"read: no parse" with functionShow

[Brent Yorgey]

Hello,

I was using the new Test.QuickCheck.Function module (which is
otherwise lovely) and ran into a problem.  The documentation states
(re: instances of the Function class) "If your type has a Show
instance, you can use functionShow to write the instance".  (Actually,
this should mention 'Read' as well, but no matter.)  So I did as
follows:

  newtype Elt = Elt { unElt :: Char }
    deriving (Eq, Read, Show)

  instance Arbitrary Elt where
    arbitrary = elements (map Elt "abcde")

  instance CoArbitrary Elt where
    coarbitrary = coarbitrary . ord . unElt

  instance Function Elt where
    function = functionShow

However, when running tests involving (Fun Elt ...), I keep getting
"Prelude.read: no parse" errors.  This puzzled me for quite a while
until I dove into the QuickCheck source.  I realized that functionShow
just calls (functionMap show read)... but functionMap only works if
the two types are *isomorphic*!  My type (and MOST types with
Show+Read instances) is definitely not isomorphic to String; it is
only isomorphic to a subset of String.  What seems to be happening is
that QuickCheck is generating random Strings and then trying to
convert them to Elts via 'read', which of course is not going to work.

I next tried

  instance Function Elt where
    function = functionMap unElt Elt

but although this no longer crashes, it has a similar problem:
arbitrary Chars are being generated and then converted to Elt, which
is wasteful since I only want to consider specifically the Chars 'a'
through 'e', as you can see in my Arbitrary instance for Elt.  Elt is
not really isomorphic to Char, at least not semantically.

It seems the only viable way to write a Function instance for Elt would be

  instance Function Elt where
    function f = Table [(Elt c, f (Elt c)) | c <- "abcde"]

but the Table constructor is not exported.  Also, even if Table were
exported, it seems ugly having to specify essentially the same
information as I already did for the Arbitrary instance.

I suppose I could also use functionMap with Either () (Either ()
(Either () (Either () ()))) but that seems like a hack.

Any thoughts are appreciated.  Thanks!

-Brent