Data.Nat

Operations which are undefined mathematically (0 / 0, infinity * 0, infinity - infinity, etc.) also have undefined results in this implementation.

Documentation

data Nat

Constructors

Zero

Succ Nat

Instances

Bounded Nat

maxBound = infinity. Not sure if this is polite.

Enum Nat

Eq Nat

Integral Nat

Num Nat

Ord Nat

Read Nat

Real Nat

Show Nat

Ix Nat

Typeable Nat

Generic Nat

Whole Nat

nat :: r -> (Nat -> r) -> Nat -> r

Shallow deconstruction. Returns the first argument if Zero, applies the second argument to the inner value if Succ.

foldNat :: r -> (r -> r) -> Nat -> r

Returns the first argument if Zero, applies the second argument recursively for each Succ.

unfoldNat :: (a -> Maybe a) -> a -> Nat

Build a Nat from a seed value: the first argument should return the next seed value if the building is to continue, or Nothing if it is to stop. A Succ is added at each iteration.

infinity :: Nat

Very big!

diff :: Nat -> Nat -> Either Nat Nat

 diff n m | n >= m    = Right (n - m)
          | otherwise = Left  (m - n)