Copyright | Guillaume Sabbagh 2022 |
---|---|
License | GPL-3 |
Maintainer | guillaumesabbagh@protonmail.com |
Stability | experimental |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
Any total (or linear) order induces a preorder category where elements are objects, there is an arrow between two objects iff the relation is satisfied.
(See Categories for the working mathematican. Saunders Mac Lane. p.11)
Synopsis
- data IsSmallerThan a = IsSmallerThan a a
- data TotalOrder a = TotalOrder
Documentation
data IsSmallerThan a Source #
IsSmallerThan
is the type of morphisms in a linear order, it reminds the fact that there is a morphism from a source to a target iff the source is smaller than the target.
IsSmallerThan a a |
Instances
data TotalOrder a Source #
A TotalOrder
category is the category induced by a total order.
(See Categories for the working mathematican. Saunders Mac Lane. p.11)
Instances
PrettyPrint (TotalOrder a) Source # | |
Defined in Math.Categories.TotalOrder pprint :: TotalOrder a -> String Source # | |
Show (TotalOrder a) Source # | |
Defined in Math.Categories.TotalOrder showsPrec :: Int -> TotalOrder a -> ShowS show :: TotalOrder a -> String showList :: [TotalOrder a] -> ShowS | |
Eq (TotalOrder a) Source # | |
Defined in Math.Categories.TotalOrder (==) :: TotalOrder a -> TotalOrder a -> Bool (/=) :: TotalOrder a -> TotalOrder a -> Bool | |
(Eq a, Ord a) => Category (TotalOrder a) (IsSmallerThan a) a Source # | |
Defined in Math.Categories.TotalOrder identity :: TotalOrder a -> a -> IsSmallerThan a Source # ar :: TotalOrder a -> a -> a -> Set (IsSmallerThan a) Source # genAr :: TotalOrder a -> a -> a -> Set (IsSmallerThan a) Source # decompose :: TotalOrder a -> IsSmallerThan a -> [IsSmallerThan a] Source # |