275 lines
6 KiB
Markdown
275 lines
6 KiB
Markdown
---
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title:
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- Applicatives
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author:
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- Sanchayan Maity
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theme:
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- default
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classoption:
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- aspectratio=169
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---
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# Agenda
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- Recap of Functors
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- Applicative
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# Functor[^1][^2]
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```haskell
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class Functor f where
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fmap :: (a -> b) -> f a -> f b
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(<$) :: a -> f b -> f a
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```
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Functors Laws
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- Must preserve identity
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```haskell
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fmap id = id
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```
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- Must preserve composition of morphism
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```haskell
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fmap (f . g) == fmap f . fmap g
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```
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[^1]: [Category Design Pattern](https://www.haskellforall.com/2012/08/the-category-design-pattern.html)
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[^2]: [Functor Design Pattern](https://www.haskellforall.com/2012/09/the-functor-design-pattern.html)
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# Higher order kinds[^3]
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- For something to be a functor, it has to be a first order kind.
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[^3]: [Haskell's Kind System](https://diogocastro.com/blog/2018/10/17/haskells-kind-system-a-primer/)
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# Applicative
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```haskell
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class Functor f => Applicative (f :: TYPE -> TYPE) where
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pure :: a -> f a
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(<*>) :: f (a -> b) -> f a -> f b
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```
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```haskell
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(<$>) :: Functor f => (a -> b) -> f a -> f b
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(<*>) :: Applicative f => f (a -> b) -> f a -> f b
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```
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```haskell
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fmap f x = pure f <*> x
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```
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# Examples
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```haskell
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pure (+1) <*> [1..3]
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[2, 3, 4]
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[(*2), (*3)] <*> [4, 5]
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[8,10,12,15]
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("Woo", (+1)) <*> (" Hoo!", 0)
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("Woo Hoo!", 1)
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(Sum 2, (+1)) <*> (Sum 0, 0)
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(Sum {getSum = 2}, 1)
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(Product 3, (+9)) <*> (Product 2, 8)
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(Product {getProduct = 6}, 17)
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(,) <$> [1, 2] <*> [3, 4]
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[(1,3),(1,4),(2,3),(2,4)]
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```
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# Use cases[^4]
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```haskell
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Person
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<$> parseString "name" o
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<*> parseInt "age" o
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<*> parseTelephone "telephone" o
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```
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Can also be written as
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```haskell
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liftA3 Person
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(parseString "name" o)
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(parseInt "age" o)
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(parseTelephone "telephone" o)
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```
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[^4]: [FP Complete - Crash course to Applicative syntax](https://www.fpcomplete.com/haskell/tutorial/applicative-syntax/)
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# Use cases[^5]
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```haskell
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parsePerson :: Parser Person
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parsePerson = do
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string "Name: "
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name <- takeWhile (/= 'n')
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endOfLine
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string "Age: "
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age <- decimal
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endOfLine
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pure $ Person name age
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```
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[^5]: [FP Complete - Crash course to Applicative syntax](https://www.fpcomplete.com/haskell/tutorial/applicative-syntax/)
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# Use cases[^6]
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```haskell
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helper :: () -> Text -> () -> () -> Int -> () -> Person
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helper () name () () age () = Person name age
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parsePerson :: Parser Person
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parsePerson = helper
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<$> string "Name: "
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<*> takeWhile (/= 'n')
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<*> endOfLine
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<*> string "Age: "
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<*> decimal
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<*> endOfLine
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```
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[^6]: [FP Complete - Crash course to Applicative syntax](https://www.fpcomplete.com/haskell/tutorial/applicative-syntax/)
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# Lifting
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- Seeing Functor as unary lifting and Applicative as n-ary lifting
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```haskell
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liftA0 :: Applicative f => (a) -> (f a)
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liftA1 :: Functor f => (a -> b) -> (f a -> f b)
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liftA2 :: Applicative f => (a -> b -> c) -> (f a -> f b -> f c)
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liftA3 :: Applicative f => (a -> b -> c -> d) -> (f a -> f b -> f c -> f d)
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liftA4 :: Applicative f => ..
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```
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Where `liftA0 = pure` and `liftA1 = fmap`.
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# Monoidal functors
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- Remember Monoid?
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```haskell
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class Monoid m where
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mempty :: m
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mappend :: m -> m -> m
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```
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```haskell
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($) :: (a -> b) -> a -> b
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(<$>) :: (a -> b) -> f a -> f b
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(<*>) :: f (a -> b) -> f a -> f b
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mappend :: f f f
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($) :: (a -> b) -> a -> b
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<*> :: f (a -> b) -> f a -> f b
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instance Monoid a => Applicative ((,) a) where
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pure x = (mempty, x)
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(u, f) <*> (v, x) = (u `mappend` v, f x)
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```
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# Where are monoids again
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```haskell
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fmap (+1) ("blah", 0)
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("blah",1)
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("Woo", (+1)) <*> (" Hoo!", 0)
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("Woo Hoo!", 1)
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(,) <$> [1, 2] <*> [3, 4]
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[(1,3),(1,4),(2,3),(2,4)]
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liftA2 (,) [1, 2] [3, 4]
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[(1,3),(1,4),(2,3),(2,4)]
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```
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# Function apply
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- Applying a function to an `effectful` argument
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```haskell
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(<$>) :: Functor m => (a -> b) -> m a -> m b
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(<*>) :: Applicative m => m (a -> b) -> m a -> m b
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(=<<) :: Monad m => (a -> m b) -> m a -> m b
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```
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# Contrasts with monad
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- No data dependency between `f a` and `f b`
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- Result of `f a` can't possibly influence the behaviour of `f b`
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- That needs something like `a -> f b`
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# Applicative laws
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```haskell
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-- Identity
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pure id <*> v = v
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-- Composition
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pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
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-- Homomorphism
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pure f <*> pure x = pure (f x)
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-- Interchange
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u <*> pure y = pure ($ y) <*> u
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```
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# Operators[^7]
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- `pure` wraps up a pure value into some kind of Applicative
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- `liftA2` applies a pure function to the values inside two `Applicative` wrapped values
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- `<$>` operator version of `fmap`
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- `<*>` apply a wrapped function to a wrapped value
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- `*>`, `<*`
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[^7]: [FP Complete - Crash course to Applicative syntax](https://www.fpcomplete.com/haskell/tutorial/applicative-syntax/)
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# Applicative vs monads
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- Applicative
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* Effects
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* Batching and aggregation
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* Concurrency/Independent
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- Parsing context free grammar
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- Exploring all branches of computation (see [`Alternative`](https://hackage.haskell.org/package/base-4.20.0.1/docs/Control-Applicative.html#t:Alternative))
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- Monads
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* Effects
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* Composition
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* Sequence/Dependent
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- Parsing context sensitive grammar
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- Branching on previous results
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# Weaker but better
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- Weaker than monads but thus also more common
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- Lends itself to optimisation (See Facebook's [Haxl](https://hackage.haskell.org/package/haxl) project)
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- Always opt for the least powerful mechanism to get things done
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- No dependency issues or branching? just use applicative
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# Resources
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- [Applicative Programming with Effects](https://www.staff.city.ac.uk/~ross/papers/Applicative.html)
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- [optparse-applicative](https://hackage.haskell.org/package/optparse-applicative)
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- [Control Applicative](https://hackage.haskell.org/package/base-4.19.1.0/docs/Control-Applicative.html)
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- [Applicative functors for fun & parsing](https://arunraghavan.net/2018/02/applicative-functors-for-fun-and-parsing/)
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# Questions
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- Reach out on
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* Email: sanchayan@sanchayanmaity.net
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* Mastodon: [sanchayanmaity.com](https://sanchayanmaity.com/@sanchayan)
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* Telegram: [t.me/SanchayanMaity](https://t.me/SanchayanMaity)
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* Blog: [sanchayanmaity.net](https://sanchayanmaity.net/)
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