From dceac9e1e44b69593ef8d8585f9f411d970b8441 Mon Sep 17 00:00:00 2001
From: Yann Esposito
F a -> G a
are the natural transformations.data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toTree :: [a] -> Tree a
+toTree [] = Empty
+toTree (x:xs) = Node x [toTree xs]
+
+toTree
is a natural transformation. It is also a morphism from []
to Tree
in the Category of \(\) endofunctors.
data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toList :: Tree a -> [a]
+toList Empty = []
+toList (Node x l) = [x] ++ concat (map toList l)
+
+toList
is a natural transformation. It is also a morphism from Tree
to []
in the Category of \(\) endofunctors.
+toMaybe :: [a] -> Maybe a ; mToList :: Maybe a -> [a]
+toMaybe [] = Nothing ; mToList Nothing = []
+toMaybe (x:xs) = Just x ; mToList Just x = [x]
+
+
+toMaybe
is a natural transformation. It is also a morphism from []
to Maybe
in the Category of \(\) endofunctors.
+toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x
+
+toMaybe
is a natural transformation. It is also a morphism from []
to Maybe
in the Category of \(\) endofunctors.
data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toTree :: [a] -> Tree a
+toTree [] = Empty
+toTree (x:xs) = Node x [toTree xs]
+
+toTree
is a natural transformation. It is also a morphism from []
to Tree
in the Category of \(\) endofunctors.
data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toTree :: [a] -> Tree a
+toTree [] = Empty
+toTree (x:xs) = Node x [toTree xs]
+
+
+`toTree` is a natural transformation.
+It is also a morphism from `[]` to `Tree` in the Category of \\(\Hask\\) endofunctors.
+
+
+
diff --git a/categories/30_How/180_Natural_Transformation_Examples.html b/categories/30_How/180_Natural_Transformation_Examples.html
new file mode 100644
index 0000000..90b6c69
--- /dev/null
+++ b/categories/30_How/180_Natural_Transformation_Examples.html
@@ -0,0 +1,14 @@
+data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toList :: Tree a -> [a]
+toList Empty = []
+toList (Node x l) = [x] ++ concat (map toList l)
+
+toList
is a natural transformation. It is also a morphism from Tree
to []
in the Category of \(\) endofunctors.
data Tree a = Empty | Node a [Tree a]
+ deriving (Show)
+toList :: Tree a -> [a]
+toList Empty = []
+toList (Node x l) = [x] ++ concat (map toList l)
+
+
+`toList` is a natural transformation.
+It is also a morphism from `Tree` to `[]` in the Category of \\(\Hask\\) endofunctors.
+
+
+
diff --git a/categories/30_How/190_Another_Nat_Trans_Example.html b/categories/30_How/190_Another_Nat_Trans_Example.html
new file mode 100644
index 0000000..193e7aa
--- /dev/null
+++ b/categories/30_How/190_Another_Nat_Trans_Example.html
@@ -0,0 +1,14 @@
+
+toMaybe :: [a] -> Maybe a ; mToList :: Maybe a -> [a]
+toMaybe [] = Nothing ; mToList Nothing = []
+toMaybe (x:xs) = Just x ; mToList Just x = [x]
+
+
+toMaybe
is a natural transformation. It is also a morphism from []
to Maybe
in the Category of \(\) endofunctors.
+toMaybe :: [a] -> Maybe a ; mToList :: Maybe a -> [a]
+toMaybe [] = Nothing ; mToList Nothing = []
+toMaybe (x:xs) = Just x ; mToList Just x = [x]
+
+
+
+`toMaybe` is a natural transformation.
+It is also a morphism from `[]` to `Maybe` in the Category of \\(\Hask\\) endofunctors.
+
+
+
diff --git a/categories/30_How/200_Another_Nat_Trans_Example.html b/categories/30_How/200_Another_Nat_Trans_Example.html
new file mode 100644
index 0000000..7e54ab4
--- /dev/null
+++ b/categories/30_How/200_Another_Nat_Trans_Example.html
@@ -0,0 +1,13 @@
+
+toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x
+
+toMaybe
is a natural transformation. It is also a morphism from []
to Maybe
in the Category of \(\) endofunctors.
+toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x
+
+
+`toMaybe` is a natural transformation.
+It is also a morphism from `[]` to `Maybe` in the Category of \\(\Hask\\) endofunctors.
+
+
+
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diff --git a/categories/30_How/220_Monads_generalize_composition.html b/categories/30_How/260_Monads_generalize_composition.html
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diff --git a/categories/img/mp/list-maybe-endofunctor-morphism.mp b/categories/img/mp/list-maybe-endofunctor-morphism.mp
new file mode 100644
index 0000000..af3fb88
--- /dev/null
+++ b/categories/img/mp/list-maybe-endofunctor-morphism.mp
@@ -0,0 +1,8 @@
+pair tree,list;
+resize(.8cm);
+list=origin;
+tree=list shifted (gu,0);
+drawState(list,"\mathtt{[]}");
+drawState(tree,"\mathtt{Maybe}");
+drawEdgeAngle(list,tree,"\mathtt{toMaybe}",30);
+drawEdgeAngle(tree,list,"\mathtt{mToList}",30);
diff --git a/categories/img/mp/list-maybe-endofunctor-morphism.png b/categories/img/mp/list-maybe-endofunctor-morphism.png
new file mode 100644
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