Parametric Specification

In Section 2 we will define “lists of E” in terms of the least fixed point specification$$E*:: = 1 + E \times E*$$ (i.e., “a list is the empty list (1 = }Λ}) or an element of E followed by a list). But the parenthetical explication just given works only in Set, whereas the specification works in any category in which polynomial functors have least fixed points. In this sense E is a “parameter” for the “lists-of-” specifier. The specific parameter E may itself arise from another data type specification and may live in a category of arbitrary complexity subject to the technical needs of semantics.