make prod(::Vector{Bool})::Int?

[StefanKarpinski]

Came up over here: #24396 (comment). We already have sum([false,false,false]) === 0 but we have prod([true,true,true]) === true. I understand the logic that the value of the product can only be true or false so it might as well be of type Bool, but I think it makes sense that sum and prod return the same type; if someone really wants a Bool result, they can always use all.

[ararslan]

Personally I like the idea of deprecating sum and prod on collections with Bool elements in favor of count and all, respectively. (Though it may only make sense to do that if we didn't have Bool <: Integer, otherwise that would be a bit inconsistent.) Regardless, +1 for the proposed change here. Never mind, Jeff has a good point.

[StefanKarpinski]

I don't think it's justifiable not to allow sum and prod on booleans unless they're made non-numbers – which we've already decided is too annoying and disruptive.

[JeffBezanson]

-1. The same difference exists for the scalar operation:

julia> false+false
0

julia> false*false
false

I don't see much reason to introduce a different result type just because a reduction is being done.

[StefanKarpinski]

Based on triage discussion, we seem to be at a local optimum, with booleans behaving as strong zero and strong one for multiplication whereas as long as booleans are numbers, summing them is useful. FWIW, Knuth is very pro strong zero as a concept: https://arxiv.org/abs/math/9205211.