[Python-ideas] Symbolic expressions (or: partials and closures from the inside out)

[Nathan Rice]

On Fri, Jan 13, 2012 at 8:45 AM, Devin Jeanpierre
<jeanpierreda at gmail.com> wrote:
> On Thu, Jan 12, 2012 at 3:45 PM, Nathan Rice
> <nathan.alexander.rice at gmail.com> wrote:
>> I'm interested in fixing both issues. I believe both issues I've had
>> could be solved by having a robust "symbolic object".  These objects
>> would basically usable like ordinary objects, however upon any
>> attribute access or other form of interaction, the object would
>> basically short circuit the calling function, and return a symbolic
>> object directly to the outer scope.  The symbolic object would behave
>> like a generator function frozen at the point of attribute access, and
>> upon send()-ing (or whatever method), it would behave exactly as if
>> the values sent had been the ones passed in originally (ideally
>> without consuming the generator).
>
> I find the way you've formalized this a bit "weird". It looks like
> you're suggesting adding laziness to Python.
>
> If that's what you want, maybe you should try PyPy and the thunk object space:

While thunk is neat, it doesn't accomplish precisely what I'm
describing in this instance.  When a function starts to run under
thunk, the computations take place as soon as the function gets to the
object inside its scope.

What I'm after is the ability to basically create functions using only
expressions, in a generative manner.  Lambda does accomplish this, but
in an extremely clunky manner... for example:

X = lambda x: x + 1
Y = lambda y: y * 2
Z = lambda z: z % 3

(or XYZ = lambda x: (((x + 1) * 2) % 3)

If I want to perform a second step after this, I need create another
lambda, because they don't chain/aren't generative.

The thing that Elementwise does that is very appealing is that most
operations are generative, so if you have an ElementwiseProxy object
x, x2 = (((x + 1) * 2) % 3) basically does the same thing as the
above, but you can then do x3 = x2 ** 3, and so on until you are ready
to get your results.  Once you have your results, you can use the same
ElementwiseProxy again with different inputs.  It is just a function
generation technique which has some elegant properties.  Having a
native object type designed to facilitate this would let people do a
lot of interesting things, and make things like Elementwise be a lot
more "consistent".  I bet you could do some really neat things by
subclassing such an object as well.

This is certainly not a common programming paradigm, but I think most
people could reap a lot of benefits from it while being oblivious to
its presence.

Nathan