CAS command question

[parisse]

I'm really not an expert in the process of parsing. I'm using flex and bison to do that, you can refer to their documentation for much better explanation. In short, the C++ code output from flex reads the strings and cut it into words with a token value according to the rules in the file input_lexer.ll from giac source code (for example "(" has token value T_BEGIN_PAR). Then the C++ code output from bison translate the string into a giac::gen expression by grouping tokens according to the grammar in the file input_parser.yy. During that step, nothing is evaluated.
If you write a program from commandline, for example "f(x):=x^2;", it is parsed to the gen expression f:=x->x^2, then evaled, evaluation stores the expression x->x^2 (of rootnode 'program') into the variable f. After that if you write from commandline "f(a+1)" it is parsed to the giac::gen of(f,a+1), an expression of rootnode 'of' (the command to eval user programs), then it is evaled. During evaluation if a is assigned, it is replaced by the value of a, then + is done, f is replaced by x->x^2, 'program' is called, the argument x is replaced by a+1 (or the value of a+1), x^2 is executed and it returns (a+1)^2. You can see these steps in action with gdb if you compile the native version of giac.