# Counting Constructors

**Gertjan Kamsteeg
**
gkamsteeg@freeler.nl

*Wed, 18 Jul 2001 01:53:57 +0200*

Unless I misunderstood the problem, the following code will 'almost' do the
(first) job (misusing the first argument of showsPrec):
instance Show a => Show (Bind a) where
showsPrec n Zero = showInt n
showsPrec n (Succ x) = showsPrec (n+1) x
Works fine in Hugs 98 (with -98 as well as with +98). It has a few
shortcomings however:
- If you call show on a term of the form Succ (Succ (... (Succ Zero)...)),
you'll have to provide its type (e.g., Zero :: Bind Int, Succ Zero :: Bind
(Bind Char), etc.). This is a general issue however, similar to trying to
show [].
- If you call show on a term of the form Succ (Succ (... (Succ x)...)), with
x of some non-Bind type, showsPrec n x is called (for some n) rather than
showsPrec 0 x. This shouldn't be much of a problem if you are prepared to
introduce some general wrapper type for x, and define a showsPrec function
for it, independent of its first argument.
Gertjan
----- Original Message -----
From: "Marcin 'Qrczak' Kowalczyk" <qrczak@knm.org.pl>
To: <haskell@haskell.org>
Sent: Tuesday, July 17, 2001 9:13 PM
Subject: Re: Counting Constructors
>* Tue, 17 Jul 2001 12:08:51 +0200 (MEST), Tobias Haeberlein
*<T.Haeberlein@gmx.de> pisze:
>*
*>* > show (Succ ( ... (Succ Zero)..)) = n
*>* > (where n is the number of Succ's)
*>* > and
*>* >
*>* > show (Succ ( ... (Succ x)..)) = show x
*>* > (when x != Zero)
*>*
*>* This is not possible in Haskell 98 - you can't overload an operation on
*>* "any type except this one". There are no "negative assertions" or
*>* "exceptions".
*>*
*>* It might be possible in Hugs run with -98 option (define "instance
*>* Count a" and "instance Count a => Count (Bind a)" and "instance Count
*>* a => Show (Bind a)", where class Count has a function of type a->Int),
*>* but I would not be surprised if it didn't work correctly in all cases,
*>* e.g. if the answer was too small sometimes. Overlapped instances is
*>* not a well behaved concept.
*>*
*>* --
*>* __("< Marcin Kowalczyk * qrczak@knm.org.pl http://qrczak.ids.net.pl/
*>* \__/
*>* ^^ SYGNATURA ZASTĘPCZA
*>* QRCZAK
*>*
*>*
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