docs for Monoid

docs/typeclasses/Monoid.md

@@ -0,0 +1,44 @@
+# Monoid
+
+A `Monoid` is a `Semigroup` with an identity element.
+
+## Parent
+
+The `Monoid` typeclass extends the `Semigroup` typeclass.
+
+## API
+
+The `Monoid` typeclass adds e single method to the `Semigroup` typeclass, providing the ability to retrieve the identity
+element for the associative operation.
+
+```php
+interface Monoid extends Semigroup
+{
+    /**
+     * @return A
+     */
+    public function mempty();
+}
+```
+
+Its simplified type is
+
+```
+mempty :: () -> A
+```
+
+## Laws
+
+The `Monoid` laws ensure that the element returned by `mempty` is in fact the identity of the associative operation.
+
+### Right identity
+
+```php
+$monoid->append($a, $monoid->mempty()) == $a
+```
+
+### Left identity
+
+```php
+$monoid->append($monoid->mempty(), $a) == $a
+```

src/Typeclass/Monoid.php

@@ -5,6 +5,8 @@
 namespace Marcosh\LamPHPda\Typeclass;
 
 /**
+ * @see https://github.com/marcosh/lamphpda/tree/master/docs/typeclasses/Monoid.md
+ *
  * @template-covariant A
  *
  * @extends Semigroup<A>