COSC 5010. Formalizing the JVM in ACL2. Spring 2004
Examination
Due Thursday 1 April 2004
•Answer these questions individually. You may only use the book, the
homework, the class notes, the class website, and the ACL2 documen-
tation. You may ask for help only from the instructor.
•Email your solutions to me at cowles@uwyo.edu.
•The subject line should identify the problem set, i.e. Exam Question 2.
•The body of the message should be a Lisp readable file in simple ascii
text format.
•The first few lines of the body should contain your name.
Exam Question 2. The Meyer and Ritchie version (1967) of Ackermann’s
function may be defined recursively on the nonnegative integers by
ack-mr(x,y) <== if y=0 then 1
else if x=0 and y=1 then 2
else if x=0 and y>1 then y+2
else ack-mr( x-1, ack-mr(x,y-1) ).
1. Define ack-mr in ACL2.
2. Prove each of the following in ACL2, for all nonegative integers x
and y.
(a) ack-mr(x,0) = 1.
(b) ack-mr(x,1) = 2.
(c) ack-mr(x,2) = 4.
(d) ack-mr(0,y) = if y=0 then 1
else if y=1 then 2
else 2+y.
(e) ack-mr(1,y) = if y=0 then 1
else 2*y.
(f) ack-mr(2,y) = exp(2,y).
(g) ack-mr(3,y) = iter-exp(2,y), where
iter-exp(x,y) = if y=0 then 1
else exp(x,iter-exp(x,y-1))
Hint: Read about a different version of Ackermann’s function in these
files on the class website.
proof-lesson3.lisp,proof-lesson4.lisp,proof-lesson5.lisp