Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Synopsis
- type Topological a = (Dioid a, Kleene a, Yoneda a)
- class (Prd r, Semiring r) => Dioid r where
- fromNatural :: Natural -> r
Documentation
class (Prd r, Semiring r) => Dioid r where Source #
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
fromNatural :: Natural -> r Source #
A dioid homomorphism from the naturals to r.