[2/24] rule based inference engine (engine itself)

[2/24] rule based inference engine (engine itself)

Here I introduce new inference engine which I'm going to use for assumptions.

When I started to play with assumptions ~ half a year ago, the firsts thing
I've noted was that:

- inference itself was intermixed with object creation etc (it was not possible
  to use logic stuff as separate subsystem)

- the rules put into assumptions.py and the code was just wrong -- in the end
  of this patch series you'll see how much tests I have to change.

So I've started to work on my own inference engine first.

Initially I prototyped a system where one could define rules of form

    a -> b  (where a & b are atoms -- e.g. integer=T -> rational=T )

and tried to hook this engine into assumptions.py, but I failed because as it
turned out, inference engine that could satisfy all our tests have to be
capable to process joined rules:

    a & b -> c  (e.g. real & positive -> !negative)

Here I give up the first time:

http://groups.google.com/group/sympy/browse_thread/thread/c436fd9cfc701138

Recently I refreshed my work and put some time into studying the topic -- its a
whole new world -- good inference engine is an art, and there are even family
of software programs which heart is inference engine (I'm talking about expert systems) ...

In short, there is a classic algorithm called RETE for this stuff

http://en.wikipedia.org/wiki/Rete_algorithm

And what is done here is a very simplistic apprach with some ideas borrowed
from there -- I could not find ready stuff for this task :(

The main design goals were:

1. to be correct, and
2. to be fast at runtime

I think 1 is acheived, and 2 is so-so (but much better than we had before), and
there is a room for improvements.

Signed-off-by: Kirill Smelkov <kirr@landau.phys.spbu.ru>
Signed-off-by: Ondrej Certik <ondrej@certik.cz>
Signed-off-by: Mateusz Paprocki <mattpap@gmail.com>