Arrows for deep application. Most of these methods could be defined using arr, but arr is not definable for some types. If your DeepArrow instance has arr, you might want to use these implementations

    idA      = arr id
    fstA     = arr fst
    dupA     = arr (\ x -> (x,x))
    sndA     = arr snd
    funF     = arr (\ (f,b) -> \ c -> (f c, b))
    funS     = arr (\ (a,f) -> \ c -> (a, f c))
    funR     = arr flip
    curryA   = arr curry
    uncurryA = arr uncurry
    swapA    = arr (\ (a,b) -> (b,a))
    lAssocA  = arr (\ (a,(b,c)) -> ((a,b),c))
    rAssocA  = arr (\ ((a,b),c) -> (a,(b,c)))

If your DeepArrow instance does not have arr, you'll have to come up with other definitions. In any case, I recommend the following definitions, which mirror Arrow defaults while avoiding arr. Be sure also to define arr or pure to yield an error message (rather than ping-ponging infinitely between them via the Arrow default definitions).

    second f = swapA >>> first f >>> swapA
    f &&& g  = dupA  >>> f *** g

In a few cases, there are default methods, as noted below. The defaults do not use arr.