CS 6520 Homework 1
Exercise 1.1
Reduce the following expressions until no more beta reductions are possible. Show all evaluation steps.
x
.
x
(
x
.
y
.
y
x
) (
y
.
y
) (
x
.
x
x
)
(
x
.
y
.
y
x
) ((
x
.
x
x
) (
x
.
x
x
))
Exercise 1.2
Prove the following equivalences by showing reductions.
x
.
x
=
y
.
y
(
x
. (
y
. (
z
.
z
z
)
y
)
x
) (
x
.
x
x
)
=
(
a
.
a
((
g
.
g
)
a
)) (
b
.
b
b
)
y
. (
x
.
y
.
x
) (
y
y
)
=
a
.
b
. (
a
a
)
(
f
.
g
.
x
.
f
x
(
g
x
)) (
x
.
y
.
x
) (
x
.
y
.
x
)
=
x
.
x
(Last problem is from Gordon, page 10.)
Last update: Thursday, January 13th, 2000
mflatt@cs.utah.edu