Re: [Haskell-cafe] Re: What does the Haskell type system do with "show (1+2)"?

On 13/01/06, Daniel Fischer wrote:

Am Freitag, 13. Januar 2006 11:12 schrieb Christian Maeder:

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Jared Updike wrote:

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http://www.haskell.org/onlinereport/decls.html#default-decls http://www.haskell.org/tutorial/numbers.html#sect10.4

I still don't see, why it works for show but not for my_show.

Says the report: Ambiguities in the class Num are most common, so Haskell provides another way to resolve them---with a default declaration:

default (t1 , ... , tn)

where n>=0, and each ti must be a type for which Num ti holds. In situations where an ambiguous type is discovered, an ambiguous type variable, v, is defaultable if:

v appears only in constraints of the form C v, where C is a class, and at least one of these classes is a numeric class, (that is, Num or a subclass of Num), and all of these classes are defined in the Prelude or a standard library (Figures ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ That's the point! ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 6.2--6.3, pages -- show the numeric classes, and Figure 6.1, page , shows the classes defined in the Prelude.) Each defaultable variable is replaced by the first type in the default list that is an instance of all the ambiguous variable's classes. It is a static error if no such type is found.

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On 1/12/06, Jeff.Harper@handheld.com wrote:

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class (Show a) => My_show a where my_show :: a -> String

If I let this be

class My_show a where my_show :: a -> String

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instance My_show Int where my_show a = show a ++ " :: Int"

instance My_show Integer where my_show a = show a ++ " :: Integer"

What is the difference to the builtin Show class?

It's not declared in the prelude or standard libraries.

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Christian

Now the question is, could that restriction be lifted, i.e., would it be possible/worthwhile to let defaulting also take place if user defined classes are involved?

So long as we're going to have a defaulting mechanism, it seems a bit odd to restrict it to Num, and to classes in the Prelude. It would be neat if this could be somewhat generalised, so that, say, the Haskell 98 defaulting behaviour could be completely specified by declarations in the Prelude, but it's a good question as to exactly how it should be generalised at all. It seems a bit tricky to come up with a way to specify the defaulting behaviour which is both general enough to express the current behaviour, and which doesn't result in conflicts in the orders in which default types are tried. The 'obvious' thing is to have a specification somewhat like: default C (t1,...,tn) where C is the name of a single parameter typeclass (or a multiparameter one, with all but one of the type variables applied; there ought to be a way to generalise to multi-parameter typeclasses if we can sort out the problems here) The problem comes when you have a type variable which is ambiguous, and to which multiple defaulting specifications apply. In which order do we try the defaults? We almost certainly wouldn't want it to depend, for example, on the order in which the class constraints in a type declaration were specified. We could pick the defaulting mechanism based on order of occurrence to some extent, but even this seems a little ugly. Also, how do these defaults interact with modules? If we want the system to be nice and general, it would be nice to have the behaviour with respect to Num specified in the Prelude and merely exported, but this potentially opens up another can of worms with regard to exporting defaults. If we always export them, it's unclear what happens with cyclic module dependency graphs. Perhaps there should be some provision to allow for writing something like "default C" in the module export/import lists. - Cale