Fixing Elm's List folds

ListFolds.elm

module ListFolds exposing (..)

{-| Alternative implementations of List.foldl and List.foldr
    
    -- this will add the `fold` and `foldBack` functions to the List module
    import ListFolds as List
    
    List.fold (++) "" [ "Hello", " ", "World", "!" ] == "Hello World!"
    
-}


{-| Fold a list from the left, properly.

    List.fold (++) "" [ "Hello", " ", "World", "!" ] == "Hello World!"

    -- Compare to built-in `foldl`:
    List.foldl (++) "" [ "Hello", " ", "World", "!" ] == "!World Hello"

    -- What you actually have to do to use built-in: flip argument order
    List.foldl (\a b -> b ++ a) "" [ "Hello", " ", "World", "!" ] == "Hello World!"

-}
fold : (b -> a -> b) -> b -> List a -> b
fold f b list =
    List.foldl (flip f) b list


{-| Right fold with visual argument order

    -- direction of processing: 4<----------3<----------2<-----------1<
    List.foldBack (::) [ "Option 3", "Option 2", "Option 1" ] [ "Select an option" ]
      == [ "Select an option", "Option 1", "Option 2", "Option 3" ]

    --                                  --------------------------------v
    -- Compare to built-in `foldr`: >1-/       4<----------3<-----------2
    List.foldr (::) [ "Select an option" ] [ "Option 3", "Option 2", "Option 1" ]
      == [ "Select an option", "Option 1", "Option 2", "Option 3" ]

-}
foldBack : (a -> b -> b) -> List a -> b -> b
foldBack f list b =
    List.foldr f b list