Kata

The purpose of this Kata is to develop an arithmetic expression evaluator.

Your task consists in implementing the methods eval and toString within the createOperator function.

Values as Terminal Expressions

Key to the understanding of the solution of this Kata is the realization that all expressions can be reduced to a value, and a value is just an expression that cannot be reduced any further. That is, if we evaluate a value expression, we get the value itself.

Somewhat like this:

function Value(value){
    this.value = value || 0;
}

Value.prototype.eval = function(){ return this; };
Value.prototype.valueOf = function(){ return this.value.valueOf(); };
Value.prototype.toString = function(){ return this.value.toString(); };

For this Kata the Value type will be preloaded in your environment.

Compound Expressions

Now, we can also define more complex expressions by combining values with operators, like 3 * 5 or 6 + 2

In this Kata we have provided a function createOperator that is capable of creating different kinds of operators. An operator is a type of expression. When they are used, they create new compound expression. You can see some predefined operators in the initial Kata's testing code.

Examples of compound expressions.

var sumExpr = new Add(new Value(3), new Value(5)); //3 + 5
var mulExpr = new Mul(new Value(6), new Value(2)); //6 * 2

We can even define more complex expressions like 3 * 5 + 6 / 2

var a = new Mul(new Value(3), new Value(5)); 
var b = new Div(new Value(6), new Value(2)); 
var c = new Add(a,b); 

Since all expressions can be evaluated (meaning reduced) to a single value, we can see now that our operator expressions are lacking two important features: the functions eval and toString.

• eval: should reduce an expression to a Value
• toString: should generate a string with a human-readable representation of the expression.

For instance

c.eval();     //should return Value(18)
c.toString(); //should return the string '3 * 5 + 6 / 2'

Can you implement this missing functionality for the operator classes?

Other Considerations

The tests will only count on binary operators (i.e. +,-,*,/,^), and it is assumed that every operator must act on at least two expressions.