{-# LANGUAGE RankNTypes, GADTs, MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-} -- | The module `Core` contains the basic functionality of the parser library. -- It defines the types and implementations of the elementary parsers and recognisers involved. module Text.ParserCombinators.UU.Core ( -- * Classes IsParser, ExtAlternative (..), -- Provides (..), Eof (..), IsLocationUpdatedBy (..), StoresErrors (..), HasPosition (..), -- * Types -- ** The parser descriptor P (), -- ** The progress information Steps (..), Cost, Progress, -- ** Auxiliary types Nat (..), Strings, -- * Functions -- ** Basic Parsers micro, amb, pErrors, pPos, pEnd, pSwitch, pSymExt, -- pSym, -- ** Calling Parsers parse, parse_h, -- ** Acessing various components getZeroP, getOneP, -- ** Evaluating the online result eval ) where import Control.Applicative import Control.Monad import Data.Char import Debug.Trace import Data.Maybe -- | In the class `IsParser` we assemble the basic properties we expect parsers to have. The class itself does not have any methods. -- Most properties come directly from the standard -- "Control.Applicative" module. The class `ExtAlternative` contains some extra methods we expect our parsers to have. class (Alternative p, Applicative p, ExtAlternative p) => IsParser p instance MonadPlus (P st) where mzero = empty mplus = (<|>) class (Alternative p) => ExtAlternative p where -- | `<<|>` is the greedy version of `<|>`. If its left hand side parser can -- make any 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. Intended use @p \<\<\|> q \<\<\|> r \<\|> x \<\|> y \<?> "string"@. Use with care! (<<|>) :: p a -> p a -> p a -- | 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 the string argument. (<?>) :: p a -> String -> p a -- | `doNotInterpret` makes a parser opaque for abstract interpretation; used when permuting parsers -- where we do not want to compare lengths doNotInterpret :: p a -> p a doNotInterpret = id -- | `must_be_non_empty` checks whether its second argument -- is a parser which can recognise the empty input. If so, an error message is -- given using the String parameter. If not, then the third argument is -- returned. This is useful in testing for illogical combinations. For its use see -- the module "Text.ParserCombinators.UU.Derived". must_be_non_empty :: String -> p a -> c -> c -- -- | `must_be_non_empties` is similar to `must_be_non_empty`, 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 :: String -> p a -> p b -> c -> c -- | If 'p' can be recognized, the return value of 'p' is used. Otherwise, -- the value 'v' is used. Note that `opt` by default is greedy. If you do not want -- this use @...\<\|> pure v@ instead. Furthermore, 'p' should not -- recognise the empty string, since this would make the parser ambiguous!! opt :: p a -> a -> p a opt p v = must_be_non_empty "opt" p (p <<|> pure v) infix 2 <?> infixl 3 <<|> infixl 2 `opt` {- -- | 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 type of @token@ is to be returned. -- Since the function is overloaded we do not have to invent all kind of different names for our elementary parsers. -- This may be a bit confusing if you are not used to this. Error messages may be a bit harder to decipher. -- The function takes as second parameter a continutation which is called with the -- recognised piece of input (the @token@) and the remaining input of type @state@. class Provides state symbol token | state symbol -> token where splitState :: symbol -> (token -> state -> Steps a) -> state -> Steps a -} -- | The class `Eof` contains a function `eof` which is used to check whether we have reached the end of the input and `deletAtEnd` -- should discard any unconsumed input at the end of a successful parse. class Eof state where eof :: state -> Bool deleteAtEnd :: state -> Maybe (Cost, state) -- | The input state may maintain a location which can be used in generating 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 this location by passing information about the part recognised. This function is typically -- called in the `splitState` functions. class Show loc => loc `IsLocationUpdatedBy` str where advance::loc -> str -> loc -- | The class `StoresErrors` is used by the function `pErrors` which retreives the generated -- correction steps since the last time it was called. -- class state `StoresErrors` error | state -> error where -- | `getErrors` retrieves the correcting steps made since the last time the function was called. The result can, -- by using it in a monad, be used to control how to proceed with the parsing process. getErrors :: state -> ([error], state) class state `HasPosition` pos | state -> pos where -- | `getPos` retreives the correcting steps made since the last time the function was called. The result can, -- by usingit as the left hand sie of a mondaic bind, be used to control how to proceed with the parsing process. getPos :: state -> pos -- | The data type `T` contains three components, all being some form of primitive parser. -- These components are used in various combinations, -- depending on whether you are in the right and side operand of a monad, -- whether you are interested in a result (if not, we use recognisers), -- and whether you want to have the results in an online way (future parsers), or just prefer to be a bit faster (history 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 -> apply2fst f . pf k) -- pure f <*> pf pr f <$ (T _ _ pr) = T ( pr . ($f)) ( \ k st -> push f ( pr k st)) pr instance Applicative (T state) where T ph pf pr <*> ~(T qh qf qr) = T ( \ k -> ph (\ pr -> qh (\ qr -> k (pr qr)))) ((apply .) . (pf .qf)) ( pr . qr) T ph pf pr <* ~(T _ _ qr) = T ( ph. (qr.)) (pf. qr) (pr . qr) T _ _ pr *> ~(T qh qf qr ) = T ( pr . qh ) (pr. qf) (pr . qr) pure a = T ($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) 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 of the non-empty part (Maybe a) -- the possibly empty alternative with value instance Show (P st a) where show (P _ nt n e) = "P _ " ++ maybe "Nothing" (const "(Just _)") nt ++ " (" ++ show n ++ ") " ++ maybe "Nothing" (const "(Just _)") e -- | `getOneP` retreives the non-zero part from a descriptor getOneP :: P a b -> Maybe (P a b) -- getOneP (P _ (Just _) (Zero Unspecified) _ ) = error "The element is a special parser which cannot be combined" getOneP (P _ Nothing l _ ) = Nothing getOneP (P _ onep l ep ) = Just( mkParser onep Nothing (getLength l)) -- | `getZeroP` retreives the possibly empty part from a descriptor getZeroP :: P t a -> Maybe a getZeroP (P _ _ _ z) = z -- | `mkParser` combines the non-empty descriptor part and the empty descriptor part into a descriptor tupled with the parser triple mkParser :: Maybe (T st a) -> Maybe a -> Nat -> P st a mkParser np@Nothing ne@Nothing l = P empty np l ne mkParser np@(Just nt) ne@Nothing l = P nt np l ne mkParser np@Nothing ne@(Just a) l = P (pure a) np l ne mkParser np@(Just nt) ne@(Just a) l = P (nt <|> pure a) np l ne -- ! `combine` creates the non-empty parser combine :: (Alternative f) => Maybe t1 -> Maybe t2 -> t -> Maybe t3 -> (t1 -> t -> f a) -> (t2 -> t3 -> f a) -> Maybe (f a) combine Nothing Nothing _ _ _ _ = Nothing -- this Parser always fails combine (Just p) Nothing aq _ op1 op2 = Just (p `op1` aq) combine (Just p) (Just v) aq nq op1 op2 = case nq of Just nnq -> Just (p `op1` aq <|> v `op2` nnq) Nothing -> Just (p `op1` aq ) -- rhs contribution is just from empty alt combine Nothing (Just v) _ nq _ op2 = case nq of Just nnq -> Just (v `op2` nnq) -- right hand side has non-empty part Nothing -> Nothing -- neither side has non-empty part instance Functor (P state) where fmap f (P ap np l me) = mkParser (fmap (fmap f) np) (f <$> me) l f <$ (P ap np l me) = mkParser (fmap (f <$) np) (f <$ me) l instance Applicative (P state) where P ap np pl pe <*> ~(P aq nq ql qe) = mkParser (combine np pe aq nq (<*>) (<$>)) (pe <*> qe) (nat_add pl ql) P ap np pl pe <* ~(P aq nq ql qe) = mkParser (combine np pe aq nq (<*) (<$)) (pe <* qe ) (nat_add pl ql) P ap np pl pe *> ~(P aq nq ql qe) = mkParser (combine np pe aq nq (*>) (flip const)) (pe *> qe ) (nat_add pl ql) pure a = mkParser Nothing (Just a ) (Zero Infinite) instance Alternative (P state) where P ap np pl pe <|> P aq nq ql qe = let (rl, b) = trace' "calling natMin from <|>" (nat_min pl ql 0) Nothing `alt` q = q p `alt` Nothing = p Just p `alt` Just q = Just (p <|>q) in mkParser ((if b then flip else id) alt np nq) (pe <|> qe) rl empty = mkParser empty empty Infinite instance ExtAlternative (P st) where P ap np pl pe <<|> P aq nq ql qe = let (rl, b) = nat_min pl ql 0 bestx :: Steps a -> Steps a -> Steps a bestx = (if b then flip else id) best choose:: T st a -> T st a -> T st a choose (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 `bestx` qh k st) (\ k st -> let left = norm (pf k st) in if has_success left then left else left `bestx` qf k st) (\ k st -> let left = norm (pr k st) in if has_success left then left else left `bestx` qr k st) in P (choose ap aq ) (maybe np (\nqq -> maybe nq (\npp -> return( choose npp nqq)) np) nq) rl (pe <|> qe) -- due to the way Maybe is instance of Alternative the left hand operator gets priority P _ np pl pe <?> label = let replaceExpected :: Steps a -> Steps a replaceExpected (Fail _ c) = (Fail [label] c) replaceExpected others = others nnp = case np of Nothing -> Nothing Just ((T ph pf pr)) -> Just(T ( \ k inp -> replaceExpected (norm ( ph k inp))) ( \ k inp -> replaceExpected (norm ( pf k inp))) ( \ k inp -> replaceExpected (norm ( pr k inp)))) in mkParser nnp pe pl -- | `doNotInterpret` forgets the computed minimal number of tokens recognised by this parser doNotInterpret (P t nep _ e) = P t nep Unspecified e must_be_non_empty msg p@(P _ _ (Zero _) _) _ = error ("The combinator " ++ msg ++ " requires that it's argument cannot recognise the empty string\n") must_be_non_empty _ _ q = q must_be_non_empties msg (P _ _ (Zero _) _) (P _ _ (Zero _) _ ) _ = error ("The combinator " ++ msg ++ " requires that not both arguments can recognise the empty string\n") must_be_non_empties _ _ _ q = q instance IsParser (P st) -- !! do not move the P constructor behind choices/patern matches 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 = fmap (\ (T h _ _ ) -> (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))) ) np combine Nothing Nothing = Nothing combine l@(Just _ ) Nothing = l combine Nothing r@(Just _ ) = r combine (Just l) (Just r) = Just (l <|> r) -- | `unParser_h` retreives the history parser from the descriptor unParser_h :: P b a -> (a -> b -> Steps r) -> b -> Steps r unParser_h (P (T h _ _ ) _ _ _ ) = h -- | `unParser_f` retreives the future parser from the descriptor unParser_f :: P b a -> (b -> Steps r) -> b -> Steps (a, r) unParser_f (P (T _ f _ ) _ _ _ ) = f -- | `unParser_r` retreives therecogniser from the descriptor unParser_r :: P b a -> (b -> Steps r) -> b -> Steps r unParser_r (P (T _ _ r ) _ _ _ ) = r return = pure -- | The function `pSymExt` converts a very basic parser, passed to at as the function `splitState`, -- the minmal number of tokens recognised by the function and and empty descriptor, and builds a @P@ parser out of this, -- i.e. lift the behaviour to a fture pareser, a histroy parser and a recogniser. pSymExt :: (forall a. (token -> state -> Steps a) -> state -> Steps a) -> Nat -> Maybe token -> P state token pSymExt splitState l e = mkParser (Just t) e l where t = T ( splitState ) ( \ k -> splitState (\ t -> push t . k) ) ( \ k -> splitState (\ _ -> k ) ) -- | `micro` inserts a `Cost` step into the sequence representing the progress the parser is making; -- for its use see `"Text.ParserCombinators.UU.Demos.Examples"` micro :: P state a -> Int -> P state a 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 mkParser nnp pe pl -- | For the precise functioning of the `amb` combinators see the paper cited in the "Text.ParserCombinators.UU.README"; -- it 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 mkParser nnp nep pl -- | `pErrors` returns the error messages that were generated since its last call pErrors :: StoresErrors 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 mkParser nnp Nothing (Zero Infinite) -- | `pPos` returns the current input position 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 -> k inp )) nep = Just (error "pPos cannot occur in lhs of bind") -- the errors consumed cannot be determined statically! in mkParser nnp Nothing (Zero Infinite) -- | `pState` returns the current input state pState :: P st st pState = let nnp = Just ( T ( \ k inp -> k inp inp) ( \ k inp -> push inp (k inp)) ($)) in mkParser nnp Nothing (Zero Infinite) -- | The function `pEnd` should be called at the end of the parsing process. It deletes any unconsumed input, turning them into error messages pEnd :: (StoresErrors 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)) in mkParser nnp Nothing (Zero Infinite) -- | @`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. -- For the second argumnet to @`pSwitch`@ (say split) we expect the following to hold: -- -- > let (n,f) = split st in f n to be equal to st 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 mkParser nnp pe pl -- | The function @`parse`@ shows the prototypical way of running a parser on -- 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 Step 0 (Step 0 (Step 0 (Step 0 (error "ambiguous parser?")))) else error "pEnd missing?") -- | The function @`parse_h`@ behaves like @`parse`@ but using the history -- parser. This parser does not give online results, but might run faster. parse_h :: (Eof t) => P t a -> t -> a parse_h (P (T ph _ _) _ _ _) = fst . eval . ph (\ a rest -> if eof rest then push a (Step 0 (Step 0 (Step 0 (Step 0 (error "ambiguous parser?"))))) else error "pEnd missing?") -- | 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.. 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 :: Int -> Steps a -> Steps a End_h :: ([a] , [a] -> Steps r) -> Steps (a,r) -> Steps (a, r) End_f :: [Steps a] -> Steps a -> Steps a type Cost = Int type Progress = Int type Strings = [String] apply :: Steps (b -> a, (b, r)) -> Steps (a, r) apply = Apply (\(b2a, br) -> let (b, r) = br in (b2a b, r)) push :: v -> Steps r -> Steps (v, r) push v = Apply (\ r -> (v, r)) apply2fst :: (b -> a) -> Steps (b, r) -> Steps (a, r) apply2fst f = Apply (\ (b, r) -> (f b, r)) succeedAlways :: Steps a succeedAlways = let steps = Step 0 steps in steps failAlways :: Steps a failAlways = Fail [] [const (0, failAlways)] noAlts :: Steps a noAlts = Fail [] [] has_success :: Steps t -> Bool has_success (Step _ _) = True has_success _ = False -- ! @`eval`@ removes the progress information from a sequence of steps, and constructs the value embedded in it. -- If you are really desparate to see how your parsers are making progress (e.g. when you have written an ambiguous parser, and you cannot find the cause of -- the exponential blow-up of your parsing process, you may switch on the trace in the function @`eval`@ -- eval :: Steps a -> a eval (Step n l) = {- trace ("Step " ++ show n ++ "\n")-} (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" -- | `norm` makes sure that the head of the seqeunce contains progress information. -- It does so by pushing information about the result (i.e. the `Apply` steps) backwards. -- 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 :: (c -> d) -> [a -> (b, c)] -> [a -> (b, d)] applyFail f = map (\ g -> \ ex -> let (c, l) = g ex in (c, f l)) -- | The function @best@ compares two streams best :: Steps a -> Steps a -> Steps a x `best` y = norm x `best'` norm y best' :: Steps b -> Steps b -> Steps b 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) Fail sl ll `best'` Fail sr rr = Fail (sl ++ sr) (ll++rr) Fail _ _ `best'` r = r -- <----------------------------- to be refined 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 l `best'` r = error "missing alternative in best'" -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -- %%%%%%%%%%%%% 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 _ v c = trace' ("traverse " ++ show' 0 v c ++ " choosing" ++ show v ++ "\n") v traverse n (Step _ l) v c = trace' ("traverse Step " ++ show' n v c ++ "\n") (traverse (n - 1 ) l (v-n) c) traverse n (Micro _ l) v c = trace' ("traverse Micro " ++ show' n v c ++ "\n") (traverse n l v c) traverse n (Apply _ l) v c = {- trace' ("traverse Apply " ++ show n ++ "\n")-} (traverse n l v c) traverse n (Fail m m2ls) v c = trace' ("traverse Fail " ++ show m ++ show' n v c ++ "\n") (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) v c = traverse n (lf a `best` removeEnd_h r) v c traverse n (End_f (l :_) r) v c = traverse n (l `best` r) v c show' :: (Show a, Show b, Show c) => a -> b -> c -> String show' n v c = "n: " ++ show n ++ " v: " ++ show v ++ " c: " ++ show c -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -- %%%%%%%%%%%%% 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 -- ** 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 function @`nat-add`@ more than necesssary. data Nat = Zero Nat -- the length of the non-zero part of the parser is remembered) | Succ Nat | Infinite | Unspecified deriving Show -- | `getlength` retrieves the length of the non-empty part of a parser getLength :: Nat -> Nat getLength (Zero l) = l getLength l = l -- | `nat_min` compares two minmal length and returns the shorter length. The second component indicates whether the left -- operand is the smaller one; we cannot use @Either@ since the fisrt component may already be inspected -- before we know which operand is finally chosen nat_min :: Nat -> Nat -> Int -> ( Nat -- the actual minimum length , Bool -- whether aternatives should be swapped ) nat_min (Zero l) (Zero r) n = (Zero (fst(nat_min l r (n+1))), False) nat_min l rr@(Zero r) n = trace' "Right Zero in nat_min\n" (let (m,_) = nat_min l r (n+1) in (Zero m, True)) nat_min ll@(Zero l) r n = trace' "Left Zero in nat_min\n" (let (m,_) = nat_min l r (n+1) in (Zero m, False)) nat_min (Succ ll) (Succ rr) n = if n > 1000 then error "problem with comparing lengths" else trace' ("Succ in nat_min " ++ show n ++ "\n") (let (v, b) = nat_min ll rr (n+1) in (Succ v, b)) nat_min Infinite r _ = trace' "Left Infinite in nat_min\n" (r, True) nat_min l Infinite _ = trace' "Right Infinite in nat_min\n" (l, False) nat_min Unspecified r _ = (r, False) -- leave the alternatives in the order they are nat_min l Unspecified _ = (l, False) -- leave the alternatives in the order they are nat_add :: Nat -> Nat -> Nat nat_add Unspecified _ = Unspecified 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)) trace' :: String -> b -> b trace' m v = {- trace m -} v