Sym.Permgram

Permutation diagrams, or permutations as monads.

Data types

type Label a = Vector a

The purpose of this data type is to assign labels to the indices of a given permutation.

data Permgram a

A permgram consists of a permutation together with a label for each index of the permutation.

Instances

Applicative Permgram

Defined in Sym.Permgram

Methods

pure :: a -> Permgram a

(<*>) :: Permgram (a -> b) -> Permgram a -> Permgram b

liftA2 :: (a -> b -> c) -> Permgram a -> Permgram b -> Permgram c

(*>) :: Permgram a -> Permgram b -> Permgram b

(<*) :: Permgram a -> Permgram b -> Permgram a

Functor Permgram

Defined in Sym.Permgram

Methods

fmap :: (a -> b) -> Permgram a -> Permgram b

(<$) :: a -> Permgram b -> Permgram a

Monad Permgram

Defined in Sym.Permgram

Methods

(>>=) :: Permgram a -> (a -> Permgram b) -> Permgram b

(>>) :: Permgram a -> Permgram b -> Permgram b

return :: a -> Permgram a

Show a => Show (Permgram a)

Defined in Sym.Permgram

Methods

showsPrec :: Int -> Permgram a -> ShowS

show :: Permgram a -> String

showList :: [Permgram a] -> ShowS

Eq a => Eq (Permgram a)

Defined in Sym.Permgram

Methods

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

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

Ord a => Ord (Permgram a)

Defined in Sym.Permgram

Methods

compare :: Permgram a -> Permgram a -> Ordering

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

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

(>) :: Permgram a -> Permgram a -> Bool

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

max :: Permgram a -> Permgram a -> Permgram a

min :: Permgram a -> Permgram a -> Permgram a

Accessors

perm :: Permgram a -> Perm

The underlying permutation.

label :: Permgram a -> Label a

The assignment of labels to indices.

size :: Permgram a -> Int

The size of a permgram is the size of the underlying permutation.

Construct permgrams

permgram :: Perm -> [a] -> Permgram a

Construct a permgram from an underlying permutation and a list of labels.

inverse :: Permgram a -> Permgram a

The inverse permgram. It's obtained by mirroring the permgram in the x=y diagonal.