add Function as Monoid

README.md

@@ -37,6 +37,22 @@ instance Monad ((->) r) where
 
 </details>
 
+<details>
+<summary>Function as Semigroup and Monoid</summary>
+
+```haskell
+-- | @since 4.9.0.0
+instance Semigroup b => Semigroup (a -> b) where
+        f <> g = \x -> f x <> g x
+        stimes n f e = stimes n (f e)
+
+-- | @since 2.01
+instance Monoid b => Monoid (a -> b) where
+        mempty _ = mempty
+```
+
+</details>
+
 <details><summary>"Komposition" of Functions (Kleisli Arrows)</summary>
 
 ```haskell
@@ -84,9 +100,10 @@ f = fn .> f3 .> f2 .> f1
 ```
 
 ```haskell
--- Functor Law
-f <$> id == f
+-- Functor Laws
 id <$> f == f
+f <$> id == f
+(f <$> g) <$> h = f <$> (g <$> h)
 ```
 
 </details>
@@ -131,6 +148,43 @@ f = f1 =<< f2
 f = f2 >>= f1
 ```
 
+```haskell
+-- Monad Laws
+pure a >>= f = f a
+f >>= pure = f
+(f >>= g) >>= h = f >>= (\x -> g x >>= h)
+```
+
+</details>
+
+<details><summary>Function as Semigroup</summary>
+
+```haskell
+f x = f1 x <> f2 x
+f = f1 <> f2
+```
+
+```haskell
+f x = f1 x <> f2 x <> f3 x <> fn x
+f = f1 <> f2 <> f3 <> fn
+```
+
+</details>
+
+<details><summary>Function as Monoid</summary>
+
+```haskell
+f x = f1 x <> mempty
+f = f1 <> mempty
+```
+
+```haskell
+-- Monoid Laws
+mempty <> f = f
+f <> mempty = f
+(f <> g) <> h = f <> (g <> h)
+```
+
 </details>
 
 <details><summary>"Komposition" of Functions (Kleisli Arrows)</summary>