No, there's not another way to do this with built-in Nats, and there probably won't ever be.
There are two advantages to the built-in Nats over hand-rolled ones: 1) Better syntax / error messages. 2) Built-in Nats are much more efficient than hand-rolled ones, because the hand-rolled ones are unary and take up space linear in the value of the number. If you re-hash your proposal for a Successor constructor down to the term level, it looks juts like (n+k)-patterns, which were discarded as a bad idea. The reason that the type-level numbers are natural numbers and not integers is because natural numbers have a simpler theory to solve for. I'm personally hoping for proper type-level integers at some point, and the type-checker plugins approach may make that a reality sooner than later. I hope this helps! Richard On Oct 25, 2014, at 9:53 AM, Barney Hilken <b.hil...@ntlworld.com> wrote: > If you define your own type level naturals by promoting > > data Nat = Z | S Nat > > you can define data families recursively, for example > > data family Power :: Nat -> * -> * > data instance Power Z a = PowerZ > data instance Power (S n) a = PowerS a (Power n a) > > But if you use the built-in type level Nat, I can find no way to do the same > thing. You can define a closed type family > > type family Power (n :: Nat) a where > Power 0 a = () > Power n a = (a, Power (n-1) a) > > but this isn't the same thing (and requires UndecidableInstances). > > Have I missed something? The user guide page is pretty sparse, and not up to > date anyway. > > If not, are there plans to add a "Successor" constructor to Nat? I would have > thought this was the main point of using Nat rather than Int. > > Barney. > > _______________________________________________ > Glasgow-haskell-users mailing list > Glasgow-haskell-users@haskell.org > http://www.haskell.org/mailman/listinfo/glasgow-haskell-users _______________________________________________ Glasgow-haskell-users mailing list Glasgow-haskell-users@haskell.org http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
