# Evaluating CLEF expressions¶

Forming expressions is nice, but completely useless unless one can evaluate them by affecting some values to the placeholder and actually do the computation.

Expressions are evaluated with the eval function

eval ( expression , placeholder_1 = value_1, placeholder_2 = value_2, ...)


The evaluation can be :

• complete: when a value has been affected to every placeholder, so the result is not an expression any more, but the result of the computation....
• partial: when some placeholder are still free (no value has been affected to them). The result is another expression where the parts that could be computed have been computed.

## Complete evaluation¶

#include <triqs/clef.hpp>
using namespace triqs::clef;
int main() {
placeholder<1> x_;
placeholder<2> y_;
std::cout << eval(x_ + 2 * y_, x_ = 1, y_ = 2) << std::endl;
std::cout << eval(x_ + 2 * y_, y_ = 2, x_ = 1) << std::endl;
}
---------- Result is -------
5
5


Note that:

• The order of placeholder does not matter in calling eval.
• It is an error to put the same placeholder twice.
• The correct version of eval is found by ADL (Argument Dependent Lookup) in the triqs::clef namespace.

## Partial evaluation¶

The evaluation can also be partial, in which case the compiler replaces the placeholder whose value is provided and rebuild a new expression tree.

Example

auto e1 = x_  + 2*y_;
// return type  ---> value
auto r  = eval( e1 , x_ =1);             // expression   ---> 1 + (2 * y_)
auto e2 = eval( e1 , x_ =x_ + y_);       // expression   ---> ((x_ + y_) + (2 * y_))
auto r  = eval( e2,  x_ = 1, y_ = 2);    // int          ---> 7


During the partial evaluation, all subtrees that can evaluated are evaluated. For example

eval(x_ + f(y_) , y_=1);                 // --> x + f(1)


In this case, the function f is called by eval.