Algebraic notation for algebraic data types

Algebra	Datatype
0	data T
1	data T = T
2	data T = L	R
a
+	data T a b = L a	R b
*	(a,b)
^	a -> b = bᵃ
--------------	--------------------------------------------------------------------
a + a	data T a = L a	R a
a + b	data T a b = L a	R b
a * a	(a,a)
a * b	(a,b)
a * b	a×b, a*b, ab, (a,b), Pair a b = (a,b)
a + b	a+b, a	b, Either a b = Left a	Right b
b ^ a	bᵃ ≅ (a -> b)
--------------	--------------------------------------------------------------------
1 + a	data T a = N	C a, Maybe a
1 * a	((), a) ≅ a
0 + a	(Void	a) ≅ a
--------------	--------------------------------------------------------------------
1 + a²	data T a = Leaf	C (T a) (T a)
1 + a³	data T a = Leaf	C a (T a) (T a)
a + a²	data T a = Leaf a	C (T a) (T a)
a + a³	data T a = Leaf a	C a (T a) (T a)
1 + a + a²	data T a = Leaf	B a	C (T a) (T a)
1 + a + a³	data T a = Leaf	B a	C a (T a) (T a)
--------------	--------------------------------------------------------------------

List a = Leaf | Node a (List a) La = 1 + a La La = 1 + a a La = 1 + a²

Tree a = Leaf | Node a (Tree a) (Tree a) Ta = 1 + a Ta Ta Ta = 1 + a a a Ta = 1 + a³

1 + 1 ≅ 1 * 2 ≅ 2 Bool = (Void, Bool)