Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
Bartleby Related Questions Icon

Related questions

Question

Given the definition in Haskell:

fmap :: (a -> b) -> [a] -> [b]

fmap g xs = reverse (map g xs)

 

With Functor law:

(fmap g . fmap h) xs = fmap (g . h) xs

 

Using list xs :: [Int], prove the definition does not satisfy the law:

Expert Solution
Check Mark
Step 1

A functor is a function that takes a function, fmap (say) that returns another function. fmap() is also known as function map

 

Let's see the functor instance for a list with id.

fmap id (x: xs)

= (id x) : fmap xs

= x : fmap xs

 

As per the question, fmap id (x: xs) = (x: xs) which satisfies the first law, we can conclude that

= (fmap g).(fmap h) (x : xs)

= fmap g (fmap h (x: xs))

= fmap g ((h x) = fmap h xs)

= (g.h x) = fmap g(fmap h xs) which doesn't satisfies the law.

Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Computer Networking: A Top-Down Approach (7th Edi...
Computer Engineering
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:PEARSON
Text book image
Computer Organization and Design MIPS Edition, Fi...
Computer Engineering
ISBN:9780124077263
Author:David A. Patterson, John L. Hennessy
Publisher:Elsevier Science
Text book image
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:9781337569330
Author:Jill West, Tamara Dean, Jean Andrews
Publisher:Cengage Learning
Text book image
Concepts of Database Management
Computer Engineering
ISBN:9781337093422
Author:Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:Cengage Learning
Text book image
Prelude to Programming
Computer Engineering
ISBN:9780133750423
Author:VENIT, Stewart
Publisher:Pearson Education
Text book image
Sc Business Data Communications and Networking, T...
Computer Engineering
ISBN:9781119368830
Author:FITZGERALD
Publisher:WILEY