Programming Languages: Concepts and Implementation

6.6 Free or Bound Variables

A variable in an expression in any programming language can appear either (1) bound to a declaration and, therefore, a value, or (2) free, meaning unbound to a declaration and, thus, a denotation or value. The qualification of a variable as free or bound is defined as follows (Friedman, Wand, and Haynes 2001, Definition 1.3.2, p. 29):

• A variable v occurs free in an expression e if and only if there is a reference to v within e that is not bound by any declaration of v within e.

• Avariable v occurs bound in an expression e if and only if there is a reference to v within e that is bound by some declaration of v in e.

For instance, in the expression , the x in the body of the lambda expression occurs bound to the declaration ...