Add work done for Chapter 16

Author: dwayne

ch16/be-kind.txt

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+Exercises: Be Kind
+
+Given a type signature, determine the kinds of each type variable:
+
+1. What's the kind of a?
+
+   a -> a
+
+Ans: *, since the kind of (->) is * -> * -> *.
+
+2. What are the kinds of b and T? (The T is capitalized on purpose!)
+
+   a -> b a -> T (b a)
+
+Ans: a has kind *, b a has kind *. So, b has kind * -> *. Also, T has kind
+     * -> *.
+
+3. What's the kind of c?
+
+   c a b -> c b a
+
+Ans: c a b has kind *. So, c has kind * -> * -> *.

ch16/constant.hs

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+newtype Constant a b
+  = Constant { getConstant :: a }
+  deriving (Eq, Show)
+-- N.B. b is a phantom type
+-- i.e. it has no corresponding witness at the value/term level
+
+
+instance Functor (Constant a) where
+  fmap _ (Constant a) = Constant a
+  -- Initially I had
+  --
+  -- fmap _ c = c
+  --
+  -- But, that doesn't work since f :: b -> c and c :: Constant a b. Hence,
+  -- the result type should be Constant a c which it isn't if we simply
+  -- return c. That's why we have to deconstruct the type and then rebuild
+  -- it and return the result.

ch16/functors.hs

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+-- 1
+-- data FixMePls
+--   = FixMe
+--   | Pls
+--   deriving (Eq, Show)
+--
+--
+-- instance Functor FixMePls where
+--   fmap = error "it doesn't matter, it won't compile"
+
+-- 2
+-- data FixMePls a
+--   = FixMe
+--   | Pls a
+--   deriving (Eq, Show)
+--
+--
+-- instance Functor FixMePls where
+--   fmap = error "it doesn't matter, it won't compile"
+
+-- 3
+data FixMePls a
+  = FixMe
+  | Pls a
+  deriving (Eq, Show)
+
+
+instance Functor FixMePls where
+  fmap _ FixMe = FixMe
+  fmap f (Pls a) = Pls (f a)
+
+-- 4
+-- data FixMePls a
+--   = FixMe
+--   | Pls a
+--   deriving (Eq, Show)
+--
+--
+-- instance Functor (FixMePls a) where
+--   fmap _ FixMe = FixMe
+--   fmap f (Pls a) = Pls (f a)

ch16/heavy-lifting.hs

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+module HeavyLifting where
+
+-- Exercises: Heavy Lifting
+
+-- 1.
+-- a = (+1) $ read "[1]" :: [Int]
+-- a = [2]
+a = fmap (+1) $ read "[1]" :: [Int]
+
+
+-- 2.
+-- b = (++ "lol") (Just ["Hi,", "Hello"])
+-- b = Just ["Hi,lol","Hellolol"]
+b = (fmap . fmap) (++ "lol") (Just ["Hi,", "Hello"])
+
+
+-- 3.
+-- c = (*2) (\x -> x - 2)
+-- c 1 = -2
+c = fmap (*2) (\x -> x - 2)
+
+
+-- 4.
+-- d = ((return '1' ++) . show) (\x -> [x, 1..3])
+-- d 0 = "1[0,1,2,3]"
+d = fmap ((return '1' ++) . show) (\x -> [x, 1..3])
+
+
+-- 5.
+-- e :: IO Integer
+-- e = let ioi = readIO "1" :: IO Integer
+--         changed = read ("123"++) show ioi
+--     in (*3) changed
+-- > e
+-- 3693
+e :: IO Integer
+e =
+  let
+    ioi = readIO "1" :: IO Integer
+    changed = fmap (read . ("123" ++) . show) ioi
+  in
+    fmap (*3) changed

ch16/io-functor.hs

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+module IOFunctor where
+
+
+main :: IO ()
+main = putStr "> " >> getInt >>= (putStrLn . show)
+
+
+getInt :: IO Int
+getInt = fmap read getLine

ch16/more-structure.hs

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+-- 16.13 More structure, more functors
+
+data Wrap f a
+  = Wrap (f a)
+  deriving (Eq, Show)
+-- This looks so strange to me
+--
+-- But let's try to break it down
+-- f and a are types
+-- (f a) has to mean that f :: * -> * and a :: *
+--
+-- So, Wrap Maybe Int is a possible type
+--
+-- let a = 1 :: Int
+-- let x = Wrap (Just a) :: Wrap Maybe Int
+
+
+instance Functor f => Functor (Wrap f) where
+  -- f :: a -> b
+  -- fa :: f a
+  --
+  -- Hence, we need to fmap f over fa. But, that would mean
+  -- we need f to be a Functor.
+  --
+  -- Thus,
+  fmap f (Wrap fa) = Wrap (fmap f fa)

ch16/natural-transformation.hs

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+{-# LANGUAGE RankNTypes #-}
+
+module NaturalTransformation where
+
+-- nat :: (f -> g) -> f a -> g a
+-- This type is impossible since f and g have kind * -> * and functions only
+-- take types of kind *.
+
+type Nat f g = forall a. f a -> g a
+
+
+-- This'll work
+maybeToList :: Nat Maybe []
+maybeToList Nothing = []
+maybeToList (Just a) = [a]
+
+
+-- This will not work, not allowed.
+-- degenerateMtl :: Nat Maybe []
+-- degenerateMtl Nothing = []
+-- degenerateMtl (Just a) = [a+1]
+
+
+-- We can try to do it without using RankNTypes but then we have no way to
+-- disallow modifying the container's contents
+-- type Nat f g a = f a -> g a
+--
+--
+-- -- This'll work
+-- maybeToList :: Nat Maybe [] a
+-- maybeToList Nothing = []
+-- maybeToList (Just a) = [a]
+--
+--
+-- -- But this will too if we tell it
+-- -- 'a' is Num a => a
+-- degenerateMtl :: Num a => Nat Maybe [] a
+-- degenerateMtl Nothing = []
+-- degenerateMtl (Just a) = [a+1]

ch16/possibly.hs

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+-- Exercise: Possibly
+
+data Possibly a
+  = LolNope
+  | Yeppers a
+  deriving (Eq, Show)
+
+
+instance Functor Possibly where
+  fmap f LolNope = LolNope
+  fmap f (Yeppers a) = Yeppers (f a)

ch16/qcFunctorInstances/.gitignore

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+.stack-work/

ch16/qcFunctorInstances/LICENSE

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+Copyright Dwayne Crooks (c) 2017
+
+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 Dwayne Crooks 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.

ch16/qcFunctorInstances/README.md

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+# qcFunctorInstances

ch16/qcFunctorInstances/Setup.hs

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+import Distribution.Simple
+main = defaultMain

ch16/qcFunctorInstances/qcFunctorInstances.cabal

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+name:                qcFunctorInstances
+version:             0.1.0.0
+homepage:            https://github.com/dwayne/qcFunctorInstances#readme
+license:             BSD3
+license-file:        LICENSE
+author:              Dwayne Crooks
+maintainer:          me@dwaynecrooks.com
+copyright:           2017 Dwayne Crooks
+category:            Text
+build-type:          Simple
+cabal-version:       >=1.10
+extra-source-files:  README.md
+
+executable qcFunctorInstances
+  hs-source-dirs:      src
+  main-is:             Main.hs
+  default-language:    Haskell2010
+  build-depends:       base >= 4.7 && < 5
+                     , QuickCheck