module Types where

import Finite
import Pretty
import Text.PrettyPrint

-- The class of conjoinable types (on the handout it is called Conjoin
-- rather than Conjoinable)

class Conjoinable c where
    conjoin :: c -> c -> c

instance Conjoinable Bool where
    conjoin x y = x && y

instance (Conjoinable b) => Conjoinable (a -> b) where
    conjoin f g x = conjoin (f x) (g x)

-- The type of binary trees

data Tree a = Leaf a | Branch (Tree a) (Tree a)
    deriving (Show)

same (Leaf x) (Leaf y) = True
same (Branch l1 r1) (Branch l2 r2) = same l1 l2 && same r1 r2
same (Leaf x) (Branch l2 r2) = False
same (Branch l1 r1) (Leaf y) = False