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 --- title: Assignment 3 --- The `Functor` is the most fundamental typeclass in the standard libraries. Intuitively, a `Functor` can be viewed as a sort of "container," coupled with an ability to apply a function to every element in the container. It is defined as follows, where the `fmap` function generalizes the `map` function. ... ... @@ -7,18 +11,19 @@ class Functor f where fmap :: (a -> b) -> f a -> f b ``` 1. The `Either` type represents values with two possibilities: a value of type `Either a b` is either `Left a` or `Right b`. ### Problem 1 The `Either` type represents values with two possibilities: a value of type `Either a b` is either `Left a` or `Right b`. By convention, the `Left` constructor is used to hold an error value and the `Right` constructor is used to hold a correct value. ```haskell data Either a b = Left a | Right b ``` By convention, the `Left` constructor is used to hold an error value and the `Right` constructor is used to hold a correct value. Define an instance of `Functor` for `Either e` for a fixed `e`. 2. The `Data.Tree` module implements a rose tree - also, a multiway tree - as follows. ### Problem 2 We can implement a rose tree - also, a multiway tree - as follows. The `Data.Tree` module has an implementation; one possible implementation is as follows: ```haskell data Tree a = Node a [Tree a] ... ... @@ -26,8 +31,8 @@ data Tree a = Node a [Tree a] Define an instance of `Functor` for this datatype. 3. Is this statement true or false? ### Problem 3 The composition of two `Functor`s is also a `Functor`. Is this statement true or false? The composition of two `Functor`s is also a `Functor`. If false, give a counterexample; if true, provide an explanation (ideally with some code). \ No newline at end of file If false, give a counterexample; if true, provide an explanation.
 Copyright Author name here (c) 2019 All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of Author name here nor the names of other contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. \ No newline at end of file
 # assignment3
 import Distribution.Simple main = defaultMain
 name: assignment3 version: 0.1.0.0 -- synopsis: -- description: homepage: https://github.com/githubuser/assignment3#readme license: BSD3 license-file: LICENSE author: Author name here maintainer: example@example.com copyright: 2019 Author name here category: Web build-type: Simple cabal-version: >=1.10 extra-source-files: README.md executable assignment3 hs-source-dirs: src main-is: Main.hs default-language: Haskell2010 build-depends: base >= 4.7 && < 5
 module Main where main :: IO () main = do putStrLn "hello world" -- Problem 1 -- -- MyEither used to distinguish from Prelude.Either data MyEither a b = Left a | Right b instance Functor (MyEither a) where fmap = undefined -- Implementation here -- Problem 2 -- data Tree a = Node a [Tree a] instance Functor Tree where fmap = undefined -- Implementation here
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