Define function p:cat represents set concatenation , which concatenates every pair of strings from both sets using racket. We can specify set concatenation as p1 p2 = {u v | u p1 v p2}. Alternatively, we give an inductive specification:

p2 =

p1 p2 = prefix(u, p2) (p'1 p2) if p1={u} p'1.