon "><<")
`Ap` (Pf (Lns c a) :| f)
`Ap` (Pf (Lns d b) :| g)
toSpine (Pf (Lns (Either a b) c)) (EITHER_LNS x f g) = EITHER_LNS `As` (icon "\\/<")
`Ap` (Pf (Fun c (Either One One)) :| x)
`Ap` (Pf (Lns a c) :| f)
`Ap` (Pf (Lns b c) :| g)
toSpine (Pf (Lns (Either c d) (Either a b))) (SUM_LNS f g) = SUM_LNS `As` (icon "-|-<")
`Ap` (Pf (Lns c a) :| f)
`Ap` (Pf (Lns d b) :| g)
toSpine (Pf (Lns (Either c d) (Either a b))) (SUMW_LNS x y f g) = SUMW_LNS `As` (pcon "sum_lns")
`Ap` (Pf (Fun (Prod a d) c) :| x)
`Ap` (Pf (Fun (Prod b c) d) :| y)
`Ap` (Pf (Lns c a) :| f)
`Ap` (Pf (Lns d b) :| g)
toSpine (Pf (Lns c One)) (BANG_LNS f) = BANG_LNS `As` (pcon "(!<)")
`Ap` (Pf (Fun One c) :| f)
toSpine (Pf (Lns c (Prod One _))) (BANGL_LNS) = BANGL_LNS `As` (pcon "bangl")
toSpine (Pf (Lns c (Prod _ One))) (BANGR_LNS) = BANGR_LNS `As` (pcon "bangr")
toSpine (Pf (Lns _ _)) ID_LNS = ID_LNS `As` (pcon "id_lns")
toSpine (Pf (Lns _ _)) SWAP_LNS = SWAP_LNS `As` (pcon "swap_lns")
toSpine (Pf (Lns _ _)) COSWAP_LNS = COSWAP_LNS `As` (pcon "coswap_lns")
toSpine (Pf (Lns _ _)) DISTL_LNS = DISTL_LNS `As` (pcon "distl_lns")
toSpine (Pf (Lns _ _)) UNDISTL_LNS = UNDISTL_LNS `As` (pcon "undistl_lns")
toSpine (Pf (Lns _ _)) DISTR_LNS = DISTR_LNS `As` (pcon "distr_lns")
toSpine (Pf (Lns _ _)) UNDISTR_LNS = UNDISTR_LNS `As` (pcon "undistr_lns")
toSpine (Pf (Lns _ _)) ASSOCL_LNS = ASSOCL_LNS `As` (pcon "assocl_lns")
toSpine (Pf (Lns _ _)) ASSOCR_LNS = ASSOCR_LNS `As` (pcon "assocr_lns")
toSpine (Pf (Lns _ _)) COASSOCL_LNS = COASSOCL_LNS `As` (pcon "coassocl_lns")
toSpine (Pf (Lns _ _)) COASSOCR_LNS = COASSOCR_LNS `As` (pcon "coassocr_lns")
toSpine (Pf (Lns _ a@(Data s _))) INN_LNS = INN_LNS `As` (pcon $ "inn" ++ s ++ "_lns")
toSpine (Pf (Lns a@(Data s _) _)) OUT_LNS = OUT_LNS `As` (pcon $ "out" ++ s ++ "_lns")
toSpine (Pf (Lns _ _)) (FMAP_LNS fctr (Fun c a) (f)) = FMAP_LNS fctr (Fun c a) `As` (pcon $ "fmap_lns " ++ show fctr)
`Ap` (Pf (Lns c a) :| f)
toSpine (Pf (Lns a b@(Data s fctr))) (ANA_LNS f) = ANA_LNS `As` (pcon $ "ana" ++ s ++ "_lns")
`Ap` (Pf (Lns a (rep fctr a)) :| f)
toSpine (Pf (Lns a@(Data s fctr) b)) (CATA_LNS f) = CATA_LNS `As` (pcon $ "cata" ++ s ++ "_lns")
`Ap` (Pf (Lns (rep fctr b) b) :| f)
toSpine (Pf (Lns la lb)) (MAP_LNS f) = MAP_LNS `As` (pcon "map_lns")
`Ap` (Pf (Lns (unlist la) (unlist lb)) :| f)
toSpine (Pf (Lns la _)) (LENGTH_LNS v) = LENGTH_LNS v `As` (pcon $ showL["length_lns",gshow (unlist la) v])
toSpine (Pf (Lns _ _)) FILTER_LEFT_LNS = FILTER_LEFT_LNS `As` (pcon "filter_left_lns")
toSpine (Pf (Lns _ _)) FILTER_RIGHT_LNS = FILTER_RIGHT_LNS `As` (pcon "filter_right_lns")
toSpine (Pf (Lns _ _)) CAT_LNS = CAT_LNS `As` (pcon "cat_lns")
toSpine (Pf (Lns _ _)) CONCAT_LNS = CONCAT_LNS `As` (pcon "concat_lns")
toSpine (Pf (Lns _ _)) SUML_LNS = SUML_LNS `As` (pcon "suml_lns")
toSpine (Pf (Lns _ _)) PLUS_LNS = PLUS_LNS `As` (pcon "plus_lns")
toSpine (Pf _) (APPLY t f) = (APPLY t `As` pcon ("apT " ++ show t)) `Ap` (Pf TP :| f)
toSpine (Pf _) (MKT t f) = (MKT t `As` pcon ("mkT " ++ show t)) `Ap` (Pf (Fun t t) :| f)
toSpine (Pf _) NOP = NOP `As` pcon "nop"
toSpine (Pf _) (SEQ f g) = (SEQ `As` pcon "seq") `Ap` (Pf TP :| f) `Ap` (Pf TP :| g)
toSpine (Pf _) (EXTT f t g) = ((\x y -> EXTT x t y) `As` pcon "extT") `Ap` (Pf TP :| f) `Ap` (Pf (Fun t t) :| g)
toSpine (Pf _) (ALL f) = (ALL `As` pcon "gmapT") `Ap` (Pf TP :| f)
toSpine (Pf _) (EVERYWHERE f) = (EVERYWHERE `As` pcon "everywhere") `Ap` (Pf TP :| f)
toSpine (Pf _) (EVERYWHERE' f) = (EVERYWHERE' `As` pcon "everywhere'") `Ap` (Pf TP :| f)
toSpine (Pf func) (APPLYQ t f) = aux func t f
where aux :: Type (a -> r) -> Type a -> Pf (Q r) -> Spine (Pf (a -> r))
aux (Fun _ r) t f = (APPLYQ t `As` pcon ("apQ " ++ show t)) `Ap` (Pf (TU r) :| f)
toSpine (Pf func) (MKQ t f) = aux func t f
where aux :: Monoid r => Type (Q r) -> Type a -> Pf (a -> r) -> Spine (Pf (Q r))
aux (TU r) t f = (MKQ t `As` pcon ("mkQ " ++ show t)) `Ap` (Pf (Fun t r) :| f)
toSpine (Pf _) EMPTYQ = EMPTYQ `As` pcon "emptyQ"
toSpine (Pf r) (UNION f g) = (UNION `As` pcon "union") `Ap` (Pf r :| f) `Ap` (Pf r :| g)
toSpine (Pf func) (EXTQ f t g) = aux func f t g
where aux :: Type (Q r) -> Pf (Q r) -> Type a -> Pf (a -> r) -> Spine (Pf (Q r))
aux (TU r) f t g = ((\x y -> EXTQ x t y) `As` pcon "extQ") `Ap` (Pf (TU r) :| f) `Ap` (Pf (Fun t r) :| g)
toSpine (Pf r) (GMAPQ f) = (GMAPQ `As` pcon "gmapQ") `Ap` (Pf r :| f)
toSpine (Pf r) (EVERYTHING f) = (EVERYTHING `As` pcon "everything") `Ap` (Pf r :| f)
toSpine (Pf (Fun Any Any)) e = e `As` (pcon "<anyfunc>")
toSpine (Pf (Lns Any Any)) e = e `As` (pcon "<anylens>")
toSpine (Pf t) f = error $ "toSpine: " ++ show t ++ " " ++ safeShow f
instance Show (Type a) where
show Any = "Any"
show (Id a) = showL["Id",show a]
show Int = "Int"
show Bool = "Bool"
show Char = "Char"
show One = "One"
show (Either x y) = showL ["Either",show x,show y]
show (Prod x y) = showL ["Prod",show x,show y]
show (Fun x y) = showL ["Fun",show x,show y]
show (Lns x y) = showL ["Lns",show x,show y]
show (Data s f) = s
show (Pf a) = showL ["Pf",show a]
show (Dynamic) = "Dynamic"
show TP = "TP"
show (TU a) = showL ["TU",show a]
instance Show Dynamic where
show (Dyn t v) = gshow t v
instance Show (Fctr f) where
show I = "Id"
show (K t) = showL ["K",show t]
show L = "L"
show (f:*!:g) = showL [show f,":*:",show g]
show (f:+!:g) = showL [show f,":+:",show g]
show (f:@!:g) = showL [show f,":@:",show g]
instance Typeable a => Show (Pf a) where
show = gshow typeof
gshow :: Type a -> a -> String
gshow (a@(Data s ((K One) :+!: ((K t) :*!: I)))) v = listify a t $ out v
where listify :: Type a -> Type c -> Either One (c,a) -> String
listify a c (Left _) = "[]"
listify a c (Right (x,xs)) = gshow c x ++ ":" ++ gshow a xs
gshow Dynamic (Dyn t x) = gshow t x
gshow (Pf t) f@(COMP _ _ _) = "(" ++ showComp (Pf t) f ++ ")"
gshow (Pf t) f@(COMP_LNS _ _ _) = "(" ++ showComp (Pf t) f ++ ")"
gshow t x = showSpine (toSpine t x)
where showSpine :: Spine a -> String
showSpine (Ap f@(Ap (_ `As` c) (a :| x)) (b :| y))
| fixity c == Infix = showL [gshow a x,name c,gshow b y]
| otherwise = showL [showSpine f,gshow b y]
showSpine (_ `As` c) = name c
showSpine (Ap f (t :| a)) = showL [showSpine f,gshow t a]
showComp :: Type a -> a -> String
showComp (Pf (Fun a c)) (COMP b f g) = showComp (Pf $ Fun b c) f ++ " . " ++ showComp (Pf $ Fun a b) g
showComp (Pf (Lns a c)) (COMP_LNS b f g) = showComp (Pf $ Lns b c) f ++ " .< " ++ showComp (Pf $ Lns a b) g
showComp t f = gshow t f
safeShow :: Pf a -> String
safeShow HOLE = "_L"
safeShow TOP = "T"
safeShow (FUN s f) = s
safeShow (CONV e f) = showL ["conv",show e,safeShow f]
safeShow (CONV_LNS e f) = showL ["lconv",show e,safeShow f]
safeShow (LNS s l) = s
safeShow (COMPF fctr _ f g) = showL ["compf",show fctr,safeShow f,safeShow g]
safeShow (COMPF_LNS fctr _ f g) = showL ["compf_lns",show fctr,safeShow f,safeShow g]
safeShow (PROTECT f) = showL ["protect",safeShow f]
safeShow (PROTECT_LNS f) = showL ["protect_lns",safeShow f]
safeShow (VAR s) = s
safeShow (PNT v) = showL ["pnt"]
safeShow BANG = "bang"
safeShow (COMP _ f g) = showL [safeShow f,".",safeShow g]
safeShow FST = "fst"
safeShow SND = "snd"
safeShow (SPLIT f g) = showL [safeShow f,"/\\",safeShow g]
safeShow (PROD f g) = showL [safeShow f,"><",safeShow g]
safeShow INL = "inl"
safeShow INR = "inr"
safeShow (EITHER f g) = showL [safeShow f,"\\/",safeShow g]
safeShow (SUM f g) = showL [safeShow f,"-|-",safeShow g]
safeShow ID = "id"
safeShow SWAP = "swap"
safeShow COSWAP = "coswap"
safeShow DISTL = "distl"
safeShow UNDISTL = "undistl"
safeShow DISTR = "distr"
safeShow UNDISTR = "undistr"
safeShow ASSOCL = "assocl"
safeShow ASSOCR = "assocr"
safeShow COASSOCL = "coassocl"
safeShow COASSOCR = "coassocr"
safeShow INN = "inn"
safeShow OUT = "out"
safeShow (FMAP _ _ f) = showL ["fmap",safeShow f]
safeShow (FZIP _ _ f) = showL ["fzip",safeShow f]
safeShow (ANA f) = showL ["ana",safeShow f]
safeShow (CATA f) = showL ["cata",safeShow f]
safeShow (GET f) = showL ["get",safeShow f]
safeShow (PUT f) = showL ["put",safeShow f]
safeShow (CREATE f) = showL ["create",safeShow f]
safeShow (COMP_LNS _ f g) = showL [safeShow f,".<",safeShow g]
safeShow (FST_LNS v) = showL ["fst_lns",safeShow v]
safeShow (SND_LNS v) = showL ["snd_lns",safeShow v]
safeShow (PROD_LNS f g) = showL [safeShow f,"><<",safeShow g]
safeShow (EITHER_LNS x f g) = showL [safeShow x,safeShow f,"\\/<",safeShow g]
safeShow (SUM_LNS f g) = showL [safeShow f,"-|-<",safeShow g]
safeShow (SUMW_LNS x y f g) = showL ["sum_lns",safeShow x,safeShow y,safeShow f,safeShow g]
safeShow (BANG_LNS v) = showL ["bang_lns",safeShow v]
safeShow (BANGL_LNS) = "bangl"
safeShow (BANGR_LNS) = "bangr"
safeShow ID_LNS = "id_lns"
safeShow SWAP_LNS = "swap_lns"
safeShow COSWAP_LNS = "coswap_lns"
safeShow DISTL_LNS = "distl_lns"
safeShow UNDISTL_LNS = "undistl_lns"
safeShow DISTR_LNS = "distr_lns"
safeShow UNDISTR_LNS = "undistr_lns"
safeShow ASSOCL_LNS = "assocl_lns"
safeShow ASSOCR_LNS = "assocr_lns"
safeShow COASSOCL_LNS = "coassocl_lns"
safeShow COASSOCR_LNS = "coassocr_lns"
safeShow INN_LNS = "inn_lns"
safeShow OUT_LNS = "out_lns"
safeShow (FMAP_LNS _ _ f) = showL ["fmap",safeShow f]
safeShow (ANA_LNS f) = showL ["ana_lns",safeShow f]
safeShow (CATA_LNS f) = showL ["cata_lns",safeShow f]
safeShow (MAP_LNS f) = showL ["map_lns",safeShow f]
safeShow (LENGTH_LNS f) = showL ["length_lns"]
safeShow FILTER_LEFT_LNS = "filter_left_lns"
safeShow FILTER_RIGHT_LNS = "filter_right_lns"
safeShow CAT_LNS = "cat_lns"
safeShow CONCAT_LNS = "concat_lns"
safeShow PLUS_LNS = "plus_lns"
safeShow (SUML_LNS) = "suml_lns"