monads
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haskell/scratch/Monadic
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haskell/scratch/Monadic
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haskell/scratch/Monadic.hi
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haskell/scratch/Monadic.hi
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haskell/scratch/Monadic.hs
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haskell/scratch/Monadic.hs
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-- We want to take a list of divisors and a number
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-- We traverse the list of divisors and check if the number is divisible by the divisor
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-- If the number is divisible by the return the number divided by the divisor
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-- If the number is not divisible repeatedly increment the number by 1 until it is divisible by the divisor
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-- If the divisor is 0, throw an error
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data MyMonad a = DivByZeroError String | NotDivisible Int | Divisible a deriving (Show)
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-- This is where we define fmap (i.e. map but for monads)
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instance Functor MyMonad where
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fmap f (DivByZeroError s) = DivByZeroError s
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fmap f (Divisible a) = Divisible (f a)
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fmap f (NotDivisible a) = NotDivisible a
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-- This is where we define <*> (i.e. apply but for monads) essentially applying the
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-- "wrapped" function to the "wrapped" value
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instance Applicative MyMonad where
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(DivByZeroError s) <*> _ = DivByZeroError s
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(Divisible a) <*> b = fmap a b
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(NotDivisible a) <*> b = NotDivisible a
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pure = Divisible
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-- This is where we define >>=, the bind operator, which chains monadic operations
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-- i.e. in this case, we chain the operations of dividing and checking if the number is divisible
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instance Monad MyMonad where
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DivByZeroError msg >>= _ = DivByZeroError msg -- if we encounter a DivByZeroError, we propagate it forward
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NotDivisible n >>= _ = NotDivisible n -- if we encounter a NotDivisible, we propagate it forward
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Divisible x >>= f = f x -- if we encounter a Divisible, we apply the function f to the value x
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-- Try to divide the number n by d
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tryDivide :: Int -> Int -> MyMonad Int
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tryDivide 0 _ = DivByZeroError "Division by zero"
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tryDivide d n
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| n `mod` d == 0 = Divisible (n `div` d)
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| otherwise = NotDivisible n
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-- Process the divisors (map out the results of tryDivide)
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sequentialDividing :: [Int] -> Int -> MyMonad Int
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sequentialDividing [] n = return n
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sequentialDividing (d:ds) n = do
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newN <- tryDivide d n
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sequentialDividing ds newN
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main :: IO ()
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main = do
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let divisors = [2, 3, 5, 9, 0]
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let number = 420
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-- 420/2 = 210
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-- 210/3 = 70
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-- 70/5 = 14
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-- 14/9 not good => 14 is returned
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print $ sequentialDividing divisors number
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let divisors2 = [2, 3, 5, 7, 0]
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let number2 = 420
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-- 420/2 = 210
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-- 210/3 = 70
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-- 70/5 = 14
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-- 14/7 = 2
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-- 2/0 not good => error
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print $ sequentialDividing divisors2 number2
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let divisors3 = [2, 3, 5, 7, 2]
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let number3 = 420
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-- 420/2 = 210
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-- 210/3 = 70
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-- 70/5 = 14
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-- 14/7 = 2
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-- 2/2 = 1, all good => 1 is returned
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print $ sequentialDividing divisors3 number3
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-- [Divisible 210,Divisible 140,Divisible 84,NotDivisible 420,DivByZeroError "Division by zero"]
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-- 420 is divisible by: [2,3,5]
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-- Wtf is the point of a monad here?
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haskell/scratch/Monadic.o
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haskell/scratch/Monadic.o
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haskell/scratch/monadDumb.hs
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haskell/scratch/monadDumb.hs
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-- error handling with a custom monad
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-- say we want to divide a list of numbers by a divisor
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-- if the divisor is even, we throw an error, then apply ^2 to the rest of the numbers
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-- if the divisor is odd, we return the result
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-- if the divisor is 0, we throw an error
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-- custom monad
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data MyMonad a = DivByZeroError String | DivByEven a | DivByOdd a deriving (Show)
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-- instance of Functor
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instance Functor MyMonad where -- Functor is where we define fmap (i.e. map)
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-- customMap, where we have 2 functions, one for even and one for odd
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fmap f (DivByZeroError s) = DivByZeroError s
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fmap f (DivByEven a) = DivByEven (f a)
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fmap f (DivByOdd a) = DivByOdd (f a)
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-- instance of Applicative
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instance Applicative MyMonad where
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(DivByZeroError s) <*> _ = DivByZeroError s
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-- DivByEvenError -> ^2
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(DivByEven a) <*> b = fmap a b --
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(DivByOdd a) <*> b = fmap a b
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pure = DivByOdd
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-- instance of Monad
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instance Monad MyMonad where
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return = pure
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(DivByZeroError s) >>= _ = DivByZeroError s
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(DivByEven a) >>= f =
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case f a of
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DivByOdd b -> DivByEven b -- propagate the "evenness context" forward
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DivByEven b -> DivByEven b -- keep even state if it continues
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DivByZeroError s -> DivByZeroError s
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(DivByOdd a) >>= f = f a
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safeDivide :: Int -> [Int] -> MyMonad [Int]
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safeDivide 0 _ = DivByZeroError "Division by zero"
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safeDivide d xs
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| even d = DivByEven (map (^2) xs)
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| otherwise = DivByOdd (map (`div` d) xs)
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main :: IO ()
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main = do
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let nums = [69, 420, 666, 1337]
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let divisor = 2
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let result = safeDivide divisor nums
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let nums2 = [1,2,3,4,5]
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let divisor2 = 0
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let result2 = safeDivide divisor2 nums2
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let nums3 = [69, 420, 666, 1337]
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let divisor3 = 3
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let result3 = safeDivide divisor3 nums3
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print result
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print result2
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print result3
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