Number.Peano.Inf

Lazy Peano numbers including observable infinity value.

Documentation

data Nat

Natural numbers and infinity.

Constructors

Zero

Succ Nat

Instances

Bounded Nat

Enum Nat

Eq Nat

Integral Nat

Num Nat

Ord Nat

Real Nat

Show Nat

infinity :: Nat

Observable infinity value.

isInfinity :: Nat -> Bool

True on (infinity), (5 + 4 * infinity) etc. Evaluates to bottom on (genericLength [1..]).

diff

Arguments

:: Nat

n

-> Nat

m

-> Either Nat Nat

n >= m: Left (n-m), n < m: Right (m-n)

Difference of two natural numbers: the result is either positive or negative.

zeroDiff

Arguments

:: Nat

n

-> Nat

m

-> Either Nat Nat

n >= m: Left (n-m), n < m: Right (m-n)

Variant of diff: infinity zeroDiff infinity == Left Zero.

infDiff

Arguments

:: Nat

n

-> Nat

m

-> Either Nat Nat

n >= m: Left (n-m), n < m: Right (m-n)

Variant of diff: infinity infDiff infinity == Left infinity.

(-|) :: Nat -> Nat -> Nat

Non-negative subtraction. For example, (5 -| 8 == 0).