符号和数值计算

Question

I'm a Computer Science student, on last semester we learned to program in Prolog. Now I'm trying to have fun with it. I'm trying to build a program that given a symbolic/mathematical input it return the result. example:

? solve(2+3+Z+K+5+Z+1, R).
R = 11+2*Z+K or R = 11+Z+K+Z

This is the snippet (for + operation)

solve(X, R) :-
    eval(X, R).

eval(X, X) :- var(X),!.
eval(X, X) :- number(X), !.  
eval(+(X, Y), R) :-
    eval(X, A),
    eval(Y, B),
    add(A, B, R), !.

add(A, B, R) :-
    number(A),
    number(B),
    !,
    R is A + B.
add(A, B, A+B) :-
    var(A); var(B),!.
add(A+X, B, R+X) :-
    number(A),
    number(B),
    var(X),
    !,
    R is A + B.
add(X+A, B, R+X) :-
    number(A),
    number(B),
    var(X),
    !,
    R is A + B.

I have some issue when numbers are separated by many variables, example:

? solve(5+Z+5+4+K+Z+6, R).
FALSE.

or, (not form source code above), if numbers are separated by many variables, they are not "processed", example:

? solve(5+Z+K+7, R).
R = 5+Z+K+7.

Thanks for help, any suggestion or reference will be appreciate.

Answer 1

This is a bit more involved than what your code is doing at the moment. At the end, you seem to want to have a solver for symbolic equations, is that so? So for example, if you type into Wolfram Alfa your equation, 2+3+Z+K+5+Z+1 = R , you get the answer K+2 Z+11 = R .

Similar functionality is provided for example by metafont:

$ mf
This is METAFONT, Version 2.7182818 (TeX Live 2014) (preloaded base=mf)
**\relax

*tracingequations:=tracingonline:=1;

*2+3+a+b+5+a+1=r;
## a=0.5r-0.5b-5.5

*x^2+3=0;
## x^2=-3

... and I guess by every program as Matlab, Mathematica, etc.

In Prolog, for integers, you get something very similar for free if you use library(clpfd) :

?- use_module(library(clpfd)).
true.

?- 2 + 3 + Z + K + Z + 1 #= R.
2*Z+K+ -1*R#= -6.

If you want to program this yourself, you should probably start with deciding how you want to represent your answers: as you see, the three programs demonstrated here choose different approaches. From there, you can either try to see how to get there yourself (see the comment by @lurker), or try to figure out how others have implemented it.