`prod(())` shouldn't return `1`

[jariji]

julia> prod(())
1

julia> prod([])
ERROR: MethodError: no method matching one(::Type{Any})

For () it's guessing that the output type is Int, which is bad. I think this should throw an error.

[mbauman]

Theoretically I agree, but pragmatically this method is often used for size tuples. This change would be surprisingly breaking for precisely that reason.

[jariji]

Ok then maybe a breaking change for 2.0.

[barucden]

@mbauman

this method is often used for size tuples

As in prod(size(A))? Maybe Julia should provide a function for getting the number of elements in a collection then?

This issue is, IMHO, quite similar to #55379 in that Julia returns an (arbitrary) value for an empty collection.

[mbauman]

I dunno, someone could try it and see just how breaking it is, but unlike #55379, this isn't giving wildly wrong answers. That tends to happen when we guess at init — this is guessing at the empty case.

[DNF2]

As in prod(size(A))? Maybe Julia should provide a function for getting the number of elements in a collection then?

That's what length(A) does.

[barucden]

Indeed! I never realized length does this. I guess I always assumed it returned the number of elements along the first dimension (influenced by python's len perhaps).

What's the motivation for prod(size(A)) then? People use it.

Is it true that any prod(size(A)) can be replaced by length(A)?

I believe the pattern prod(size(A)[c:d] cannot be replaced by length, but size(A)[c:d] should never return (), unless c>d, which seems like a very marginal case.

[nsajko]

For any empty collection c, isone(prod(c)) must hold, right? Given that, returning 1 doesn't seem that bad. It's not ideal for element types that don't subtype Number, though.

[barucden]

Oh, I see now that I completely missed what OP was reporting! My apologies, I'll hide my previous comments. Let me make it clear for any other confused contributors.

The issue is not returning the multiplicative identity for an empty collection. That is the standard definition in math. And programming languages (R, Common Lisp, numpy) follow that definition, including Julia:

julia> prod(Int[])
1

The documentation for prod says that:

The value returned for empty itr can be specified by init. It must be the multiplicative identity (i.e. one) as it is unspecified whether init is used for non-empty collections.

The issue is guessing what the multiplicative identity is for an empty tuple. We do not guess it for Any[], but we guess it for Tuple(Any[]).

julia> A = []
Any[]

julia> prod(A)
ERROR: MethodError: no method matching one(::Type{Any})

julia> prod(Tuple(A))
1