Evaluation is the computational process that reduces expressions to values. When performing evaluation, we need not only the expression to be evaluated but also a collection of bindings that map names in the expression to values. This collection of bindings, which is just a finite mapping, is often referred to as an environment (for evaluation). For instance, suppose that we want to evaluate the following expression:
We start with the empty environment ENV0; we evaluate 3.14 to itself and 10.0 * 10.0 to 100.0 under the environment ENV0; we then extend ENV0 to ENV1 with two bindings mapping PI to 3.14 and radius2 to 100.0; we then evaluate PI * radius2 under ENV1 to 3.14 * radius2, then to 3.14 * 100.0, and finally to 314.0, which is the value of the let-expression.