From 2af9f911ecf6b64fad8afbf1730803f40973d762 Mon Sep 17 00:00:00 2001
From: Gabi Volpe <gabriel.volpe@paddypower.com>
Date: Wed, 17 Aug 2016 16:39:04 +0100
Subject: [PATCH] Functors.

---
 category-theory/functor-example1.hs |  3 +++
 category-theory/functor-example2.hs |  5 +++++
 category-theory/functors-module.hs  | 18 ++++++++++++++++++
 category-theory/functors.hs         | 13 +++++++++++++
 paths.txt => problems/paths.txt     |  0
 5 files changed, 39 insertions(+)
 create mode 100644 category-theory/functor-example1.hs
 create mode 100644 category-theory/functor-example2.hs
 create mode 100644 category-theory/functors-module.hs
 create mode 100644 category-theory/functors.hs
 rename paths.txt => problems/paths.txt (100%)

diff --git a/category-theory/functor-example1.hs b/category-theory/functor-example1.hs
new file mode 100644
index 0000000..a3615fa
--- /dev/null
+++ b/category-theory/functor-example1.hs
@@ -0,0 +1,3 @@
+main = do line <- fmap reverse getLine  
+          putStrLn $ "You said " ++ line ++ " backwards!"  
+          putStrLn $ "Yes, you really said" ++ line ++ " backwards!"
diff --git a/category-theory/functor-example2.hs b/category-theory/functor-example2.hs
new file mode 100644
index 0000000..762a6ce
--- /dev/null
+++ b/category-theory/functor-example2.hs
@@ -0,0 +1,5 @@
+import Data.Char  
+import Data.List  
+  
+main = do line <- fmap (intersperse '-' . reverse . map toUpper) getLine  
+          putStrLn line
diff --git a/category-theory/functors-module.hs b/category-theory/functors-module.hs
new file mode 100644
index 0000000..a7760fa
--- /dev/null
+++ b/category-theory/functors-module.hs
@@ -0,0 +1,18 @@
+-- few examples on List, Mabe and Either
+a1 = fmap (replicate 3) [1,2,3,4]  
+a2 = fmap (replicate 3) (Just 4)  
+a3 = fmap (replicate 3) (Right "blah")  
+a4 = fmap (replicate 3) Nothing  
+a5 = fmap (replicate 3) (Left "foo")
+
+----------- functor laws in action 
+
+-- identity function (\x -> x). Formerly: fmap id = id
+b1 = fmap id (Just 3)
+b2 = id (Just 3)  
+b3 = fmap id [1..5]  
+b4 = id [1..5]  
+b5 = fmap id []  
+b6 = fmap id Nothing
+
+-- composition: fmap (f . g) F = fmap f (fmap g F)
diff --git a/category-theory/functors.hs b/category-theory/functors.hs
new file mode 100644
index 0000000..1277df6
--- /dev/null
+++ b/category-theory/functors.hs
@@ -0,0 +1,13 @@
+-- Defined in the standard library
+instance Functor IO where  
+    fmap f action = do  
+        result <- action  
+        return (f result)
+
+-- defined in Control.Monad.Instances
+instance Functor ((->) r) where  
+    fmap f g = (\x -> f (g x))
+
+-- same as aboved using composition
+instance Functor ((->) r) where  
+    fmap = (.)
diff --git a/paths.txt b/problems/paths.txt
similarity index 100%
rename from paths.txt
rename to problems/paths.txt