When a function is admitted to the logic, ACL2 tries to ``guess'' what type
of object it returns. This guess is codified as a term that expresses a
property of the value of the function. For
app the term is
(OR (CONSP (APP X Y)) (EQUAL (APP X Y) Y))which says that
appreturns either a cons or its second argument. This formula is added to ACL2's rule base as a
type-prescriptionrule. Later we will discuss how rules are used by the ACL2 theorem prover. The point here is just that when you add a definition, the database of rules is updated, not just by the addition of the definitional axiom, but by several new rules.
You should now return to the Walking Tour.