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