APPmust have several properties to be admitted to the logic as a new axiom
The key property a recursive definition must have is that the recursion terminate. This, along with some syntactic criteria, ensures us that there exists a function satisfying the definition.
Termination must be proved before the definition is admitted. This is done in general by finding a measure of the arguments of the function and a well-founded relation such that the arguments ``get smaller'' every time a recursive branch is taken.
app the measure is the ``size'' of the first argument,
as determined by the primitive function
acl2-count . The
well-founded relation used in this example is
, which is the standard ordering on the ordinals less than
``epsilon naught.'' These particular choices for
app were made
``automatically'' by ACL2. But they are in fact determined by
various ``default'' settings. The user of ACL2 can change the
defaults or specify a ``hint'' to the
defun command to
specify the measure and relation.
You should now return to the Walking Tour.