Maintainer	Anders Claesson <anders.claesson@gmail.com>
Safe Haskell	Safe-Inferred

Math.Spe

Contents

The species type synonym
Constructions
Specific species

Description

License : BSD-3

Species lite

Synopsis

The species type synonym

type Spe a c = [a] -> [c]Source

A species is an endofunctor on finite sets with bijections. We approximate this by a function as defined.

data BTree a Source

Binary trees

Constructors

Empty
BNode a (BTree a) (BTree a)

Instances

Eq a => Eq (BTree a)
Show a => Show (BTree a)

Constructions

add :: Spe a b -> Spe a c -> Spe a (Either b c)Source

Species addition

assemble :: [Spe a c] -> Spe a cSource

The sum of a list of species of the same type

mul :: Spe a b -> Spe a c -> Spe a (b, c)Source

Species multiplication

mulL :: Spe a b -> Spe a c -> Spe a (b, c)Source

Ordinal L-species multiplication

prod :: [Spe a b] -> Spe a [b]Source

The product of a list of species

prodL :: [Spe a b] -> Spe a [b]Source

The ordinal product of a list of L-species

power :: Spe a b -> Int -> Spe a [b]Source

The power F^k for species F

powerL :: Spe a b -> Int -> Spe a [b]Source

The ordinal power F^k for L-species F

compose :: Spe [a] b -> Spe a c -> Spe a (b, [c])Source

The composition F(G) of two species F and G

o :: Spe [a] b -> Spe a c -> Spe a (b, [c])Source

This is just a synonym for compose. It is usually used infix.

kDiff :: Int -> Spe (Maybe a) b -> Spe a bSource

The derivative d^k/dX^k F of a species F

diff :: Spe (Maybe a) b -> Spe a bSource

The first derivative

Specific species

set :: Spe a [a]Source

The species of sets

one :: Spe a [a]Source

The species characteristic of the empty set; the identity with respect to species multiplication.

x :: Spe a [a]Source

The singleton species

ofSize :: Spe a c -> Int -> Spe a cSource

f ofSize n is like f on n element sets, but empty otherwise.

nonempty :: Spe a c -> Spe a cSource

No structure on the empty set, but otherwise the same.

kBal :: Int -> Spe a [[a]]Source

The species of ballots with k blocks

bal :: Spe a [[a]]Source

The species of ballots

par :: Spe a [[a]]Source

The species of set partitions

kList :: Int -> Spe a [a]Source

The species of lists (linear orders) with k elements

list :: Spe a [a]Source

The species of lists

cyc :: Spe a [a]Source

The species of cycles

perm :: Spe a [[a]]Source

The species of permutations, where a permutation is a set of cycles.

kSubset :: Int -> Spe a ([a], [a])Source

The species of k element subsets

subset :: Spe a ([a], [a])Source

The species of subsets

btree :: Spe a (BTree a)Source

The species of binary trees