Function Theory

Abstract

We are always allowed to invent new syntax if we explain the rules for its use. A ready source of new syntax is names (identifiers), and the rules for their use are most easily given by some axioms. We might say something like “let pi = 3.14 ”, meaning that we introduce the name pi and the axiom pi = 3.14. A similar example is “let x be an element such that x: nat”, or more briefly, “let x: nat”. We call pi a constant because the axiom constrains it to one value, and we call x a variable because the axiom allows it many possible values.