maddy

data Btree a = ND | Data a |  Branch (Btree a) (Btree a)
               deriving (Show,Eq)

data Dir = L | R 
           deriving (Show,Eq)

type Path =  [Dir] 
    
--- Part a)

extract :: Path  -> Btree a -> Error a
-- function returns the data at the end of the path
extract p ND=Fail
extract [] (Data a)=Ok(a)
extract (L:p) (Branch t1 t2)=extract p t1
extract (R:p) (Branch t1 t2)=extract p t2
extract _ _= Fail

--- Part b)

add :: a -> Path -> Btree a -> Error (Btree a)
add d [] (Data a)=Fail
add d [] (Branch t1 t2)=Fail
add d [] (ND)= Ok(Data d)
add d (L:p) (Branch t1 t2)=add d p t1
add d (R:p) (Branch t1 t2)=add d p t2