SWI Prolog - Simplifying expressions

Question

I want to write a procedure simplify (E, E1) which is able to simplify expressions. I have only one operation +, and symbolic and numeric operands. Examples of this procedur

Answer 1

Well, this is obviously a homework question, but here's an SWI Prolog program anyway:

:- op(500, xfy, user:(+)).

simplify(Expr, Simplified) :-
  split(Expr, Syms0, Nums0),
  sumlist(Nums0, Nums),
  append(Syms0, [Nums], Syms),
  unparse(Syms, Simplified).

split(X+Y, [X|Syms], Nums) :- atom(X), split(Y, Syms, Nums).
split(X+Y, Syms, [X|Nums]) :- integer(X), split(Y, Syms, Nums).
split(X, [X], [])          :- atom(X).
split(X, [], [X])          :- integer(X).

unparse([X], X).
unparse([X|Xs], X+Y)       :- unparse(Xs, Y).

:- simplify(a+1+b+5, a+b+6).
:- simplify(1+b+9+a+5+c, b+a+c+15).