The 4 different AUFs. U, U', U2, and nothing. Use these value constructors together with @all when you need to construct in different ways.

A nonempty list containing all the possible aufs. Could for example be used to generate a random auf or generate all the possible versions of an algorithm

import List.Nonempty


-- They are all there!
List.Nonempty.length all --> 4


-- Generate a random one
List.Nonempty.sample all


import PLL


-- Get all versions of a Y perm
all
    |> List.Nonempty.map (Tuple.pair PLL.Y)
    |> List.Nonempty.map (\(pll, postAuf) ->
        List.Nonempty.map
            (\preAuf -> (preAuf, pll, postAuf))
            all
    )

Get the algorithm that corresponds to the AUF

import Algorithm


toAlgorithm Halfway
-->  Algorithm.build
-->    [ Algorithm.Turn
-->        Algorithm.U
-->        Algorithm.Halfway
-->        Algorithm.Clockwise
-->    ]

Get an algorithm string representation of the AUF

toString Halfway --> "U2"

Attempts to parse an algorithmic representation of an AUF

fromString "U'" --> Ok CounterClockwise


fromString "" --> Ok None


fromString "U B"
--> Err
-->     ("An AUF must be no move or "
-->         ++ "a single turn of the U layer"
-->     )