CS 6520 Homework 4
Exercise 4.1
Which of the following pairs of expressions are =
v
? Which are observationally equivalent?
x
.
x
and
y
.
y
x
.
x
(
x
x
)
and
x
. (
x
x
)
x
((
x
.
x
x
) (
x
.
x
x
))
and
((
x
.
x
x
) (
x
.
x
x
) (
x
.
x
x
))
y
.
1+
y
and
a
. (
b
.
c
.
c
) (
y
. ((
x
.
x
x
) (
x
.
x
x
))) (
1+
a
)
x
.
y
.
x
y
and
x
. (
z
.
y
.
z
y
)
x
(
Y
v
(
g
.
x
.
x
))
and
(
g
.
x
.
x
) (
Y
v
(
g
.
x
.
x
))
y
. ((
x
.
x
x
) (
x
.
x
x
))
and
Y
v
(
f
.
f
f
)
Exercise 4.2
Given
Z
=
Y
v
f
.
x
. (
if0
x
0 (
f
(
1-
x
)))
prove that (
Z
n
) ->> 0 for any number
n
.
Last update: Thursday, January 20th, 2000
mflatt@cs.utah.edu