Remove initial value for reduce()

[ivarne]

It is unclear how a initial value to reduce should be interpreted, as the associativity for reduce is undefined.

see https://groups.google.com/forum/#!topic/julia-users/7PDUKNcBtQA

[lindahua]

I support deprecating the reduce method with v0, and ask people to use foldl instead when they want to fold a sequence from an initial value.

[kmsquire]

I believe the initial value allows one to reduce on an empty iterable, whereas without it, the default value may be unclear.

[JeffBezanson]

I agree the initial value is silly given our definition of reduce. It can throw an error for an empty container.

[stevengj]

I suppose that anyone who really needs a behavior for an empty container can do isempty(x) ? v0 : reduce(+, x). One question is whether this is a gotcha behavior. Also, isempty doesn't currently work for general iterables (though I suppose this could be fixed?), so the lack of a reduce(+, v0, x) method makes this behavior harder to implement in a general way.

[quinnj]

What else is left to do here? Just deprecate the initial value variable? @lindahua

[lindahua]

Currently, when v0 is present, we simply delegate to foldl. We may deprecate this method in favor of foldl. But I don't really have a strong opinion.

[dlfivefifty]

In 0.6, reduce and foldr/foldl are inconsistent for empty vectors:

julia> reduce(+,Float64[])
0.0

julia> foldr(+,Float64[])
ERROR: BoundsError: attempt to access 0-element Array{Float64,1} at index [0]
Stacktrace:
 [1] foldr(::Function, ::Array{Float64,1}) at ./reduce.jl:160

julia> foldl(+,Float64[])
0.0

Is this a separate issue?

[stevengj]

@dlfivefifty, I think that's a separate issue.

[TotalVerb]

v0 is still meaningful when the operation is both associative and commutative, and so I don't think it should be removed.

[simonbyrne]

I think the ship has sailed on this one: v0 now is a keyword argument init, and we define reduce to have implementation dependent associativity.