In this assignment, you add three methods to Expr and implement them in each expression subclass. Don't forget tests, of course.

1. Implement interp, which returns an int for the value of an expression.

• • The value of a number is the number
  • The value of an addition expression is the sum of the subexpression values
  • The value of a multiplication expression is the product of the subexpression values
  • A variable has no value, so interp for a variable should throw a std::runtime_error exception

To throw an exception, use #include <stdexcept> and

throw std::runtime_error("message");

The message text is up to you.

To write a test that checks whether an exception is raised, use CHECK_THROWS_WITH:

CHECK_THROWS_WITH( (new Var("x"))->interp(), "no value for variable" );

But the second string should be the error message that you chose to use with throw.

Note: An interp method should never change its object. In general in this class, only the constructor for an object should change the object’s fields. Otherwise, assign only to new local variables within a method.

2. Implement has_variable, which returns a bool. The result should be true if the expression is a variable or contains a variable, false otherwise.

3. Eventually, our interpreter will need to handle function calls, and we'll do that (at first, anyway) in the same way you worked with functions in Algebra class. If f is defined as f(x) = x + 7, then you can simplify f(10) by starting with x+7 and replacing each x with 10 to get 10+7. You could even simplify f(y) by starting with x+7 and replacing each x with y. to get y+7. Were not doing functions, yet, but we can implement the substitution part.

Implement subst, which takes two arguments: a std::string and an Expr*. The result is an Expr*. Everywhere that the expression (whose subst method is called) contains a variable matching the string, the result Expr* should have the given replacement, instead.

Here's one test, although it's possible that you have different class names:

CHECK( (new Add(new Var("x"), new Num(7)))
       ->subst("x", new Var("y"))
       ->equals(new Add(new Var("y"), new Num(7))) );

Your subst should not use has_variable, because it's not needed.

Note: The general rule against assigning to fields still applies here. The subst method should never change its object by assigning to fields. It should return a new object without changing the current object.