ELynx.Data.Tree.Subset

Creation date: Fri Dec 13 11:02:43 2019.

Documentation

data Subset a

A Subset is a set of elements of type a. For example, on phylogenetic trees, a Subset is a set of leaves. In this case, a Subset is induced, for example, by a node on the (rooted) tree. The Subsets of leaf nodes are singletons. The Subsets of the root node is the set of all leaves. Subsets are the building blocks of partitions. Each branch on the tree induces a bipartition, or a pair of Subsets, see Bipartition. Multifurcations induce multipartitions, see Multipartition.

Internally, a subset is just an Set, since the order of elements within the subset is not important, but the uniqueness of elements is.

Instances

Foldable Subset

Defined in ELynx.Data.Tree.Subset

Methods

fold :: Monoid m => Subset m -> m

foldMap :: Monoid m => (a -> m) -> Subset a -> m

foldr :: (a -> b -> b) -> b -> Subset a -> b

foldr' :: (a -> b -> b) -> b -> Subset a -> b

foldl :: (b -> a -> b) -> b -> Subset a -> b

foldl' :: (b -> a -> b) -> b -> Subset a -> b

foldr1 :: (a -> a -> a) -> Subset a -> a

foldl1 :: (a -> a -> a) -> Subset a -> a

toList :: Subset a -> [a]

null :: Subset a -> Bool

length :: Subset a -> Int

elem :: Eq a => a -> Subset a -> Bool

maximum :: Ord a => Subset a -> a

minimum :: Ord a => Subset a -> a

sum :: Num a => Subset a -> a

product :: Num a => Subset a -> a

Eq a => Eq (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

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

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

Ord a => Ord (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

compare :: Subset a -> Subset a -> Ordering

(<) :: Subset a -> Subset a -> Bool

(<=) :: Subset a -> Subset a -> Bool

(>) :: Subset a -> Subset a -> Bool

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

max :: Subset a -> Subset a -> Subset a

min :: Subset a -> Subset a -> Subset a

(Read a, Ord a) => Read (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

readsPrec :: Int -> ReadS (Subset a)

readList :: ReadS [Subset a]

readPrec :: ReadPrec (Subset a)

readListPrec :: ReadPrec [Subset a]

Show a => Show (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

showsPrec :: Int -> Subset a -> ShowS

show :: Subset a -> String

showList :: [Subset a] -> ShowS

Ord a => Semigroup (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

(<>) :: Subset a -> Subset a -> Subset a

sconcat :: NonEmpty (Subset a) -> Subset a

stimes :: Integral b => b -> Subset a -> Subset a

Ord a => Monoid (Subset a)

Defined in ELynx.Data.Tree.Subset

Methods

mempty :: Subset a

mappend :: Subset a -> Subset a -> Subset a

mconcat :: [Subset a] -> Subset a

sfromset :: Set a -> Subset a

Create a subset from a set.

sfromlist :: Ord a => [a] -> Subset a

Create a subset from a list. Throws an error if duplicate elements are present in the list.

smap :: Ord b => (a -> b) -> Subset a -> Subset b

Map a function over all elements in a subset.

snull :: Subset a -> Bool

Is the subset empty?

sempty :: Subset a

The empty subset.

ssingleton :: a -> Subset a

A subset with one element.

sunion :: Ord a => Subset a -> Subset a -> Subset a

Unite two subsets.

sunions :: Ord a => [Subset a] -> Subset a

Unite a list of subsets.

sdifference :: Ord a => Subset a -> Subset a -> Subset a

Difference of two subsets.

sintersection :: Ord a => Subset a -> Subset a -> Subset a

Intersection of two subsets.

sdisjoint :: Ord a => Subset a -> Subset a -> Bool

Are two subsets disjoint?

smember :: Ord a => a -> Subset a -> Bool

Check if an element is member of a subset.

sshow :: (a -> String) -> Subset a -> String

Show the elements of a subset in a human readable way.