Exercise 4.15. Given a one-argument procedure p and an object a, p is said to ‘‘halt’’ on a if evaluating the expression (p a) returns a value (as opposed to terminating with an error message or running forever). Show that it is impossible to write a procedure halts? that correctly determines whether p halts on a for any procedure p and object a. Use the following reasoning: If you had such a procedure halts?, you could implement the following program:

.. code: scheme

(define (run-forever) (run-forever))

(define (try p) (if (halts? p p) (run-forever) ‘halted))

Now consider evaluating the expression (try try) and show that any possible outcome (either halting or running forever) violates the intended behavior of halts?.