Answered: eval skipl_false : SKIP1 INC (PAIR…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

See similar textbooks

Related questions

Question

Lambda calculus

--------------------------------------------------------------------------------
-- Booleans
--------------------------------------------------------------------------------

let TRUE = \x y -> x
let FALSE = \x y -> y
let ITE = \b x y -> b x y
let AND = \b1 b2 -> ITE b1 b2 FALSE
let OR = \b1 b2 -> ITE b1 TRUE b2

--------------------------------------------------------------------------------
-- Numbers
--------------------------------------------------------------------------------

let ZERO = \f x -> x
let ONE = \f x -> f x
let TWO = \f x -> f (f x)
let INC = \n f x -> f (n f x)

--------------------------------------------------------------------------------
-- Pairs
--------------------------------------------------------------------------------

let PAIR = \x y b -> ITE b x y
let FST = \p -> p TRUE
let SND = \p -> p FALSE

--------------------------------------------------------------------------------
-- Ignore this definition; it's a hack to allow you to test some parts before
-- completing others
--------------------------------------------------------------------------------

let TODO = \i g n o r e -> i g n o r e

--------------------------------------------------------------------------------
-- do not modify text BEFORE this line
--------------------------------------------------------------------------------

let SKIP1 = TODO -- (a)
let DEC = TODO -- (b)
let SUB = TODO -- (c)
let ISZ = TODO -- (d)
let EQL = TODO -- (e)

--------------------------------------------------------------------------------
-- do not modify text AFTER this line
--------------------------------------------------------------------------------

-- Part (a)

eval skip1_false :
SKIP1 INC (PAIR FALSE ZERO)
=~> (\b -> b TRUE ZERO) -- PAIR TRUE ZERO

eval skip1_true_zero :
SKIP1 INC (PAIR TRUE ZERO)
=~> (\b -> b TRUE ONE) -- PAIR TRUE ONE

eval skip1_true_one :
SKIP1 INC (PAIR TRUE ONE)
=~> (\b -> b TRUE TWO) -- PAIR TRUE TWO

--------------------------------------------------------------------------------

-- Part (b)

eval decr_zero :
DEC ZERO
=~> ZERO

eval decr_one :
DEC ONE
=~> ZERO

eval decr_two :
DEC TWO
=~> ONE