Applied mathematical modeling

[hurufu]

In natural sciences formulas are often quite complex and they are hard to describe using regular Prolog syntax (is/2) and even with CLP(ℤ) in many cases you have to juggle dozens of variables at a time. Post #2576 reminded me about my old forgotten project that I did as an assignment at the university. The idea was the following, instead of writing:

p_air(1007.8).
t_air(17.4).
heat_transfer_coeficient(X) :-
    p_air(P_air),
    t_air(T_air),
    X is 0.013 * P_air - 0.04 * T_air - 0.503.

And then trying not to get lost in a sea of different variables, what if that could be written as:

t_air := 17.4.
p_air := 1007.8.
heat_transfer_coeficient := 0.013 * p_air - 0.04 * t_air - 0.503.

So all variables would've been implicit and then write code that will try to piece together complex formula and allocate all variables as needed. Here is a gist with a real world formula: https://gist.github.com/hurufu/5f6ba83290837fc410f8e0bf79a3b094.
All in all I somehow managed to pass that assignment by implementing it in Perl :), but I also have 3 different implementations in Prolog of that idea and they are all equally bad (not even fully working or extremely slow), so I don't wish to share any of them, but what do you think about notation per-se? Also I very like Iverson bracket, and it is very useful for that kind of notation too.

[hurufu]

Such hypothetical system should be reasonably smart:

1. It should fully utilize backtracking to find all possible concrete formulas that describe your desired property
2. For example if value isn't available (e.g. mass in my gist) then it should only try formulas that don't use mass in this case it should assume average body surface s_body if mass of the human isn't known.
3. It should compute all values only once
4. It should report inconsistencies via exceptions
5. Bonus constraints, eg. sun elevation should never be larger then 90°.

[hurufu]

Similar idea to this one is already implemented https://github.com/JanWielemaker/GarpSim/blob/master/predator.pl, and way better then me. Very cool.