# Principles of Evaluation

The fundamental operation that the Wolfram Language performs is *evaluation*. Whenever you enter an expression, the Wolfram Language evaluates the expression, then returns the result.

Evaluation in the Wolfram Language works by applying a sequence of definitions. The definitions can either be ones you explicitly entered, or ones that are built into the Wolfram Language.

Thus, for example, the Wolfram Language evaluates the expression 6+7 using a built‐in procedure for adding integers. Similarly, the Wolfram Language evaluates the algebraic expression x-3x+1 using a built‐in simplification procedure. If you had made the definition x=5, then the Wolfram Language would use this definition to reduce x-3x+1 to -9.

The two most central concepts in the Wolfram Language are probably *expressions* and *evaluation*. "Expressions" discusses how all the different kinds of objects that the Wolfram Language handles are represented in a uniform way using expressions. This tutorial describes how all the operations that the Wolfram Language can perform can also be viewed in a uniform way as examples of evaluation.

Some interpretations of evaluation.

The Wolfram Language is an *infinite evaluation* system. When you enter an expression, the Wolfram Language will keep on using definitions it knows until it gets a result to which no definitions apply.

In[3]:= |

When the Wolfram Language has used all the definitions it knows, it gives whatever expression it has obtained as the result. Sometimes the result may be an object such as a number. But usually the result is an expression in which some objects are represented in a symbolic form.

The Wolfram Language follows the principle of applying definitions until the result it gets no longer changes. This means that if you take the final result that the Wolfram Language gives, and enter it as Wolfram Language input, you will get back the same result again. (There are some subtle cases discussed in "Controlling Infinite Evaluation" in which this does not occur.)

At any given time, the Wolfram Language can only use those definitions that it knows at that time. If you add more definitions later, however, the Wolfram Language will be able to use these. The results you get from the Wolfram Language may change in this case.

The simplest examples of evaluation involve using definitions such as f[x_]=x^2 which transform one expression directly into another. But evaluation is also the process used to execute programs written in the Wolfram Language. Thus, for example, if you have a procedure consisting of a sequence of Wolfram Language expressions, some perhaps representing conditionals and loops, the execution of this procedure corresponds to the evaluation of these expressions. Sometimes the evaluation process may involve evaluating a particular expression several times, as in a loop.