Copyright	Guillaume Sabbagh 2021
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Set.FinOrdSet

Contents

The morphism of the category : FinOrdMap
The category itself : FinOrdSet

Description

Same as FinOrdSet but using Data.Set as objects, it is more optimized but needs its elements to be ordered.

Synopsis

data FinOrdMap a = FinOrdMap {
- codomain :: Set a
- function :: Map a a
}
data FinOrdSet a = FinOrdSet {
- sets :: [Set a]
}
powerFinOrdSet :: Ord a => Set a -> FinOrdSet a

The morphism of the category : `FinOrdMap`

data FinOrdMap a Source #

FinOrdMap is the morphism of the FinOrdSet category.

It is represented by a Map. The domain is the list of keys. We need to store the codomain of the map in order to differentiate different maps which would be the same if we couldn't compare codomains. For example, f : {1,2,3} -> {1,2,3} and g : {1,2,3} -> {1,2,3,4} would have the same Map but are different.

Constructors

FinOrdMap
Fields codomain :: Set a function :: Map a a

Instances

Instances details

Eq a => Eq (FinOrdMap a) Source #
Instance details Defined in Set.FinOrdSet Methods (==) :: FinOrdMap a -> FinOrdMap a -> Bool (/=) :: FinOrdMap a -> FinOrdMap a -> Bool
Show a => Show (FinOrdMap a) Source #
Instance details Defined in Set.FinOrdSet Methods showsPrec :: Int -> FinOrdMap a -> ShowS show :: FinOrdMap a -> String showList :: [FinOrdMap a] -> ShowS
(PrettyPrintable a, Ord a) => PrettyPrintable (FinOrdMap a) Source #
Instance details Defined in Set.FinOrdSet Methods pprint :: FinOrdMap a -> String Source #
Ord a => Morphism (FinOrdMap a) (Set a) Source #
Instance details Defined in Set.FinOrdSet Methods (@) :: FinOrdMap a -> FinOrdMap a -> FinOrdMap a Source # source :: FinOrdMap a -> Set a Source # target :: FinOrdMap a -> Set a Source #
Ord a => GeneratedFiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a) Source #
Instance details Defined in Set.FinOrdSet Methods genAr :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a] Source # decompose :: FinOrdSet a -> FinOrdMap a -> [FinOrdMap a] Source # genArrows :: FinOrdSet a -> [FinOrdMap a] Source #
Ord a => FiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a) Source #
Instance details Defined in Set.FinOrdSet Methods ob :: FinOrdSet a -> [Set a] Source # identity :: FinOrdSet a -> Set a -> FinOrdMap a Source # ar :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a] Source # arrows :: FinOrdSet a -> [FinOrdMap a] Source #

The category itself : `FinOrdSet`

data FinOrdSet a Source #

FinOrdSet stores the sets which constitutes its objects.

Constructors

FinOrdSet
Fields sets :: [Set a]

Instances

Instances details

Ord a => Eq (FinOrdSet a) Source #
Instance details Defined in Set.FinOrdSet Methods (==) :: FinOrdSet a -> FinOrdSet a -> Bool (/=) :: FinOrdSet a -> FinOrdSet a -> Bool
Show a => Show (FinOrdSet a) Source #
Instance details Defined in Set.FinOrdSet Methods showsPrec :: Int -> FinOrdSet a -> ShowS show :: FinOrdSet a -> String showList :: [FinOrdSet a] -> ShowS
PrettyPrintable a => PrettyPrintable (FinOrdSet a) Source #
Instance details Defined in Set.FinOrdSet Methods pprint :: FinOrdSet a -> String Source #
Ord a => GeneratedFiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a) Source #
Instance details Defined in Set.FinOrdSet Methods genAr :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a] Source # decompose :: FinOrdSet a -> FinOrdMap a -> [FinOrdMap a] Source # genArrows :: FinOrdSet a -> [FinOrdMap a] Source #
Ord a => FiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a) Source #
Instance details Defined in Set.FinOrdSet Methods ob :: FinOrdSet a -> [Set a] Source # identity :: FinOrdSet a -> Set a -> FinOrdMap a Source # ar :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a] Source # arrows :: FinOrdSet a -> [FinOrdMap a] Source #

powerFinOrdSet :: Ord a => Set a -> FinOrdSet a Source #

Returns the FinOrdSet category such that every subset of the set given is an object of the category.

The morphism of the category : FinOrdMap

Instances

The category itself : FinOrdSet

Instances

The morphism of the category : `FinOrdMap`

The category itself : `FinOrdSet`