This merits some discussion:

Do we need both Tensor and Scalar?

This was briefly discussed in email thread around May 3 2008.

On Sat, May 03, 2008 at 10:29:39PM -0400, Olivier Breuleux wrote:
> They are not semantically equivalent. Tensor is a container, scalars are
> the things tensors contain. Scalar is different from Tensor in the same
> sense that int is different from vector. Typically, you won't
> really see the difference in Python code because of all the overloading
> and dynamic type dispatching, but the C code for both cases is just not
> the same at all.
>
> The distinction between 0-d tensor and scalar is difficult to gauge in a
> dynamically typed language or a language with overloading, but theano is
> neither.
>
> I agree that the Scalar/Tensor division is a bit awkward right now but I
> think we should just make as_tensor and as_scalar instantiate conversion
> ops when needed.

Be all this as it may, I understand that the code is syntactically quite close
to working if we just replace the Scalar class with the Tensor one. The catch I
anticipate would be having to rename the c_code() functions of Scalar Op
classes, to c_code_elem() or something, so that the broadcasting mechanism can
automatically infer the c_code() implementation which would work on entire
tensors. What else would be necessary?

This would be a win because
- it would eliminate confusion between scalar and 0-d tensors,
- also the confusion between scalar ops and broadcasted scalar ops
- it would cut a file from the project
- the generated C would be just as fast


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The decision at the time was to keep both, and encourage users to use Tensor results. Scalars were to be used internally as necessary.