Data.Dioid

Documentation

type Topological a = (Dioid a, Kleene a, Yoneda a)

class (Prd a, Semiring a) => Dioid a

Right pre-dioids and dioids.

A right-dioid is a semiring with a right-canonical pre-order relation relative to <>: a <~ b iff b ≡ a <> c for some c.

In other words we have that:

a <~ (a <> b) ≡ True

Consequently <~ is both reflexive and transitive:

a <~ a ≡ True
a <~ b && b <~ c ==> a <~ c ≡ True

Finally <~ is an order relation:

(a =~ b) == (a == b)

See Property

Instances

Dioid Bool

Defined in Data.Bool.Instance

Dioid Natural

Defined in Data.Word.Instance

Dioid Word

Defined in Data.Word.Instance

Dioid Word8

Defined in Data.Word.Instance

Dioid Word16

Defined in Data.Word.Instance

Dioid Word32

Defined in Data.Word.Instance

Dioid Word64

Defined in Data.Word.Instance