What do we call this (new?) higher-order function?

Question

I am trying to name what I think is a new idea for a higher-order function. To the important part, here is the code in Python and Haskell to demonstrate the concept, which will

Answer 1

Hmm... a counterpoint.

(`ap` tail) . zipWith

doesn't deserve a name.

BTW, quicksilver says:

 zip`ap`tail

The Aztec god of consecutive numbers

Answer 2

Here's another implementation for Python which works if l is a generator too

import itertools as it

def apply_pairwise(f, l):
    left, right = it.tee(l)
    next(right)
    return it.starmap(f, it.izip(left, right))

I think apply_pairwise is a better name

Answer 3

BinaryOperate or BinaryMerge

Answer 4

Using Mathematica

Plus @@@ Partition[{0, 1, 2, 3}, 2, 1] or either of these more verbose alternatives

Apply[Plus, Partition[{0, 1, 2, 3}, 2, 1], {1}]
Map[Apply[Plus, #] &, Partition[{0, 1, 2, 3}, 2, 1]]

I have used and enjoyed this higher order function in many languages but I have enjoyed it the most in Mathematica; it seems succinct and flexible broken down into Partition and Apply with levelspec option.

Answer 5

in C++ Standard Template Library, it is called adjacent_difference (though the operator can be any operation, not just subtraction)

Answer 6

I vote for smearWith or smudgeWith because it's like you are smearing/smudging the operation across the list.