Add Monoid and Semigroup instances (#276)

* Add `Monoid` and `Semigroup` instances

Fixes #269.

* Add documentation

* Update src/Algebra/Graph/Labelled.hs

Co-authored-by: Andrey Mokhov <[email protected]>

src/Algebra/Graph.hs

@@ -295,6 +295,14 @@ instance MonadPlus Graph where
     mzero = Empty
     mplus = Overlay
 
+-- | Defined via 'overlay'.
+instance Semigroup (Graph a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Monoid (Graph a) where
+    mempty = empty
+
 -- | Construct the /empty graph/. An alias for the constructor 'Empty'.
 --
 -- @

src/Algebra/Graph/AdjacencyIntMap.hs

@@ -203,6 +203,14 @@ instance Num AdjacencyIntMap where
 instance NFData AdjacencyIntMap where
     rnf (AM a) = rnf a
 
+-- | Defined via 'overlay'.
+instance Semigroup AdjacencyIntMap where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Monoid AdjacencyIntMap where
+    mempty = empty
+
 -- | Construct an 'AdjacencyIntMap' from an 'AM.AdjacencyMap' with vertices of
 -- type 'Int'.
 -- Complexity: /O(n + m)/ time and memory.

src/Algebra/Graph/AdjacencyMap.hs

@@ -207,6 +207,14 @@ instance IsString a => IsString (AdjacencyMap a) where
 instance NFData a => NFData (AdjacencyMap a) where
     rnf (AM a) = rnf a
 
+-- | Defined via 'overlay'.
+instance Ord a => Semigroup (AdjacencyMap a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Ord a => Monoid (AdjacencyMap a) where
+    mempty = empty
+
 -- | Construct the /empty graph/.
 --
 -- @

src/Algebra/Graph/Bipartite/AdjacencyMap.hs

@@ -230,6 +230,14 @@ instance (Ord a, Ord b, Show a, Show b) => Show (AdjacencyMap a b) where
         eShow es       = showString "edges " . showsPrec 11 es
         veShow xs      = vShow (lefts xs) (rights xs)
 
+-- | Defined via 'overlay'.
+instance (Ord a, Ord b) => Semigroup (AdjacencyMap a b) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance (Ord a, Ord b) => Monoid (AdjacencyMap a b) where
+    mempty = empty
+
 -- | Construct the /empty graph/.
 --
 -- @

src/Algebra/Graph/Labelled.hs

@@ -92,6 +92,14 @@ instance (NFData e, NFData a) => NFData (Graph e a) where
     rnf (Vertex  x    ) = rnf x
     rnf (Connect e x y) = e `seq` rnf x `seq` rnf y
 
+-- | Defined via 'overlay'.
+instance Monoid e => Semigroup (Graph e a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Monoid e => Monoid (Graph e a) where
+    mempty = empty
+
 -- TODO: This is a very inefficient implementation. Find a way to construct an
 -- adjacency map directly, without building intermediate representations for all
 -- subgraphs.

src/Algebra/Graph/Labelled/AdjacencyMap.hs

@@ -113,6 +113,14 @@ instance (Eq e, Dioid e, Num a, Ord a) => Num (AdjacencyMap e a) where
 instance IsString a => IsString (AdjacencyMap e a) where
     fromString = vertex . fromString
 
+-- | Defined via 'overlay'.
+instance (Ord a, Eq e, Monoid e) => Semigroup (AdjacencyMap e a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance (Ord a, Eq e, Monoid e) => Monoid (AdjacencyMap e a) where
+    mempty = empty
+
 -- | Construct the /empty graph/.
 --
 -- @

src/Algebra/Graph/NonEmpty.hs

@@ -195,6 +195,10 @@ instance Ord a => Eq (Graph a) where
 instance Ord a => Ord (Graph a) where
     compare = ord
 
+-- | Defined via 'overlay'.
+instance Semigroup (Graph a) where
+    (<>) = overlay
+
 -- TODO: Find a more efficient equality check.
 -- | Check if two graphs are equal by converting them to their adjacency maps.
 eq :: Ord a => Graph a -> Graph a -> Bool

src/Algebra/Graph/NonEmpty/AdjacencyMap.hs

@@ -180,6 +180,10 @@ instance (Ord a, Show a) => Show (AdjacencyMap a) where
         eshow xs       = showString "edges1 "    . showsPrec 11 xs
         used           = Set.toAscList $ Set.fromList $ uncurry (++) $ unzip es
 
+-- | Defined via 'overlay'.
+instance Ord a => Semigroup (AdjacencyMap a) where
+    (<>) = overlay
+
 -- Unsafe creation of a NonEmpty list.
 unsafeNonEmpty :: [a] -> NonEmpty a
 unsafeNonEmpty = fromMaybe (error msg) . nonEmpty

src/Algebra/Graph/Relation.hs

@@ -197,6 +197,14 @@ instance (Ord a, Num a) => Num (Relation a) where
 instance IsString a => IsString (Relation a) where
     fromString = vertex . fromString
 
+-- | Defined via 'overlay'.
+instance Ord a => Semigroup (Relation a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Ord a => Monoid (Relation a) where
+    mempty = empty
+
 -- | Construct the /empty graph/.
 --
 -- @

src/Algebra/Graph/Relation/Symmetric.hs

@@ -130,6 +130,14 @@ instance (Ord a, Num a) => Num (Relation a) where
     abs         = id
     negate      = id
 
+-- | Defined via 'overlay'.
+instance Ord a => Semigroup (Relation a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Ord a => Monoid (Relation a) where
+    mempty = empty
+
 -- | Construct a symmetric relation from a given "Algebra.Graph.Relation".
 -- Complexity: /O(m*log(m))/ time.
 --

src/Algebra/Graph/Undirected.hs

@@ -198,6 +198,14 @@ instance Ord a => Eq (Graph a) where
 instance Ord a => Ord (Graph a) where
     compare = ordR
 
+-- | Defined via 'overlay'.
+instance Semigroup (Graph a) where
+    (<>) = overlay
+
+-- | Defined via 'overlay' and 'empty'.
+instance Monoid (Graph a) where
+    mempty = empty
+
 -- TODO: Find a more efficient equality check.
 -- Check if two graphs are equal by converting them to symmetric relations.
 eqR :: Ord a => Graph a -> Graph a -> Bool