Glob in Haskell

Glob.hs

{-# LANGUAGE EmptyDataDecls, GADTs #-}

module Glob where
  
data L -- Witness for globs that begin/end with a literal
data S -- Witness for globs that begin/end with a star

data Glob a b e where -- Globs over [a] that begin with b and end with e
    L    :: [a]  -> Glob a L L                      -- Literal glob
    S    :: Glob a S S                              -- Star glob
    (:>) :: Glob a b S -> Glob a L e -> Glob a b e  -- Concatenation of a glob that ends with a star and a glob that starts with a literal
    (:<) :: Glob a b L -> Glob a S e -> Glob a b e  -- Concatenation of a glob that ends with a literal and a glob that starts with a star

infixl 0 :>, :<

instance Eq a => Eq (Glob a b e) where
  L as         == L bs         = as == bs
  S            == S            = True
  (gs1 :> gl1) == (gs2 :> gl2) = gs1 == gs2 && gl1 == gl2
  (gs1 :< gl1) == (gs2 :< gl2) = gs1 == gs2 && gl1 == gl2

instance Show a => Show (Glob a b e) where
  show (L ls) = show ls
  show S = "*"
  show (gs1 :> gl1) = show gs1 ++ " " ++ show gl1
  show (gl1 :< gs1) = show gl1 ++ " " ++ show gs1


-- to be continued...

Sample GHC output:

*Glob> L "foo" :< S :> L "bar" :< S :> L "baz"
"foo" * "bar" * "baz"
*Glob> :t L "foo" :< S :> L "bar" :< S :> L "baz"
L "foo" :< S :> L "bar" :< S :> L "baz" :: Glob Char L L
*Glob> :t L "foo" :< S :> L "bar" :< S 
L "foo" :< S :> L "bar" :< S :: Glob Char L S