```-- --------------------------------------------------------------------------
--  \$Revision: 262 \$ \$Date: 2007-04-12 12:19:50 +0200 (Thu, 12 Apr 2007) \$
-- --------------------------------------------------------------------------

-- |
--
-- Module      :  PureFP.Parsers.ExTrie
-- Copyright   :  Peter Ljunglof 2002
--
-- Maintainer  :  otakar.smrz mff.cuni.cz
-- Stability   :  provisional
-- Portability :  portable
--
-- Chapters 3 and 4 of /Pure Functional Parsing &#150; an advanced tutorial/
-- by Peter Ljungl&#246;f
--
-- <http://www.ling.gu.se/~peb/pubs/p02-lic-thesis.pdf>
--
-- <http://www.ling.gu.se/~peb/software/functional-parsing/>

--------------------------------------------------
-- the extended trie from section 4.3.3

module PureFP.Parsers.ExTrie (ExTrie) where

import PureFP.OrdMap
import PureFP.Parsers.Parser

data ExTrie s a = Shift (Map s (ExTrie s a))    |
a ::: ExTrie s a              |
forall b . FMap (b -> a) (ExTrie s b)

unfold :: Ord s => (a -> b) -> ExTrie s a -> ExTrie s b
unfold f (Shift pmap) = Shift (mapMap (FMap f) pmap)
unfold f (a ::: p)    = f a ::: FMap f p
unfold f (FMap g p)   = FMap (f . g) p

instance Ord s => Monoid (ExTrie s) where
zero                      = Shift emptyMap

(a ::: p)  <+> q          = a ::: (p <+> q)
p          <+> (b ::: q)  = b ::: (p <+> q)
FMap f p   <+> q          = unfold f p <+> q
p          <+> FMap f q   = p <+> unfold f q
Shift pmap <+> Shift qmap = Shift (mergeWith (<+>) pmap qmap)

instance Ord s => Monad (ExTrie s) where
return a         = a ::: zero

(a ::: p)  >>= k = k a <+> (p >>= k)
FMap f p   >>= k = unfold f p >>= k
Shift pmap >>= k = Shift (mapMap (>>=k) pmap)

instance Ord s => Functor (ExTrie s) where
fmap = FMap

instance Ord s => Sequence (ExTrie s)

instance InputSymbol s => Symbol (ExTrie s) s where
sym s = Shift (s |-> return s)
sat p = anyof (map sym (filter p symbols))

instance Ord s => Parser (ExTrie s) s where
parse     p inp = parse'     p inp id
parseFull p inp = parseFull' p inp id

parse' :: Ord s => ExTrie s a -> [s] -> (a -> b) -> [([s], b)]
parse' (FMap f p)   inp     k = parse' p inp (k . f)
parse' (a ::: p)    inp     k = (inp, k a) : parse' p inp k
parse' _            []      k = []
parse' (Shift pmap) (s:inp) k = case pmap ? s of
Just p  -> parse' p inp k
Nothing -> []

parseFull' :: Ord s => ExTrie s a -> [s] -> (a -> b) -> [b]
parseFull' (FMap f p)   inp     k = parseFull' p inp (k . f)
parseFull' (a ::: p)    []      k = k a : parseFull' p [] k
parseFull' (a ::: p)    inp     k = parseFull' p inp k
parseFull' _            []      k = []
parseFull' (Shift pmap) (s:inp) k = case pmap ? s of
Just p  -> parseFull' p inp k
Nothing -> []
```