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


-- 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.fromTurnList
-->    [ Algorithm.Turn
-->        Algorithm.U
-->        Algorithm.Halfway
-->        Algorithm.Clockwise
-->    ]

Get the algorithm that corresponds to the AUF, but be able to specify which turnable to use to do the AUF. This is especially relevant for usecases such as an algorithm does an x or z rotation (or wide move) in the algorithm so the AUF is actually executed on a non-U face

import Algorithm


toAlgorithmWithCustomTurnable Algorithm.B Halfway
-->  Algorithm.fromTurnList
-->    [ Algorithm.Turn
-->        Algorithm.B
-->        Algorithm.Halfway
-->        Algorithm.Clockwise
-->    ]

Get an algorithm string representation of the AUF

toString Halfway --> "U2"

Explains an issue that occurred while parsing an AUF

InvalidAUFAlgorithm: The algorithm was parsed correctly but was not either an empty move or a turn of the U face

AlgorithmParsingProblem: The string was not a valid algorithm string and the contained Algorithm.FromStringError has the problem with the string

Describes the error as a string, and is not recommended to be displayed to end-users, but rather to be used in error mesages logged for developer's eyes etc.

case fromString aufString of
    Ok _ ->
        doSomethingOnSuccess


    Err error ->
        logError (debugFromStringError error)

Attempts to parse an algorithmic representation of an AUF

fromString "U'" --> Ok CounterClockwise


fromString "" --> Ok None


fromString "U B"
--> Err (InvalidAUFAlgorithm "U B")

Add a pre and postAUF to an algorithm outputting the resulting algorithm. This also supports algorithms that change orientation. So for example this would do the AUF on R instead of on U for the postAUF

import Algorithm


addToAlgorithm
    ( Halfway, Clockwise )
    (Algorithm.fromTurnList [ Algorithm.Turn Algorithm.Z Algorithm.OneQuarter Algorithm.Clockwise ])


--> Algorithm.fromTurnList
-->     [ Algorithm.Turn Algorithm.U Algorithm.Halfway Algorithm.Clockwise
-->     , Algorithm.Turn Algorithm.Z Algorithm.OneQuarter Algorithm.Clockwise
-->     , Algorithm.Turn Algorithm.R Algorithm.OneQuarter Algorithm.Clockwise
-->     ]