Copyright | Guillaume Sabbagh 2022 |
---|---|
License | GPL-3 |
Maintainer | guillaumesabbagh@protonmail.com |
Stability | experimental |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
An OrdinalCategory
is a TotalOrder
category where the total order is an order induced by ordinal numbers.
Concretely the type parameter must implement the Enum typeclass.
For example, the TotalOrder
category induced by (R,<=) is not an OrdinalCategory
whereas (N,<=) is.
It induces a non trivial generating set of arrows thanks to the succ
function.
Synopsis
- newtype OrdinalCategory a = OrdinalCategory (TotalOrder a)
- module Math.Categories.TotalOrder
Documentation
newtype OrdinalCategory a Source #
An OrdinalCategory
is a TotalOrder
where the type a follows the Enum typeclass.
Instances
Show a => PrettyPrint (OrdinalCategory a) Source # | |
Defined in Math.Categories.OrdinalCategory pprint :: OrdinalCategory a -> String Source # | |
Show (OrdinalCategory a) Source # | |
Defined in Math.Categories.OrdinalCategory showsPrec :: Int -> OrdinalCategory a -> ShowS show :: OrdinalCategory a -> String showList :: [OrdinalCategory a] -> ShowS | |
Eq (OrdinalCategory a) Source # | |
Defined in Math.Categories.OrdinalCategory (==) :: OrdinalCategory a -> OrdinalCategory a -> Bool (/=) :: OrdinalCategory a -> OrdinalCategory a -> Bool | |
(Enum a, Ord a) => Category (OrdinalCategory a) (IsSmallerThan a) a Source # | |
Defined in Math.Categories.OrdinalCategory identity :: OrdinalCategory a -> a -> IsSmallerThan a Source # ar :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a) Source # genAr :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a) Source # decompose :: OrdinalCategory a -> IsSmallerThan a -> [IsSmallerThan a] Source # |
module Math.Categories.TotalOrder