I had to enable undecidable instances, but I'm very very very happy with the U trick, no TH or other things needed. Thanks :)
On Mon, Mar 17, 2014 at 2:52 PM, Carter Schonwald < carter.schonw...@gmail.com> wrote: > (aside, pardon my earlier tone, been a bit overloaded the past few weeks, > that crossed over to the list) > > OOO > that works? > I guess that gives a decent way of using TypeLits as a concrete input > syntax for Peano numbers. Thanks for pointing that out > > I think i'm gonna go drop 7.6 support on some code i'm working on if this > works :) > > > > > > On Mon, Mar 17, 2014 at 2:05 PM, Richard Eisenberg <e...@cis.upenn.edu>wrote: > >> So much to respond to! >> >> First, a little relevant context: Iavor Diatchki is the primary >> implementor of the type-lits stuff; I am not. But, he and I are playing in >> the same playground, so to speak, so we confer a fair amount and I may have >> some helpful perspective on all of this. >> >> Henning asks: >> > How can I convince GHC that n+1 is always at least 1? >> >> You can ramrod facts like this down GHC's throat when necessary. For >> example, the following works: >> >> > foo :: (1 <= n + 1) => Proxy n -> () >> > foo _ = () >> > >> > lt :: Proxy n -> (1 <=? n + 1) :~: True >> > lt _ = unsafeCoerce Refl >> > >> > bar :: forall (n :: Nat). Proxy n -> () >> > bar p = gcastWith (lt p) (foo p) >> >> >> In case you're unfamiliar with them, here are some helpful definitions >> from Data.Type.Equality, used above: >> >> > data a :~: b where >> > Refl :: a :~: a >> > gcastWith :: (a :~: b) -> ((a ~ b) => r) -> r >> >> Also helpful when doing things like this is this definition, from Edward >> Kmett's `constraints` package: >> >> > data Dict c where >> > Dict :: c => Dict c >> >> An `unsafeCoerce Dict` can be used to satisfy any arbitrary constraint. >> >> Of course, it is often possible to use an inductive proof (er, recursive >> function) to produce Refl or Dict without resorting to unsafeCoerce. But, >> as the TypeLits Nat isn't inductive, we're forced to use drastic measures >> here. >> >> Carter says: >> > I've been toying with the idea that the type lits syntax should be just >> that, a type level analogue of from integer that you can give to user land >> types, but I'm not going to suggest that till 7.8 is fully released. >> >> >> I like this idea. >> >> Christiaan says: >> > Iavor is working on a branch that allows the constraint solver to call >> an external solver: https://github.com/ghc/ghc/tree/decision-procedure >> >> >> Yes, though I don't know how active this branch is currently. There are >> whispers afoot of going in the direction of strapping an SMT solver into >> GHC, though much work remains to be done before this happens. My sense is >> that an SMT solver will be necessary before TypeLits really becomes >> fluently useful. I'm confident this will happen eventually, but it may be >> over a year out, still. It's even possible that I will be the one to do it, >> but it's not on my short-to-do-list. >> >> Christiaan says: >> > I myself worked on a patch that can only work with equalities: >> https://gist.github.com/christiaanb/8396614 >> >> >> Cool! Have you conferred with Iavor about this? >> >> Carter says: >> > The current typeLits story for nats is kinda a fuster cluck to put it >> politely . We have type lits but we cant use them (well, we can't compute >> on them, which is the same thing). >> >> I disagree on both counts here. TypeLits is a work in progress, as are >> many parts of GHC. That's one of the beautiful things about Haskell/GHC! Is >> there more progress to be made? Absolutely. But, without the work that's >> already been done, I'm not sure we would be as convinced as we are (still >> not 100%, to be sure, but getting there) that we need an SMT solver. We >> have to build on previous work, and to do that, we have to write >> potentially incomplete features. And, I've been able to use TypeLits most >> of the way toward implementing my `units` library (a way of type-checking >> with respect to units-of-measure). The only feature that they couldn't >> support was automatic unit conversions. >> >> Carter says: >> > I'm still waiting (2 years later) for a solver we can actually include >> in ghc or even a user land solver! >> >> >> I've done some thinking about user-land solvers and am quite interested >> in seeing it done. My chief thrust right now is about dependent types in >> Haskell, not this, but Iavor's "decision-procedure" branch lays a lot of >> the groundwork down for integrating perhaps multiple solvers in with GHC. >> >> Henning says: >> > A minimal invasive solution would be to provide a kind for unary type >> level numbers and type functions that convert between Unary and Nat. >> >> >> This definition is quite straightforward and works beautifully: >> >> > data Nat1 = Zero | Succ Nat1 >> > type family U n where >> > U 0 = Zero >> > U n = Succ (U (n-1)) >> >> Iavor made sure that subtraction worked specifically in this case because >> it was so useful. >> >> I hope this is helpful! >> Richard >> >> On Mar 16, 2014, at 4:52 PM, Henning Thielemann < >> lemm...@henning-thielemann.de> wrote: >> >> > Am 16.03.2014 20:02, schrieb Carter Schonwald: >> >> respectfully, >> >> The current typeLits story for nats is kinda a fuster cluck to put it >> >> politely . We have type lits but we cant use them (well, we can't >> >> compute on them, which is the same thing). >> >> >> >> For the past 2 years, every ghc release cycle, I first discover, then >> >> have to communicate to everyone else "you can't compute on type lits". >> > >> > A minimal invasive solution would be to provide a kind for unary type >> level numbers and type functions that convert between Unary and Nat. >> > >> > _______________________________________________ >> > Glasgow-haskell-users mailing list >> > Glasgow-haskell-users@haskell.org >> > http://www.haskell.org/mailman/listinfo/glasgow-haskell-users >> >> >
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