Number.Peano.Inf

Lazy Peano numbers including observable infinity value.

Note that the following equation does not hold for this number type:

• 1 + a > a, because 1 + infinity == infinity.

The following operation is undefined:

• infinity - infinity

There are variants of (-) with different behaviour regarding this, see below.

The following operations are naturally undefined:

• fromEnum infinity

• toInteger infinity

• 0 - n, if n > 0
• fromInteger n, if n < 0
• toEnum n, if n < 0

• pred 0

Documentation

data Nat

Natural numbers and infinity.

Instances

Bounded Nat

Enum Nat

Eq Nat

Integral Nat

Num Nat

Ord Nat

Real Nat

Show Nat

infinity :: Nat

Observable infinity value.

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: zeroDiff infinity infinity == Left 0.

infDiff

Arguments

:: Nat

n

-> Nat

m

-> Either Nat Nat

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

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

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

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