On Mon, Mar 10, 2014 at 07:02:40AM -0700, Niles Johnson wrote:
> I would prefer not to use "mathematical context" or "semantic" when trying
> to read code (for debugging, or for learning). My reason for this is that
> I don't believe the computer "knows" mathematics, so I wouldn't use my
> mathematical knowledge to try to guess what the code is doing. Using
> mathematical or other semantic information is useful to guess what
> developers were thinking when they wrote the code. But (especially when
> debugging) I don't assume that every developer knows what I know.
> Therefore I will want a more reliable way to determine where/how methods
> are implemented.
Hmm, as is, the argument is a bit general, and I believe it would rule
out the very principle underlying categories :-) So let's make this
more concrete. Here is the kind of knowledge we are speaking about:
- a finite field is a ring, but also a finite set, etc.
- a unital magma that is associative is a unital semigroup, that is a monoid
- a finite division ring is a field
Sage "knows" about those, either because the information is directly
hardcoded (e.g. a unital semigroup is a monoid, a finite division ring
is a field), or deduced iteratively from such. The role of categories
is to make the code manageable by using more deductions to reduce the
amount of information you need to hardcode. Similar strategies have
been successfully used in one form or the other in GAP, Magma, Axiom,
MuPAD, and since we are getting bigger than those, we are exploring
further.
As an analogy, in plain Python, when one creates a class one does not
hard code all the super classes. Only the direct ones. And as in plain
Python, the easiest way to recover where/how a method is implemented
is to use introspection (rather than exploring the hierarchy by
looking at the code).
This being said, where would you put the threshold between appropriate
and overboard use of "math knowledge"?
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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