Documentation

Running the function show_demos should give the following output:

>>> run pa  "a"
 Result: "a"

>>> run pa  ""
 Result: "a"
 Correcting steps: 
   Inserted  'a' at position LineColPos 0 0 0 expecting 'a'

>>> run pa  "b"
 Result: "a"
 Correcting steps: 
   Deleted   'b' at position LineColPos 0 0 0 expecting 'a'
   Inserted  'a' at position LineColPos 0 1 1 expecting 'a'

>>> run ((++) <$> pa <*> pa)  "bbab"
 Result: "aa"
 Correcting steps: 
   Deleted   'b' at position LineColPos 0 0 0 expecting 'a'
   Deleted   'b' at position LineColPos 0 1 1 expecting 'a'
   Deleted   'b' at position LineColPos 0 3 3 expecting 'a'
   Inserted  'a' at position LineColPos 0 4 4 expecting 'a'

>>> run pa  "ba"
 Result: "a"
 Correcting steps: 
   Deleted   'b' at position LineColPos 0 0 0 expecting 'a'

>>> run pa  "aa"
 Result: "a"
 Correcting steps: 
   The token 'a' was not consumed by the parsing process.

>>> run (pCount pa :: Parser Int)  "aaa"
 Result: 3

>>> run (do  {l <- pCount pa; pExact l pb})  "aaacabbbbb"
 Result: ["b","b","b","b"]
 Correcting steps: 
   Deleted   'c' at position LineColPos 0 3 3 expecting one of ['b', 'a']
   The token 'b' was not consumed by the parsing process.

>>> run (amb ( (++) <$> pa2 <*> pa3 <|> (++) <$> pa3 <*> pa2))  "aaaaa"
 Result: ["aaaaa","aaaaa"]

>>> run (pList pLower)  "doaitse"
 Result: "doaitse"

>>> run paz  "abc2ez"
 Result: "abcez"
 Correcting steps: 
   Deleted   '2' at position LineColPos 0 3 3 expecting 'a'..'z'

>>> run (max <$> pParens ((+1) <$> wfp) <*> wfp `opt` 0)  "((()))()(())"
 Result: 3

>>> run (pa <|> pb <?> justamessage)  "c"
 Result: "b"
 Correcting steps: 
   Deleted   'c' at position LineColPos 0 0 0 expecting justamessage
   Inserted  'b' at position LineColPos 0 1 1 expecting 'b'

>>> run (amb (pEither  parseIntString  pIntList))  "(123;456;789)"
 Result: [Left ["123","456","789"],Right [123,456,789]]

The fuction run runs the parser and shows both the result, and the correcting steps which were taken during the parsing process.

Our first two parsers are simple; one recognises a single a character and the other one a single b. Since we will use them later we convert the recognised character into String so they can be easily combined.

The applicative style makes it very easy to merge recogition and computing a result. As an example we parse a sequence of nested well formed parentheses pairs and compute the maximum nesting depth with wfp:

It is very easy to recognise infix expressions with any number of priorities and operators:

operators       = [[('+', (+)), ('-', (-))],  [('*' , (*))], [('^', (^))]]
same_prio  ops  = msum [ op <$ pSym c | (c, op) <- ops]
expr            = foldr pChainl ( pNatural <|> pParens expr) (map same_prio operators) -- 

which we can call:

run expr "15-3*5+2^5"

Result: 32

Note that also here correction takes place:

run expr "2 + + 3 5"

Result: 37
Correcting steps: 
   Deleted  ' ' at position 1 expecting one of ['0'..'9', '^', '*', '-', '+']
   Deleted  ' ' at position 3 expecting one of ['(', '0'..'9']
   Inserted '0' at position 4 expecting '0'..'9'
   Deleted  ' ' at position 5 expecting one of ['(', '0'..'9']
   Deleted  ' ' at position 7 expecting one of ['0'..'9', '^', '*', '-', '+']

A common case where ambiguity arises is when we e.g. want to recognise identifiers, but only those which are not keywords. The combinator micro inserts steps with a specfied cost in the result of the parser which can be used to disambiguate:

ident ::  Parser String
ident = ((:) <$> pSym ('a','z') <*> pMunch (\x -> 'a' <= x && x <= 'z') `micro` 2) <* spaces
idents = pList1 ident
pKey keyw = pToken keyw `micro` 1 <* spaces
spaces :: Parser String
spaces = pMunch (==' ')
takes_second_alt =   pList ident 
               \<|> (\ c t e -> ["IfThenElse"] ++  c   ++  t  ++  e) 
                   \<$ pKey "if"   <*> pList_ng ident 
                   \<* pKey "then" <*> pList_ng ident
                   \<* pKey "else" <*> pList_ng ident  

A keyword is followed by a small cost 1, which makes sure that identifiers which have a keyword as a prefix win over the keyword. Identifiers are however followed by a cost 2, with as result that in this case the keyword wins. Note that a limitation of this approach is that keywords are only recognised as such when expected!

test13 = run takes_second_alt "if a then if else c"
test14 = run takes_second_alt "ifx a then if else c"

with results for test13 and test14:

Result: ["IfThenElse","a","if","c"]
Result: ["ifx","a","then","if", "else","c"]

A mistake which is made quite often is to construct a parser which can recognise a sequence of elements using one of the derived combinators (say pList), but where the argument parser can recognise the empty string. The derived combinators check whether this is the case and terminate the parsing process with an error message:

run (pList spaces) ""
Result: *** Exception: The combinator pList
 requires that it's argument cannot recognise the empty string

run (pMaybe spaces) " "
Result: *** Exception: The combinator pMaybe
requires that it's argument cannot recognise the empty string