A symbol is an atomic datum with no internal structure. Whereas a variable is given meaning by substitution, a symbol is given meaning by a family of operations indexed by symbols. A symbol is therefore just a name, or index, for an instance of a family of operations. Many different interpretations may be given to symbols according to the operations we choose to consider, giving rise to concepts such as fluid binding, dynamic classification, mutable storage, and communication channels. With each symbol is associated a type whose interpretation depends on the particular application. The type of a symbol influences the type of its associated operations under each interpretation. For example, in the case of mutable storage, the type of symbol constrains the contents of the cell named by that symbol to values of that type. It is important to bear in mind that a symbol is not a value of its associated type, but only a constraint on how that symbol may be interpreted by the operations associated with it.

In this chapter we consider two constructs for computing with symbols. The first is a means of declaring new symbols for use within a specified scope. The expression v a:ρ in e introduces a “new” symbol a with associated type ρ for use within e. The declared symbol a is new in the sense that it is bound by the declaration within e, and so may be renamed at will to ensure that it differs from any finite set of active symbols.