A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).

The following are QuickCheck specifications of what the combinators do. These can be seen as formal specifications of the behavior of the combinators.

We use bags to give semantics to the combinators.

  type Bag a = [a]

Equality on bags does not care about the order of elements.

  (=~) :: Ord a => Bag a -> Bag a -> Bool
  xs =~ ys = sort xs == sort ys

A special equality operator to avoid unresolved overloading when testing the properties.

  (=~.) :: Bag (Int,String) -> Bag (Int,String) -> Bool
  (=~.) = (=~)

Here follow the properties:

  prop_Get_Nil =
    readP_to_S get [] =~ []

  prop_Get_Cons c s =
    readP_to_S get (c:s) =~ [(c,s)]

  prop_Look s =
    readP_to_S look s =~ [(s,s)]

  prop_Fail s =
    readP_to_S pfail s =~. []

  prop_Return x s =
    readP_to_S (return x) s =~. [(x,s)]

  prop_Bind p k s =
    readP_to_S (p >>= k) s =~.
      [ ys''
      | (x,s') <- readP_to_S p s
      , ys''   <- readP_to_S (k (x::Int)) s'
      ]

  prop_Plus p q s =
    readP_to_S (p +++ q) s =~.
      (readP_to_S p s ++ readP_to_S q s)

  prop_LeftPlus p q s =
    readP_to_S (p <++ q) s =~.
      (readP_to_S p s +<+ readP_to_S q s)
   where
    [] +<+ ys = ys
    xs +<+ _  = xs

  prop_Gather s =
    forAll readPWithoutReadS $ \p -> 
      readP_to_S (gather p) s =~
	 [ ((pre,x::Int),s')
	 | (x,s') <- readP_to_S p s
	 , let pre = take (length s - length s') s
	 ]

  prop_String_Yes this s =
    readP_to_S (string this) (this ++ s) =~
      [(this,s)]

  prop_String_Maybe this s =
    readP_to_S (string this) s =~
      [(this, drop (length this) s) | this `isPrefixOf` s]

  prop_Munch p s =
    readP_to_S (munch p) s =~
      [(takeWhile p s, dropWhile p s)]

  prop_Munch1 p s =
    readP_to_S (munch1 p) s =~
      [(res,s') | let (res,s') = (takeWhile p s, dropWhile p s), not (null res)]

  prop_Choice ps s =
    readP_to_S (choice ps) s =~.
      readP_to_S (foldr (+++) pfail ps) s

  prop_ReadS r s =
    readP_to_S (readS_to_P r) s =~. r s