From Haskell's documentation:

The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

Originally based on fatho's labyrinth project.

example 1

Given a string a and a list of integers, test each integer b. If b is odd, append it to a, and multiply it by 10 inside the list.

a = ""
b = [ 1, 2, 3, 4 ]


func : Int -> String -> ( Int, String )
func b a =
    if b % 2 == 0 then
        -- even
        ( b, a )
    else
        -- odd
        ( b * 10, a ++ "," ++ toString b )


mapAccumL func "" [ 1, 2, 3, 4 ]
    -- == `( [ 10, 2, 30, 4], ",1,3" )`.

example 2

Given a string a and a list of integers, test each integer b. If b is odd, append it to a, and remove it from the list.

a = ""
b = [ 1, 2, 3, 4 ]


func : Int -> String -> ( Maybe Int, String )
func b a =
    if b % 2 == 0 then
        -- even
        ( Just b, a )
    else
        -- odd
        ( Nothing, a ++ "," ++ toString b )


justSomethings : (List (Maybe a), b) -> (List a, b)
justSomethings =
    (\( list, b ) -> ( list |> Maybe.Extra.values, b ))


mapAccumL func "" [ 1, 2, 3, 4 ]
    |> justSomethings
    -- == `( [ 2, 4], ",1,3" )`.

example 3

Given a string a and a list of integers, test a and each integer b. If b is odd, append it to a, and remove it from the list. If b is 42, the final a must equal towel!, and no further bs should be removed from the list.

a = ""
b = [ 1, 2, 3, 4 ]


func : Int -> String -> ( Maybe Int, String )
func b a =
    if a == "towel!" then
        ( Just b, a )
    else if b == 42 then
        ( Just b, "towel!" )
    else if b % 2 == 0 then
        -- even
        ( Just b, a )
    else
        -- odd
        ( Nothing, a ++ "," ++ toString b )


justSomethings : (List (Maybe a), b) -> (List a, b)
justSomethings =
    (\( list, b ) -> ( list |> Maybe.Extra.values, b ))


mapAccumL func "" [ 1, 2, 3, 42, 5, 6, 7 ]
    |> justSomethings
    -- == `( [ 2, 42, 5, 6, 7 ], "towel!" )`