Presentation on Haskell applicative

This commit is contained in:
Sanchayan Maity 2024-04-15 23:17:57 +05:30
parent dbce183f0a
commit a920b9ff13
5 changed files with 205 additions and 0 deletions

11
applicative/Makefile Normal file
View file

@ -0,0 +1,11 @@
all:
make slide slideshow
slide:
pandoc -t beamer --include-in-header=./style.tex applicative.md -f markdown-implicit_figures -V colorlinks=true -V linkcolor=blue -V urlcolor=red -o applicative.pdf
slideshow:
pandoc -t beamer --include-in-header=./style.tex applicative.md -f markdown-implicit_figures -V colorlinks=true -V linkcolor=blue -V urlcolor=red -i -o applicative-slideshow.pdf
view:
zathura --mode=presentation applicative.pdf &

Binary file not shown.

193
applicative/applicative.md Normal file
View file

@ -0,0 +1,193 @@
---
title:
- Applicatives
author:
- Sanchayan Maity
theme:
- default
classoption:
- aspectratio=169
---
# Agenda
- Recap of Functors
- Applicative
# Functor[^1][^2]
```haskell
class Functor f where
fmap :: (a -> b) -> f a -> f b
(<$) :: a -> f b -> f a
```
Functors Laws
- Must preserve identity
```haskell
fmap id = id
```
- Must preserve composition of morphism
```haskell
fmap (f . g) == fmap f . fmap g
```
[^1]: [Category Design Pattern](https://www.haskellforall.com/2012/08/the-category-design-pattern.html)
[^2]: [Functor Design Pattern](https://www.haskellforall.com/2012/09/the-functor-design-pattern.html)
# Higher order kinds[^3]
- For something to be a functor, it has to be a first order kind.
[^3]: [Haskell's Kind System](https://diogocastro.com/blog/2018/10/17/haskells-kind-system-a-primer/)
# Applicative
```haskell
class Functor f => Applicative (f :: TYPE -> TYPE) where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
```
```haskell
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
```
```haskell
fmap f x = pure f <*> x
```
# Examples
```haskell
pure (+1) <*> [1..3]
[2, 3, 4]
[(*2), (*3)] <*> [4, 5]
[8,10,12,15]
("Woo", (+1)) <*> (" Hoo!", 0)
("Woo Hoo!", 1)
(Sum 2, (+1)) <*> (Sum 0, 0)
(Sum {getSum = 2}, 1)
(Product 3, (+9)) <*> (Product 2, 8)
(Product {getProduct = 6}, 17)
(,) <$> [1, 2] <*> [3, 4]
[(1,3),(1,4),(2,3),(2,4)]
```
# Lifting
- Seeing Functor as unary lifting and Applicative as n-ary lifting
```haskell
liftA0 :: Applicative f => (a) -> (f a)
liftA1 :: Functor f => (a -> b) -> (f a -> f b)
liftA2 :: Applicative f => (a -> b -> c) -> (f a -> f b -> f c)
liftA3 :: Applicative f => (a -> b -> c -> d) -> (f a -> f b -> f c -> f d)
liftA4 :: Applicative f => ..
```
Where `liftA0 = pure` and `liftA1 = fmap`.
# Monoidal functors
- Remember Monoid?
```haskell
class Monoid m where
mempty :: m
mappend :: m -> m -> m
```
```haskell
($) :: (a -> b) -> a -> b
(<$>) :: (a -> b) -> f a -> f b
(<*>) :: f (a -> b) -> f a -> f b
mappend :: f f f
($) :: (a -> b) -> a -> b
<*> :: f (a -> b) -> f a -> f b
instance Monoid a => Applicative ((,) a) where
pure x = (mempty, x)
(u, f) <*> (v, x) = (u `mappend` v, f x)
```
# Function apply
- Applying a function to an `effectful` argument
```haskell
(<$>) :: Functor m => (a -> b) -> m a -> m b
(<*>) :: Applicative m => m (a -> b) -> m a -> m b
(=<<) :: Monad m => (a -> m b) -> m a -> m b
```
# Contrasts with monad
- No data dependency between `f a` and `f b`
- Result of `f a` can't possibly influence the behaviour of `f b`
- That needs something like `a -> f b`
# Applicative laws
```haskell
-- Identity
pure id <*> v = v
-- Composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
-- Homomorphism
pure f <*> pure x = pure (f x)
-- Interchange
u <*> pure y = pure ($ y) <*> u
```
# Applicative vs monads
- Applicative
* Effects
* Batching and aggregation
* Concurrency/Independent
- Parsing context free grammar
- Exploring all branches of computation (see `Alternative`)
- Monads
* Effects
* Composition
* Sequence/Dependent
- Parsing context sensitive grammar
- Branching on previous results
# Weaker but better
- Weaker than monads but thus also more common
- Lends itself to optimisation (See Facebook's [Haxl](https://hackage.haskell.org/package/haxl) project)
- Always opt for the least powerful mechanism to get things done
- No dependency issues or branching? just use applicative
# Resources
- [Applicative Programming with Effects](https://www.staff.city.ac.uk/~ross/papers/Applicative.html)
- [optparse-applicative](https://hackage.haskell.org/package/optparse-applicative)
- [Control Applicative](https://hackage.haskell.org/package/base-4.19.1.0/docs/Control-Applicative.html)
# Questions
- Reach out on
* Email: sanchayan@sanchayanmaity.net
* Mastodon: [sanchayanmaity.com](https://sanchayanmaity.com/@sanchayan)
* Telegram: [t.me/SanchayanMaity](https://t.me/SanchayanMaity)
* Blog: [sanchayanmaity.net](https://sanchayanmaity.net/)

BIN
applicative/applicative.pdf Normal file

Binary file not shown.

1
applicative/style.tex Normal file
View file

@ -0,0 +1 @@
\logo{\includegraphics[height=0.5cm]{../images/Haskell.jpg}\vspace{220pt}\hspace{8pt}}