Haskell' - class aliases
John Meacham
john at repetae.net
Fri May 2 05:50:20 EDT 2008
This isn't really a response to your email, but I have been mulling the
last few hours away from a computer and wanted to get this stream of
conciousness out when it is fresh in my mind.
The more I think about it, I think 'superclass' is just the wrong
terminology for dealing with class aliases. Superclass implies a strict
partial order on classes, which just isn't the case for class aliases,
for instance
> class alias Foo a => Foo a = Bar a where ...
Has a defined (if not very useful) meaning with class aliases, but is
really odd if you consider 'Foo a' a "superclass". So, I think the
following terminology should be used:
Context of --+
alias | The alias -+ +--- The expansion of the alias
| | |
v v v
> class alias (S1 a .. Sn a) => A a = (C1 a ... Cn a) where
> fd1 = ....
> ....
> fdn = ....
^
+---- The defaults of the alias
given this, the expansion of 'A a' in any context other than an instance
head is
> A a --> reduce(S1 a .. Sn a, C1 a ... Cn a)
where reduce is standard entailment reduction on class contexts (like (Eq
a,Ord a, Eq a) reduces to (Ord a))
This expansion is carried out iteratively on all class aliases until a
fixed point is reached, then all class aliases are deleted from the
result and the remaining context is the final result. (This will always
terminate due to there being a finite number of class aliases that can
be pulled into the expansion)
likewise, for instance declarations:
> instance A a where ...
-->
> foreach C in C1 .. Cn:
> instance (S1 a ... Sn a) => C a where ...
I left out the default methods here. I need to think about them a bit
more to come up with a formal expansion as it is a bit trickier (to
typeset if nothing else), but I hope this is somewhat more clear for
some...
John
--
John Meacham - ⑆repetae.net⑆john⑈
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