Safe Haskell	Safe-Inferred

Data.Nat

Description

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

Synopsis

Documentation

data Nat Source

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 -> rSource

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

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

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

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

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 Source

Very big!

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

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