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“Maybe a” emulation: monadic properties - Pastebin.com
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“Maybe a” emulation: monadic properties
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- -- "Maybe a" emulation: monadic properties
- data OptionType a
- = Empty
- | NonEmpty a
- deriving (Show, Eq)
- instance Functor OptionType where
- fmap _ Empty = Empty
- fmap f (NonEmpty a) = NonEmpty $ f a
- instance Applicative OptionType where
- pure = NonEmpty
- (<*>) (NonEmpty a) (NonEmpty b) = NonEmpty $ a b
- instance Monad OptionType where
- return = NonEmpty
- -- the 'bind' operator is the >>= thingy :-)
- (>>=) Empty f = Empty
- (>>=) (NonEmpty a) f = f a
- increment :: Int -> OptionType Int
- increment x = NonEmpty (x + 1)
- feedingEmptyOptionalValue :: OptionType Int
- feedingEmptyOptionalValue = Empty >>= increment
- singleFeeding :: OptionType Int
- singleFeeding = NonEmpty 7 >>= increment
- doubleFeeding :: OptionType Int
- doubleFeeding = NonEmpty 7 >>= increment >>= increment
- fuckUpPipeline :: OptionType Int
- fuckUpPipeline = NonEmpty 7 >>= increment >>= (\_ -> Empty) >>= increment
- outputText =
- [ "1. An empty optional value: "
- , show (Empty :: OptionType Int)
- , "2. An non-empty optional value: "
- , show (NonEmpty 7)
- , "3. Feeding an empty optional value to the increment function:"
- , "Empty >>= increment → "
- , show feedingEmptyOptionalValue
- , "4. Feeding an non-empty optional value to the increment function:"
- , "NonEmpty 7 >>= increment → "
- , show singleFeeding
- , "5. A two-section pipeline with the increment function:"
- , "NonEmpty 7 >>= increment >>= increment → "
- , show doubleFeeding
- , "6. A three-section pipeline showcasing failure propagation:"
- , "NonEmpty 7 >>= increment >>= (\\_ -> Empty) >>= increment → "
- , show fuckUpPipeline
- , "7. The first monadic law: return a >>= h ≡ h a:"
- , "(return 7 >>= increment) == increment 7 →"
- , show $ (return 7 >>= increment) == increment 7
- , "8. The second monadic law: m >>= return ≡ m:"
- , "(NonEmpty 7 >>= return) == NonEmpty 7 →"
- , show $ (NonEmpty 7 >>= return) == NonEmpty 7
- , "9. The third monadic law: (m >>= g) >>= h ≡ m >>= (\\x -> g x >>= h):"
- , "((NonEmpty 7 >>= (\\_ -> Empty)) >>= increment) == (NonEmpty 7 >>= (\\x -> (\\_ -> Empty) x >>= increment)) →"
- , show $ ((NonEmpty 7 >>= (\_ -> Empty)) >>= increment) == (NonEmpty 7 >>= (\x -> (\_ -> Empty) x >>= increment))
- ]
- main :: IO ()
- main = mapM_ putStrLn outputText
- -- 1. An empty optional value:
- -- Empty
- -- 2. An non-empty optional value:
- -- NonEmpty 7
- -- 3. Feeding an empty optional value to the increment function:
- -- Empty >>= increment →
- -- Empty
- -- 4. Feeding an non-empty optional value to the increment function:
- -- NonEmpty 7 >>= increment →
- -- NonEmpty 8
- -- 5. A two-section pipeline with the increment function:
- -- NonEmpty 7 >>= increment >>= increment →
- -- NonEmpty 9
- -- 6. A three-section pipeline showcasing failure propagation:
- -- NonEmpty 7 >>= increment >>= (\_ -> Empty) >>= increment →
- -- Empty
- -- 7. The first monadic law: return a >>= h ≡ h a:
- -- (return 7 >>= increment) == increment 7 →
- -- True
- -- 8. The second monadic law: m >>= return ≡ m:
- -- (NonEmpty 7 >>= return) == NonEmpty 7 →
- -- True
- -- 9. The third monadic law: (m >>= g) >>= h ≡ m >>= (\x -> g x >>= h):
- -- ((NonEmpty 7 >>= (\_ -> Empty)) >>= increment) == (NonEmpty 7 >>= (\x -> (\_ -> Empty) x >>= increment)) →
- -- True
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