CS 6520 Homework 18

Exercise 18.1

Let o = [a =

(x)x, b =

(y)y.a, c =

(x)[d =

(y)x.b]].

Show the reduction of o.c.d.

Exercise 18.2

Let o = [a =

(x)(x.a:=

(y)(y.a:=

(z)[ ]))].

Show the reduction of o.a.a.

Exercise 18.3

Develop an encoding of true and false as objects with three methods: not, if, and ifnot. The if and ifnot methods should each return a binary function, relying our syntactic sugar for functions and application.

The encoding must obey the following laws:

true.not = false

false.not = true

true.if v₁ v₂ = v₁

true.ifnot v₁ v₂ = v₂

false.if v₁ v₂ = v₂

false.ifnot v₁ v₂ = v₁

Important: Remember that true and false will just be abbreviations, so thay cannot be defined recursively, as in true = [not =

(x)false, ...] and false = [not =

(x)true, ...].

Exercise 18.4

Optional Challenge: Define versions of true and false that provide only the methods not and if.

Last update: Tuesday, March 28th, 2000

mflatt@cs.utah.edu