25 Oct 15:53 2014

### Recursion on TypeNats

Barney Hilken <b.hilken <at> ntlworld.com>

2014-10-25 13:53:19 GMT

2014-10-25 13:53:19 GMT

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.