2.0: make Bool !<: Integer?

[jariji]

I find (1, 0) == (true, false) causes confusion. I think it would be clearer and less bug-prone without this feature.

It would be good to list use cases for the current behavior and find good replacements for them.

• sum(bools) could be count(bools)
• mean(bools) could be mean(float, bools)

[jakobnissen]

What kind of confusion does it lead to?

[jariji]

For example, in indexing, the basic property that x == y implies f(x) == f(y) fails.

julia> let ix1 = [true, true]
           ix2 = [1, 1]
           v = [10, 20]
           ix1 == ix2, v[ix1] == v[ix2]
           end
                   
(true, false)

This example is also due to the unfortunate type-based overloading of getindex.

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It also behaves differently from all the other built-in integers - it widens rather than wrapping:

julia> typemax(Int) + 1
-9223372036854775808

julia> typemax(Bool) + 1
2

julia> true + true
2

[jariji]

Fixing getindex is a better solution. Its behavior shouldn't depend on the type of the index argument.

[StefanKarpinski]

I've reopened this because I do think it's worth considering for 2.0 whether Bool should be a subtype of Integer or not. As long as Bool is a number then I think we need to have true == 1 and false == 0 but if we moved Bool out of the numeric hierarchy entirely, then it could be ok to not have those equalities. Then we'd probably need to introduce a UInt1 type that basically behaves like Bool currently does, however, at which point you have to wonder a little if we should have bothered. But like I said, worth keeping an issue open to remind us to consider it. Whether indexing should treat booleans specially is another question; it's certainly a bit strange for Bool to be a kind of number but have indexing with a boolean vector do something completely different. If booleans weren't integers then it would be more justifiable, but I also think that removing boolean indexing might be a good idea too.

[nsajko]

https://en.wikipedia.org/wiki/Boolean_ring

[jariji]

I just meant to write rand() < .36 to get 36% trues and instead wrote rand(Bool) < .36 which gives 50% trues. A MethodError would've caught that.