Cool

haskell/scratch/Monadic.hs

@@ -6,21 +6,34 @@
 data MyMonad a = DivByZeroError String | NotDivisible Int | Divisible a deriving (Show)
 
 -- This is where we define fmap (i.e. map but for monads)
+-- Essentially, this is where we define what happens when we apply a function to a monad
+-- i.e.:
+-- fmap (+1) (Divisible 3) => Divisible 4
+-- fmap (+1) (NotDivisible 3) => NotDivisible 3
+-- fmap (+1) (DivByZeroError "error") => DivByZeroError "error"
 instance Functor MyMonad where
-    fmap f (DivByZeroError s) = DivByZeroError s
+    fmap f (DivByZeroError s) = DivByZeroError s -- Note the error
-    fmap f (Divisible a) = Divisible (f a)
+    fmap f (Divisible a) = Divisible (f a) -- Apply the function f to the value a
-    fmap f (NotDivisible a) = NotDivisible a
+    fmap f (NotDivisible a) = NotDivisible a -- Not divisible, propagate the value forward
 
 -- This is where we define <*> (i.e. apply but for monads) essentially applying the 
 -- "wrapped" function to the "wrapped" value
+-- i.e.:
+-- (Divisible (+1)) <*> (Divisible 3) => Divisible 4
+-- (Divisible (+1)) <*> (NotDivisible 3) => NotDivisible 3
+-- (Divisible (+1)) <*> (DivByZeroError "error") => DivByZeroError "error"
 instance Applicative MyMonad where
-    (DivByZeroError s) <*> _ = DivByZeroError s
+    (DivByZeroError s) <*> _ = DivByZeroError s -- Note the error
-    (Divisible a) <*> b = fmap a b
+    (Divisible a) <*> b = fmap a b -- Apply the function a to the value b
-    (NotDivisible a) <*> b = NotDivisible a
+    (NotDivisible a) <*> b = NotDivisible a -- Not divisible, propagate the value forward
-    pure = Divisible
+    pure = Divisible -- Wrap the value in the Divisible constructor
 
 -- This is where we define >>=, the bind operator, which chains monadic operations
--- i.e. in this case, we chain the operations of dividing and checking if the number is divisible
+-- i.e. in this case, we chain:
+-- tryDivide 2 420 >>= tryDivide 3 >>= tryDivide 5 >>= tryDivide 9 >>= tryDivide 0
+-- If we encounter a DivByZeroError, we propagate it forward (i.e. we don't do anything)
+-- If we encounter a NotDivisible, we propagate it forward
+-- If we encounter a Divisible, we apply the function f to the value x
 instance Monad MyMonad where
     DivByZeroError msg >>= _ = DivByZeroError msg -- if we encounter a DivByZeroError, we propagate it forward
     NotDivisible n >>= _ = NotDivisible n -- if we encounter a NotDivisible, we propagate it forward
@@ -34,11 +47,11 @@ tryDivide d n
     | n `mod` d == 0 = Divisible (n `div` d)
     | otherwise = NotDivisible n
 
--- Process the divisors (map out the results of tryDivide)
+-- Sequentially divide the number n by the divisors in the list
 sequentialDividing :: [Int] -> Int -> MyMonad Int
 sequentialDividing [] n = return n
 sequentialDividing (d:ds) n = do
-    newN <- tryDivide d n
+    newN <- tryDivide d n -- Note how we're not doing any pattern matching here, we're just applying the function, and the monad takes care of the rest
     sequentialDividing ds newN
 
 main :: IO ()