Predicates

Abstract

In section 1.3, a state was defined as a function from identifiers to the set of values {T, F}. The notion of a state is now extended to allow identifiers to be associated with other values, e.g. integers, sequences of characters, and sets. The notion of a proposition will then be generalized in two ways:

• 1. In a proposition, an identifier may be replaced by any expression (e.g. x⩽y) that has the value T or F.

• 2. The quantifiers E, meaning “there exists”; A, meaning “for all”; and N, meaning “number of”, are introduced. This requires an explanation of the notions of free identifier and bound identifier and a careful discussion of scope of identifiers in expressions.