{-# LANGUAGE RankNTypes,
GADTs,
MultiParamTypeClasses,
FunctionalDependencies #-}
-- | The module `Core` contains the basic functionality of the parser library.
-- It uses the breadth-first module to realise online generation of results, the error
-- correction administration, dealing with ambigous grammars; it defines the types of the elementary parsers
-- and recognisers involved.For typical use cases of the libray see the module @"Text.ParserCombinators.UU.Examples"@
module Text.ParserCombinators.UU.Core ( module Text.ParserCombinators.UU.Core
, module Control.Applicative) where
import Control.Applicative hiding (many, some, optional)
import Char
import Debug.Trace
import Maybe
infix 2 -- should be the last element in a sequence of alternatives
infixl 3 <<|> -- intended use p <<|> q <<|> r <|> x <|> y z
-- ** `Provides'
-- | The function `splitState` playes a crucial role in splitting up the state. The `symbol` parameter tells us what kind of thing, and even which value of that kind, is expected from the input.
-- The state and and the symbol type together determine what kind of token has to be returned. Since the function is overloaded we do not have to invent
-- all kind of different names for our elementary parsers.
class Provides state symbol token | state symbol -> token where
splitState :: symbol -> (token -> state -> Steps a) -> state -> Steps a
-- ** `Eof'
class Eof state where
eof :: state -> Bool
deleteAtEnd :: state -> Maybe (Cost, state)
-- ** `Location`
-- | The input state may contain a location which can be used in error messages. Since we do not want to fix our input to be just a @String@ we provide an interface
-- which can be used to advance the location by passing its information in the function splitState
class loc `IsLocationUpdatedBy` a where
advance::loc -> a -> loc
-- ** An extension to @`Alternative`@ which indicates a biased choice
-- | In order to be able to describe greedy parsers we introduce an extra operator, whch indicates a biased choice
class ExtAlternative p where
(<<|>) :: p a -> p a -> p a
-- * The triples containg a history, a future parser and a recogniser: @`T`@
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% Triples %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- actual parsers
data T st a = T (forall r . (a -> st -> Steps r) -> st -> Steps r ) -- history parser
(forall r . ( st -> Steps r) -> st -> Steps (a, r) ) -- future parser
(forall r . ( st -> Steps r) -> st -> Steps r ) -- recogniser
instance Functor (T st) where
fmap f (T ph pf pr) = T ( \ k -> ph ( k .f ))
( \ k -> pushapply f . pf k) -- pure f <*> pf
pr
f <$ (T _ _ pr) = T ( pr . ($f))
( \ k st -> push f ( pr k st))
pr
-- ** Triples are Applicative: @`<*>`@, @`<*`@, @`*>`@ and @`pure`@
instance Applicative (T state) where
T ph pf pr <*> ~(T qh qf qr) = T ( \ k -> ph (\ pr -> qh (\ qr -> k (pr qr))))
((apply .) . (pf .qf))
( pr . qr)
T ph pf pr <* ~(T _ _ qr) = T ( ph. (qr.)) (pf. qr) (pr . qr)
T _ _ pr *> ~(T qh qf qr ) = T ( pr . qh ) (pr. qf) (pr . qr)
pure a = T ($a) ((push a).) id
instance Alternative (T state) where
T ph pf pr <|> T qh qf qr = T (\ k inp -> ph k inp `best` qh k inp)
(\ k inp -> pf k inp `best` qf k inp)
(\ k inp -> pr k inp `best` qr k inp)
empty = T ( \ k inp -> noAlts) ( \ k inp -> noAlts) ( \ k inp -> noAlts)
-- instance ExtAlternative (T st) where
-- unfortunatelythis is not possible since we have to make the choice for swapping elsewhere
choose:: (forall a . Steps a -> Steps a -> Steps a) -> T st a -> T st a -> T st a
choose best (T ph pf pr) (T qh qf qr) =
T (\ k st -> let left = norm (ph k st)
in if has_success left then left else left `best` qh k st)
(\ k st -> let left = norm (pf k st)
in if has_success left then left else left `best` qf k st)
(\ k st -> let left = norm (pr k st)
in if has_success left then left else left `best` qr k st)
instance ExtAlternative Maybe where
Nothing <<|> r = r
l <<|> Nothing = l
l <<|> r = l -- choosing the high priority alternative ? is this the right choice?
-- * The descriptor @`P`@ of a parser, including the tupled parser corresponding to this descriptor
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% Parser Descriptors %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
data P st a = P (T st a) -- actual parsers
(Maybe (T st a)) -- non-empty parsers; Nothing if they are absent
Nat -- minimal length
(Maybe a) -- possibly empty with value
getOneP (P _ _ Zero _) = error "The element is a special parser which cannot be combined"
getOneP (P _ Nothing l _ ) = Nothing
getOneP (P _ onep l _ ) = Just( P (mkParser onep Nothing) onep l Nothing)
getZeroP (P _ _ l Nothing) = Nothing
getZeroP (P _ _ l pe) = Just ( P (mkParser Nothing pe) Nothing l pe)
mkParser Nothing Nothing = empty
mkParser (Just nt) Nothing = nt
mkParser Nothing (Just a) = pure a
mkParser (Just nt) (Just a) = nt <|> pure a
-- ** Parsers are functors: @`fmap`@
instance Functor (P state) where
fmap f (P ap np l me) = let nnp = fmap (fmap f) np
nep = f <$> me
in P (mkParser nnp nep) nnp l nep
f <$ (P ap np l me) = let nnp = fmap (f <$) np
nep = f <$ me
in P (mkParser nnp nep) nnp l nep
-- ** Parsers are Applicative: @`<*>`@, @`<*`@, @`*>`@ and @`pure`@
instance Applicative (P state) where
P ap np pl pe <*> ~(P aq nq ql qe) = let nnp = do {npp <- np ; return (npp <*> aq)}
nep = (pe <*> qe)
in P (mkParser nnp nep) nnp (nat_add pl ql) nep
P ap np pl pe <* ~(P aq nq ql qe) = let nnp = do {npp <- np ; return (npp <* aq)}
nep = (pe <* qe)
in P (mkParser nnp nep) nnp (nat_add pl ql) nep
P ap np pl pe *> ~(P aq nq ql qe) = let nnp = do {npp <- np ; return (npp *> aq)}
nep = (pe *> qe)
in P (mkParser nnp nep) nnp (nat_add pl ql) nep
pure a = P (pure a) Nothing Zero (Just a)
-- ** Parsers are Alternative: @`<|>`@ and @`empty`@
instance Alternative (P state) where
P ap np pl pe <|> P aq nq ql qe
= let (rl, b) = nat_min pl ql
Nothing `alt` q = q
p `alt` Nothing = p
Just p `alt` Just q = Just (p <|>q)
in let nnp = (if b then (nq `alt` np) else (np `alt` nq))
nep = (case (pe, qe) of
(Nothing, _ ) -> qe
(_ , Nothing) -> pe
(_ , _ ) -> error "ambiguous parser because two sides of choice can be empty")
in P (mkParser nnp nep) nnp rl nep
empty = P empty empty Infinite Nothing
-- ** An alternative for the Alternative, which is greedy: @`<<|>`@
-- | `<<|>` is the greedy version of `<|>`. If its left hand side parser can make some progress that alternative is committed. Can be used to make parsers faster, and even
-- get a complete Parsec equivalent behaviour, with all its (dis)advantages. use with are!
instance ExtAlternative (P st) where
P ap np pl pe <<|> P aq nq ql qe
= let (rl, b) = nat_min pl ql
bestx = if b then flip best else best
in P (choose bestx ap aq )
(maybe np (\nqq -> maybe nq (\npp -> return( choose bestx npp nqq)) np) nq)
rl
(pe <|> qe)
-- ** Parsers can recognise single tokens: @`pSym`@ and @`pSymExt`@
-- Many parsing libraries do not make a distinction between the terminal symbols of the language recognised
-- and the tokens actually constructed from the input.
-- This happens e.g. if we want to recognise an integer or an identifier:
-- we are also interested in which integer occurred in the input, or which identifier.
-- The function `pSymExt` takes as argument a value of some type `symbol', and returns a value of type `token'.
-- The parser will in general depend on some
-- state which is maintained holding the input. The functional dependency fixes the `token` type, based on the `symbol` type and the type of the parser `p`.
-- | Since `pSymExt' is overloaded both the type and the value of symbol determine how to decompose the input in a `token`
-- and the remaining input.
-- `pSymExt` takes two extra parameters: one describing the minimal number of tokens recognised,
-- and the second whether the symbol can recognise the empty string and the value which is to be returned in that case
pSymExt :: (Provides state symbol token) => Nat -> Maybe token -> symbol -> P state token
pSymExt l e a = P t (Just t) l e
where t = T ( \ k inp -> splitState a k inp)
( \ k inp -> splitState a (\ t inp' -> push t (k inp')) inp)
( \ k inp -> splitState a (\ _ inp' -> k inp') inp)
-- | @`pSym`@ covers the most common case of recognsiing a symbol: a single token is removed form the input,
-- and it cannot recognise the empty string
pSym :: (Provides state symbol token) => symbol -> P state token
pSym s = pSymExt (Succ Zero) Nothing s
-- ** Parsers are Monads: @`>>=`@ and @`return`@
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% Monads %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
unParser_h (P (T h _ _ ) _ _ _ ) = h
unParser_f (P (T _ f _ ) _ _ _ ) = f
unParser_r (P (T _ _ r ) _ _ _ ) = r
-- pas op de P moet aan de buitenkant !!
instance Monad (P st) where
p@(P ap np lp ep) >>= a2q =
(P newap newnp (nat_add lp (error "cannot compute minimal length of right hand side of monadic parser")) newep)
where (newep, newnp, newap) = case ep of
Nothing -> (Nothing, t, maybe empty id t)
Just a -> let P aq nq lq eq = a2q a
in ( eq, combine t nq , t `alt` aq)
Nothing `alt` q = q
Just p `alt` q = p <|> q
t = case np of
Nothing -> Nothing
Just (T h _ _ ) -> Just (T ( \k -> h (\ a -> unParser_h (a2q a) k))
( \k -> h (\ a -> unParser_f (a2q a) k))
( \k -> h (\ a -> unParser_r (a2q a) k)))
combine Nothing Nothing = Nothing
combine l@(Just _ ) Nothing = l
combine Nothing r@(Just _ ) = r
combine (Just l) (Just r) = Just (l <|> r)
return = pure
-- * Additional useful combinators
-- ** Controlling the text of error reporting: @``@
-- | The parsers build a list of symbols which are expected at a specific point.
-- This list is used to report errors.
-- Quite often it is more informative to get e.g. the name of the non-terminal.
-- The @``@ combinator replaces this list of symbols by it's righ-hand side argument.
() :: P state a -> String -> P state a
P _ np pl pe label
= let nnp = case np of
Nothing -> Nothing
Just ((T ph pf pr)) -> Just(T ( \ k inp -> replaceExpected ( ph k inp))
( \ k inp -> replaceExpected ( pf k inp))
( \ k inp -> replaceExpected ( pr k inp)))
replaceExpected (Fail _ c) = (Fail [label] c)
replaceExpected others = others
in P (mkParser nnp pe) nnp pl pe
-- ** Parsers can be disambiguated using micro-steps: @`micro`@
-- | `micro` inserts a `Cost` step into the sequence representing the progress the parser is making; for its use see `Text.ParserCombinators.UU.Examples`
P _ np pl pe `micro` i
= let nnp = case np of
Nothing -> Nothing
Just ((T ph pf pr)) -> Just(T ( \ k st -> ph (\ a st -> Micro i (k a st)) st)
( \ k st -> pf (Micro i .k) st)
( \ k st -> pr (Micro i .k) st))
in P (mkParser nnp pe) nnp pl pe
-- ** Dealing with (non-empty) Ambigous parsers: @`amb`@
-- For the precise functionng of the combinators we refer to the technical report mentioned in the README file
-- @`amb`@ converts an ambiguous parser into a parser which returns a list of possible recognitions.
amb :: P st a -> P st [a]
amb (P _ np pl pe)
= let combinevalues :: Steps [(a,r)] -> Steps ([a],r)
combinevalues lar = Apply (\ lar -> (map fst lar, snd (head lar))) lar
nnp = case np of
Nothing -> Nothing
Just ((T ph pf pr)) -> Just(T ( \k -> removeEnd_h . ph (\ a st' -> End_h ([a], \ as -> k as st') noAlts))
( \k inp -> combinevalues . removeEnd_f $ pf (\st -> End_f [k st] noAlts) inp)
( \k -> removeEnd_h . pr (\ st' -> End_h ([undefined], \ _ -> k st') noAlts)))
nep = (fmap pure pe)
in P (mkParser nnp nep) nnp pl nep
-- ** Parse errors can be retreived from the state: @`pErrors`@
-- | `getErrors` retreives the correcting steps made since the last time the function was called. The result can,
-- using a monad, be used to control how to-- proceed with the parsing process.
class state `Stores` error | state -> error where
getErrors :: state -> ([error], state)
pErrors :: Stores st error => P st [error]
pErrors = let nnp = Just (T ( \ k inp -> let (errs, inp') = getErrors inp in k errs inp' )
( \ k inp -> let (errs, inp') = getErrors inp in push errs (k inp'))
( \ k inp -> let (errs, inp') = getErrors inp in k inp' ))
nep = (Just (error "pErrors cannot occur in lhs of bind")) -- the errors consumed cannot be determined statically!
in P (mkParser nnp nep) nnp Zero nep
-- ** The current position can be retreived from the state: @`pPos`@
-- | `pPos` retreives the correcting steps made since the last time the function was called. The result can,
-- using a monad, be used to control how to-- proceed with the parsing process.
class state `HasPosition` pos | state -> pos where
getPos :: state -> pos
pPos :: HasPosition st pos => P st pos
pPos = let nnp = Just ( T ( \ k inp -> let pos = getPos inp in k pos inp )
( \ k inp -> let pos = getPos inp in push pos (k inp))
( \ k inp -> let pos = getPos inp in k inp ))
nep = Just (error "pPos cannot occur in lhs of bind") -- the errors consumed cannot be determined statically!
in P (mkParser nnp nep) nnp Zero nep
-- ** Starting and finalising the parsing process: @`pEnd`@ and @`parse`@
-- | The function `pEnd` should be called at the end of the parsing process. It deletes any unsonsumed input, and reports its preence as an eror.
pEnd :: (Stores st error, Eof st) => P st [error]
pEnd = let nnp = Just ( T ( \ k inp -> let deleterest inp = case deleteAtEnd inp of
Nothing -> let (finalerrors, finalstate) = getErrors inp
in k finalerrors finalstate
Just (i, inp') -> Fail [] [const (i, deleterest inp')]
in deleterest inp)
( \ k inp -> let deleterest inp = case deleteAtEnd inp of
Nothing -> let (finalerrors, finalstate) = getErrors inp
in push finalerrors (k finalstate)
Just (i, inp') -> Fail [] [const ((i, deleterest inp'))]
in deleterest inp)
( \ k inp -> let deleterest inp = case deleteAtEnd inp of
Nothing -> let (finalerrors, finalstate) = getErrors inp
in (k finalstate)
Just (i, inp') -> Fail [] [const (i, deleterest inp')]
in deleterest inp))
nep = Nothing -- (error "Unforeseen use of pEnd function; pEnd should only be used in function running the actual parser")
in P (mkParser nnp nep) nnp Zero nep
-- The function @`parse`@ shows the prototypical way of running a parser on a some specific input
-- By default we use the future parser, since this gives us access to partal result; future parsers are expected to run in less space
parse :: (Eof t) => P t a -> t -> a
parse (P (T _ pf _) _ _ _) = fst . eval . pf (\ rest -> if eof rest then succeedAlways else error "pEnd missing?")
parse_h (P (T ph _ _) _ _ _) = fst . eval . ph (\ a rest -> if eof rest then push a failAlways else error "pEnd missing?")
-- ** The state may be temporarily change type: @`pSwitch`@
-- | `pSwitch` takes the current state and modifies it to a different type of state to which its argument parser is applied.
-- The second component of the result is a function which converts the remaining state of this parser back into a valuee of the original type.
pSwitch :: (st1 -> (st2, st2 -> st1)) -> P st2 a -> P st1 a -- we require let (n,f) = split st in f n to be equal to st
pSwitch split (P _ np pl pe)
= let nnp = fmap (\ (T ph pf pr) ->T (\ k st1 -> let (st2, back) = split st1
in ph (\ a st2' -> k a (back st2')) st2)
(\ k st1 -> let (st2, back) = split st1
in pf (\st2' -> k (back st2')) st2)
(\ k st1 -> let (st2, back) = split st1
in pr (\st2' -> k (back st2')) st2)) np
in P (mkParser nnp pe) nnp pl pe
-- * Maintaining Progress Information
-- | The data type @`Steps`@ is the core data type around which the parsers are constructed.
-- It is a describes a tree structure of streams containing (in an interleaved way) both the online result of the parsing process,
-- and progress information. Recognising an input token should correspond to a certain amount of @`Progress`@,
-- which tells how much of the input state was consumed.
-- The @`Progress`@ is used to implement the breadth-first search process, in which alternatives are
-- examined in a more-or-less synchonised way. The meaning of the various @`Step`@ constructors is as follows:
--
-- [@`Step`@] A token was succesfully recognised, and as a result the input was 'advanced' by the distance @`Progress`@
--
-- [@`Apply`@] The type of value represented by the `Steps` changes by applying the function parameter.
--
-- [@`Fail`@] A correcting step has to made to the input; the first parameter contains information about what was expected in the input,
-- and the second parameter describes the various corrected alternatives, each with an associated `Cost`
--
-- [@`Micro`@] A small cost is inserted in the sequence, which is used to disambiguate. Use with care!
--
-- The last two alternatives play a role in recognising ambigous non-terminals. For a full description see the technical report referred to from the README file..
type Cost = Int
type Progress = Int
type Strings = [String]
data Steps a where
Step :: Progress -> Steps a -> Steps a
Apply :: forall a b. (b -> a) -> Steps b -> Steps a
Fail :: Strings -> [Strings -> (Cost , Steps a)] -> Steps a
Micro :: Cost -> Steps a -> Steps a
End_h :: ([a] , [a] -> Steps r) -> Steps (a,r) -> Steps (a, r)
End_f :: [Steps a] -> Steps a -> Steps a
succeedAlways = let steps = Step 0 steps in steps
failAlways = Fail [] [const (0, failAlways)]
noAlts = Fail [] []
has_success (Step _ _) = True
has_success _ = False
-- ! @`eval`@ removes the progress information from a sequence of steps, and constructs the value contained in it.
eval :: Steps a -> a
eval (Step _ l) = eval l
eval (Micro _ l) = eval l
eval (Fail ss ls ) = trace' ("expecting: " ++ show ss) (eval (getCheapest 3 (map ($ss) ls)))
eval (Apply f l ) = f (eval l)
eval (End_f _ _ ) = error "dangling End_f constructor"
eval (End_h _ _ ) = error "dangling End_h constructor"
push :: v -> Steps r -> Steps (v, r)
push v = Apply (\ r -> (v, r))
apply :: Steps (b -> a, (b, r)) -> Steps (a, r)
apply = Apply (\(b2a, ~(b, r)) -> (b2a b, r))
pushapply :: (b -> a) -> Steps (b, r) -> Steps (a, r)
pushapply f = Apply (\ (b, r) -> (f b, r))
norm :: Steps a -> Steps a
norm (Apply f (Step p l )) = Step p (Apply f l)
norm (Apply f (Micro c l )) = Micro c (Apply f l)
norm (Apply f (Fail ss ls )) = Fail ss (applyFail (Apply f) ls)
norm (Apply f (Apply g l )) = norm (Apply (f.g) l)
norm (Apply f (End_f ss l )) = End_f (map (Apply f) ss) (Apply f l)
norm (Apply f (End_h _ _ )) = error "Apply before End_h"
norm steps = steps
applyFail f = map (\ g -> \ ex -> let (c, l) = g ex in (c, f l))
best :: Steps a -> Steps a -> Steps a
x `best` y = norm x `best'` norm y
best' :: Steps b -> Steps b -> Steps b
Fail sl ll `best'` Fail sr rr = Fail (sl ++ sr) (ll++rr)
Fail _ _ `best'` r = r
l `best'` Fail _ _ = l
Step n l `best'` Step m r
| n == m = Step n (l `best'` r)
| n < m = Step n (l `best'` Step (m - n) r)
| n > m = Step m (Step (n - m) l `best'` r)
ls@(Step _ _) `best'` Micro _ _ = ls
Micro _ _ `best'` rs@(Step _ _) = rs
ls@(Micro i l) `best'` rs@(Micro j r)
| i == j = Micro i (l `best'` r)
| i < j = ls
| i > j = rs
End_f as l `best'` End_f bs r = End_f (as++bs) (l `best` r)
End_f as l `best'` r = End_f as (l `best` r)
l `best'` End_f bs r = End_f bs (l `best` r)
End_h (as, k_h_st) l `best'` End_h (bs, _) r = End_h (as++bs, k_h_st) (l `best` r)
End_h as l `best'` r = End_h as (l `best` r)
l `best'` End_h bs r = End_h bs (l `best` r)
l `best'` r = l `best` r
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% getCheapest %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
getCheapest :: Int -> [(Int, Steps a)] -> Steps a
getCheapest _ [] = error "no correcting alternative found"
getCheapest n l = snd $ foldr (\(w,ll) btf@(c, l)
-> if w < c -- c is the best cost estimate thus far, and w total costs on this path
then let new = (traverse n ll w c)
in if new < c then (new, ll) else btf
else btf
) (maxBound, error "getCheapest") l
traverse :: Int -> Steps a -> Int -> Int -> Int
traverse 0 _ = trace' ("traverse " ++ show 0 ++ "\n") (\ v c -> v)
traverse n (Step _ l) = trace' ("traverse Step " ++ show n ++ "\n") (traverse (n - 1 ) l)
traverse n (Micro _ l) = trace' ("traverse Micro " ++ show n ++ "\n") (traverse n l)
traverse n (Apply _ l) = trace' ("traverse Apply " ++ show n ++ "\n") (traverse n l)
traverse n (Fail m m2ls) = trace' ("traverse Fail " ++ show n ++ "\n") (\ v c -> foldr (\ (w,l) c' -> if v + w < c' then traverse (n - 1 ) l (v+w) c'
else c'
) c (map ($m) m2ls)
)
traverse n (End_h ((a, lf)) r) = traverse n (lf a `best` removeEnd_h r)
traverse n (End_f (l :_) r) = traverse n (l `best` r)
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% Handling ambiguous paths %%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
removeEnd_h :: Steps (a, r) -> Steps r
removeEnd_h (Fail m ls ) = Fail m (applyFail removeEnd_h ls)
removeEnd_h (Step ps l ) = Step ps (removeEnd_h l)
removeEnd_h (Apply f l ) = error "not in history parsers"
removeEnd_h (Micro c l ) = Micro c (removeEnd_h l)
removeEnd_h (End_h (as, k_st ) r ) = k_st as `best` removeEnd_h r
removeEnd_f :: Steps r -> Steps [r]
removeEnd_f (Fail m ls) = Fail m (applyFail removeEnd_f ls)
removeEnd_f (Step ps l) = Step ps (removeEnd_f l)
removeEnd_f (Apply f l) = Apply (map' f) (removeEnd_f l)
where map' f ~(x:xs) = f x : map f xs
removeEnd_f (Micro c l ) = Micro c (removeEnd_f l)
removeEnd_f (End_f(s:ss) r) = Apply (:(map eval ss)) s
`best`
removeEnd_f r
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%% Auxiliary Functions and Types %%%%%%%%%%%%%%%%%%%
-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-- * Auxiliary functions and types
-- ** Checking for non-sensical combinations: @`must_be_non_empty`@ and @`must_be_non_empties`@
-- | The function checks wehther its second argument is a parser which can recognise the mety sequence. If so an error message is given
-- using the name of the context. If not then the third argument is returned. This is useful in testing for loogical combinations. For its use see
-- the module Text>parserCombinators.UU.Derived
must_be_non_empty :: [Char] -> P t t1 -> t2 -> t2
must_be_non_empty msg p@(P _ _ Zero _) _
= error ("The combinator " ++ msg ++ "\n" ++
" requires that it's argument cannot recognise the empty string\n")
must_be_non_empty _ _ q = q
-- | This function is similar to the above, but can be used in situations where we recognise a sequence of elements separated by other elements. This does not
-- make sense if both parsers can recognise the empty string. Your grammar is then highly ambiguous.
must_be_non_empties :: [Char] -> P t1 t -> P t3 t2 -> t4 -> t4
must_be_non_empties msg (P _ _ Zero _) (P _ _ Zero _ ) _
= error ("The combinator " ++ msg ++ "\n" ++
" requires that not both arguments can recognise the empty string\n")
must_be_non_empties msg _ _ q = q
-- ** The type @`Nat`@ for describing the minimal number of tokens consumed
-- | The data type @`Nat`@ is used to represent the minimal length of a parser.
-- Care should be taken in order to not evaluate the right hand side of the binary functions @`nat_min`@ and @`nat-add`@ more than necesssary.
data Nat = Zero
| Succ Nat
| Infinite
deriving Show
nat_min Zero _ = trace' "Left Zero in nat_min\n" (Zero, True)
nat_min Infinite r = trace' "Left Infinite in nat_min\n" (r, False)
nat_min l Infinite = trace' "Right Zero in nat_min\n" (l, True)
nat_min _ Zero = trace' "Right Zero in nat_min\n" (Zero, False)
nat_min (Succ ll) (Succ rr) = trace' "Succs in nat_min\n" (let (v, b) = ll `nat_min` rr in (Succ v, b))
nat_add Infinite _ = trace' "Infinite in add\n" Infinite
nat_add Zero r = trace' "Zero in add\n" r
nat_add (Succ l) r = trace' "Succ in add\n" (Succ (nat_add l r))
-- get_length (P _ _ l _) = l
trace' v m = m