Is the list is guaranteed non-empty? Do you want to enforce that at the type level (compile time), or "fail" at runtime when it is?
runtime error
You should probably be a bit more explicit about what you mean by "concurrently". Do you know in advance that the list length is sufficiently short to make it reasonable to immediately fork an async thread for each?
the list can have 100000 images of 1 million of pixels, and it is not that short per image.
Is that at least one? O(1) per core, ... hundreds, tens of thousands?
for now I have 100000 images to merge on 24 core.
Do you have space constraints on the number of not yet folded together cubes that can be in memory at the same time?
On my computer I have 256 Go of memory enought to load all the images first, but I need to target smaller computer. the biggest stack that I processed was 60Go for a final cube of 2000x2000x2000 of int32. but most of the time it will be around 1000x1000x1000 of int32
Is it actually a Monoid (has an identity), or only a Semigroup?
I can have a identiy which is an empty cube.
Which is the (more) expensive operation, computing a cube or merging two already computed cubes?
computing the cube is constant in time for a given image size. merging cube is slower and slower with time, since the cube grows from merge to merge.
That is still ultimately order preserving (but associative): (a1 + a2) + (a3 + a4). Is the semigroup also commutative, would: (a2 + a4) + (a1 + a3) also work?
yes Fred