[Haskell-cafe] Type inference for infinite structures

Hi everyone, I'm relatively new to Haskell and was a bit troubled by the problem of assigning a type to infinite structures. To give a clear example, suppose we have data Nat = Zero | Succ Nat omega = Succ omega What type then does omega have? According to GHCi, omega :: Nat. But surely this can only be the case if we already have that omega :: Nat (on the right hand side of the equation)? I can see that the type assignment is valid, but is it necessarily the case? Does it not, somehow, sidestep the inductive base case of the definition of a Nat? Thanks, Matt