Hello,
shouldn't the check go the other way? (i.e., if the RHSs unify, then the
LHS must be the same). Here is an example:
-- This function is not injective.
type instance F a = Int
type instance F b = Int
Still, Conal's example would not work if we just added support for injective
type functions because + is not injective (e.g., 2 + 3 = 1 + 4). Instead,
what we'd need to say is that it is injective in each argument separately,
which would basically amount to adding functional dependencies to type
functions. Perhaps something like this:
type family (a :+: b) ~ c | c b -> a, c a -> b
This seems like a feature which could be useful.
-Iavor
PS: Conal, I have been working on a GHC extension which has direct support
for working with natural numbers at the type-level (e.g., + is a built-in
type function which supports cancellation and other properties of the normal
+ operation). I am keen on collecting different ways in which people use
type-level naturals to make sure that my implementation supports them (or at
least report a decent error). I wasn't sure if the :+ from your example was
just meant to illustrate the issue with injectivity, but if you have a use
case for type nats, I'd be curious to find out more.
On Mon, Feb 14, 2011 at 3:26 PM, Simon Peyton-Jones
Injective type families are a perfectly reasonable idea, but we have not implemented them (yet). The idea would be:
* You declare the family to be injective
injective type family T a :: *
* At every type instance, injectivity is checked. That is, if you say
type instance T (a,Int) = Either a Bool
then we must check that every type instance whose LHS unifies with this has the same RHS under the unifying substitution. Thus
type instance T (a,Bool) = [a] -- OK; does not unify type instance T (Int,b) = Either Int Bool -- OK; same RHS on (Int,Int)
I think it's mainly a question of tiresome design questions (notably do we want a new keyword "injective"? Should it go before "type"?) and hacking to get it all implemented.
Simon
| -----Original Message----- | From: glasgow-haskell-users-bounces@haskell.org [mailto: glasgow-haskell-users- | bounces@haskell.org] On Behalf Of Dan Doel | Sent: 14 February 2011 23:14 | To: glasgow-haskell-users@haskell.org | Subject: Re: Injective type families? | | On Monday 14 February 2011 5:51:55 PM Daniel Peebles wrote: | > I think what you want is closed type families, as do I and many others :) | > Unfortunately we don't have those. | | Closed type families wouldn't necessarily be injective, either. What he wants | is the facility to prove (or assert) to the compiler that a particualr type | family is in fact injective. | | It's something that I haven't really even seen developed much in fancy | dependently typed languages, though I've seen the idea before. That is: prove | things about your program and have the compiler take advantage of it. | | -- Dan | | _______________________________________________ | Glasgow-haskell-users mailing list | Glasgow-haskell-users@haskell.org | http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
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