Set.FinOrdSet

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

The morphism of the category : FinOrdMap

data FinOrdMap a

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

Eq a => Eq (FinOrdMap a)

Defined in Set.FinOrdSet

Methods

(==) :: FinOrdMap a -> FinOrdMap a -> Bool

(/=) :: FinOrdMap a -> FinOrdMap a -> Bool

Show a => Show (FinOrdMap a)

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)

Defined in Set.FinOrdSet

Methods

pprint :: FinOrdMap a -> String

Ord a => Morphism (FinOrdMap a) (Set a)

Defined in Set.FinOrdSet

Methods

(@) :: FinOrdMap a -> FinOrdMap a -> FinOrdMap a

source :: FinOrdMap a -> Set a

target :: FinOrdMap a -> Set a

Ord a => GeneratedFiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a)

Defined in Set.FinOrdSet

Methods

genAr :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a]

decompose :: FinOrdSet a -> FinOrdMap a -> [FinOrdMap a]

genArrows :: FinOrdSet a -> [FinOrdMap a]

Ord a => FiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a)

Defined in Set.FinOrdSet

Methods

ob :: FinOrdSet a -> [Set a]

identity :: FinOrdSet a -> Set a -> FinOrdMap a

ar :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a]

arrows :: FinOrdSet a -> [FinOrdMap a]

The category itself : FinOrdSet

data FinOrdSet a

FinOrdSet stores the sets which constitutes its objects.

Constructors

FinOrdSet

Fields

• sets :: [Set a]

Instances

Ord a => Eq (FinOrdSet a)

Defined in Set.FinOrdSet

Methods

(==) :: FinOrdSet a -> FinOrdSet a -> Bool

(/=) :: FinOrdSet a -> FinOrdSet a -> Bool

Show a => Show (FinOrdSet a)

Defined in Set.FinOrdSet

Methods

showsPrec :: Int -> FinOrdSet a -> ShowS

show :: FinOrdSet a -> String

showList :: [FinOrdSet a] -> ShowS

PrettyPrintable a => PrettyPrintable (FinOrdSet a)

Defined in Set.FinOrdSet

Methods

pprint :: FinOrdSet a -> String

Ord a => GeneratedFiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a)

Defined in Set.FinOrdSet

Methods

genAr :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a]

decompose :: FinOrdSet a -> FinOrdMap a -> [FinOrdMap a]

genArrows :: FinOrdSet a -> [FinOrdMap a]

Ord a => FiniteCategory (FinOrdSet a) (FinOrdMap a) (Set a)

Defined in Set.FinOrdSet

Methods

ob :: FinOrdSet a -> [Set a]

identity :: FinOrdSet a -> Set a -> FinOrdMap a

ar :: FinOrdSet a -> Set a -> Set a -> [FinOrdMap a]

arrows :: FinOrdSet a -> [FinOrdMap a]

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

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