Applicative style programming

Applicative style
programming
jlgarhdez HaskellMADpepegar

Pepe García
Scala Engineer @ Fidesmo
Co-organizer @ HaskellMad & FP-MAD
Scala fan
Haskell Acolyth
Functional Programming Devotee

About this talk
Slides are available here:
http://es.slideshare.net/JosLuisGarcaHernndez/applicative-style-programming
Code is available here:
https://github.com/pepegar/Control.Applicative.Talk

What are we learning today?
● What are applicatives?
● When do we use them?
● Who is using them?
● How to use them?

What are applicatives?
Applicatives are an abstraction between functions and monads. And they open the
doors for the so called applicative style!

@jlgarhdez
class Functor f => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b

Let’s understand the typeclass:
It exposes a `pure` function, that puts a value inside the applicative context
And a `<*>` function, that applies a function inside an applicative context to the
content of another value with the same applicative context

Do you remember fmap from functors? Try to compare it with <*>
fmap :: (a -> b) -> f a -> f b
(<*>) :: f (a -> b) -> f a -> f b

Basically an Applicative is a Functor that can also apply a function contained in a
container to other container of the same type.
Prelude Control.Monad> let fn1 = x-> x * x
Prelude Control.Monad> let fn2 = x -> x + 33
Prelude Control.Monad> let fns = [fn1, fn2]
Prelude Control.Monad> :t fns
fns :: Num a => [a -> a]
Prelude Control.Monad> let nums = [1,2,3,4]
Prelude Control.Monad> :t nums
nums :: Num t => [t]
Prelude Control.Monad> fns <*> nums

A small example
As an example of Applicative Programming, let’s see how Applicative and
Monadic styles compare:

A small example
data Person = Person {
name :: String,
lastName :: String
} deriving Show
data Err = String
validateName :: String -> Either Err String
validateName n = if n == "Pepe" then Right n
else Left "name is not Pepe"
validateLastName :: String -> Either Err String
validateLastName l = if l == "García" then Right l
else Left "last name is not García"

A small example. Monadic
validatePersonM :: String -> String -> Either String Person
validatePersonM n l = do
vName <- validateName n
vLast <- validateLastName l
return $ Person vName vLast

A small example. Applicative
validatePersonA :: String -> String -> Either String Person
validatePersonA n l = Person <$> validateName n <*> validateLastName l

A small example. Applicative (2)
Why does the previous example work? Let’s dig a bit deeper on it:
Prelude> :t Person
Person :: String -> String -> Person
Prelude> :t Person <$> validateName "pepe"
Person <$> validateName "pepe" :: Either String (String -> Person)
Prelude> :t Person <$> validateName "pepe" <*> validateLastName "Garcia"
Person <$> validateName "pepe" <*> validateLastName "Garcia" :: Either String Person

A small example. Recap
So, what do we learn from our small example?
Monads are not a silver bullet, and can be replaced easily by Applicative Functors
when ordering is not important.

When to use applicatives?
When we need more than a functor, and less than a monad…
Sounds appealing, but WTF is this!?

When to use applicatives? Functor
Functor defines containers that can be mapped over.
class Functor f where
fmap :: (a -> b) -> f a -> f b

When to use applicatives? Monad
Monad defines containers allow operation sequencing!
class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a

Some rule-o-thumbs I use for detecting Monad overkill
● import Control.Applicative
● replace return with pure, liftM with (<$>) (or fmap or liftA), liftM2 with liftA2,
etc, and ap with (<*>)
● If your function signature was Monad m => ..., change to Applicative m => ...
(and maybe rename m to f or whatever).

When your do block can be substituted by liftM2/3/4...
becomes
validatePersonA n l = liftM2 Person $ validateName n $ validateLastName l

When your operations does not depend on each other
becomes
validatePersonA n l = Person <$> validateName n <*> validateLastName l

Who uses Applicative?
Applicative is being used all over the place nowadays. Some interesting examples
of its use are:
● HAXL. Efficient data access
● CmdTheLine. Command line argument parsing
● Validation. Data validation library
● Attoparsec. ByteString parsing library

How to use Applicatives?
@jlgarhdez
Applicatives are really easy to use. You just need to provide an instance of the
typeclass for your data type.
data Maybe a = Just a
| Nothing
instance Applicative Maybe where
pure = Just
Just f <*> m = fmap f m
Nothing <*> _m = Nothing

Or, you can go Free!

Free Applicatives
Create an applicative from any Functor

Free Applicatives.
data Ap f a where
Pure :: a -> Ap f a
Ap :: f a -> Ap f (a -> b) -> Ap f b
@jlgarhdez

Free Applicatives.
instance Functor (Ap f) where
fmap f (Pure a) = Pure (f a)
fmap f (Ap x y) = Ap x ((f .) <$> y)
instance Apply (Ap f) where
Pure f <.> y = fmap f y
Ap x y <.> z = Ap x (flip <$> y <.> z)
instance Applicative (Ap f) where
pure = Pure
Pure f <*> y = fmap f y
Ap x y <*> z = Ap x (flip <$> y <*> z)
@jlgarhdez

Free applicatives
@jlgarhdez
Now let’s create a small ADT and create a Free Applicative out of it!
import Control.Applicative.Free
import Control.Applicative
type Author = String
type Post = String
type Id = String
data BlogF a where
GetPost :: Id -> BlogF Post
GetAuthor :: Id -> BlogF Author
type Blog a = Ap BlogF a

And a bit of syntax…
getPost :: Id -> Blog Post
getPost id = liftAp $ GetPost id
getAuthor :: Id -> Blog Author
getAuthor id = liftAp $ GetAuthor id
Free applicatives
@jlgarhdez

Free applicatives
@jlgarhdez
Now, we might want to render a page of our blog:
data Page = Page {
post :: Post,
author :: Author
} deriving Show

Now, let’s do Applicative magic!

Free applicatives
@jlgarhdez
With all we have already learned, how would you implement the following?
renderPage :: Id -> Id -> Blog Page

Free applicatives
@jlgarhdez
With all we have already learned, how would you implement the following?
renderPage postId authorId = Page <$> getPost postId
<*> getAuthor authorId

But we are not doing anything in that
renderPage function

Let’s do, let’s interpret!

Free applicatives
@jlgarhdez
First, we need an interpreter. This interpreter is called Natural Transformation in
Category Theory, and transforms a value `f a` into a `g a`.
interpIO :: BlogF a -> IO a
interpIO (GetPost id) = putStrLn ("getting post " ++ show id ++ " from DB") *> pure "this is the post"
interpIO (GetAuthor id) = putStrLn ("getting author " ++ show id ++ " from DB") *> pure "Pepe García"

Free applicatives
@jlgarhdez
And, last but not least, wire everything together:
main :: IO ()
main = do
page <- runAp interpIO $ renderPage 1 1
print page

Abstract Syntax Trees
As you know, the most important part of functional programming is referential
transparency. This means creating values, not executing effects.
That’s what our free applicatives does, they create little programs, or Abstract
Syntax Trees

Applicatives AST
As you imagine from our
implementation, this Blog does
nothing, just create values. It does
not go to the DB to fetch
users/posts/whatever.
It just creates what is called an
Abstract Syntax Tree

Monadic AST
And, if we compare this AST with the
one created by its monadic
counterpart, implemented in terms of
monadic bind, we can see something
interesting.
We need to evaluate getPost 1 in
order to evaluate getAuthor 1

Applicative AST. Static Analysis
@jlgarhdez
Applicative functors’ ASTs allow you to explore them from the top down without
evaluating a single line of code! This technique is called static analysis, and is
awesome for:
● Optimizing performance (deduplicate requests, in a series of HTTP requests)
● Calculate dependencies automatically
● Lint your code

Static Analysis
Analysis of a program that does not evaluate the program.
It is possible with our Applicatives!

Static Analysis
@jlgarhdez
To demonstrate static analysis, let’s keep with our blog example:
data BlogF a where
GetPost :: Id -> BlogF Post
GetAuthor :: Id -> BlogF Author
GetComments :: Id -> BlogF [(Comment, Author)]
type Blog a = Ap BlogF a

Static Analysis
@jlgarhdez
Also some convenience functions:
getPost :: Id -> Blog Post
getPost id = liftAp $ GetPost id
getAuthor :: Id -> Blog Author
getAuthor id = liftAp $ GetAuthor id
getComments :: Id -> Blog [(Comment, Author)]
getComments id = liftAp $ GetComments id

Static Analysis
@jlgarhdez
Then, our renderPage would look like this:
renderPage post author = Page <$> getPost post
<*> getAuthor author
<*> getComments post

Static Analysis
@jlgarhdez
And, as explained before, we will need to interpret the AST
interpIO :: BlogF a -> IO a
interpIO (GetPost id) = putStrLn ("getting post " ++ show id ++ " from DB") *> pure "this is the
post"
interpIO (GetAuthor id) = putStrLn ("getting author " ++ show id ++ " from DB") *> pure "@pepe"
interpIO (GetComments id) = putStrLn ("getting comments for post " ++ show id ++ " from DB")
*> pure [
("this post rocks" , "@anler"),
("you're right, @anler" , "@lorenzo"),
("Oh boy, I love haskell so bad!" , "@dani"),
("Indeed, Haskell is better than Erlang!" , "@joseluis" )
]

Static Analysis
@jlgarhdez
But, the most amazing thing is that we can calculate the number of operations that
our renderProgram does, for example:
instance Monoid Int where
mempty = 0
mappend = (+)
countInstructions :: BlogF a -> Int
countInstructions _ = 1

Static Analysis
@jlgarhdez
But, the most amazing thing is that we can calculate the number of operations that
our renderProgram does, for example:
main :: IO ()
main = do
putStrLn "NUMBER OF REQUESTS TO THE DB:"
print instructions
putStrLn ""
putStrLn "PAGE RENDERING:"
page <- runAp interpIO page
print page
where instructions = runAp_ countInstructions page
page = renderPage 1 1

Composing Applicative
Functors
Unlike Monads, our Applicatives are closed on composition. This means that you
can provide an instance of Applicative for the product of any other two
applicatives!

Composing Applicative Functors
@jlgarhdez
data Product m n a = Product {
first :: m a,
second :: n a
}
instance (Functor m, Functor n) => Functor (Product m n) where
fmap f fa = Product (f <$> first fa) (f <$> second fa)
instance (Applicative m, Applicative n) => Applicative (Product m n) where
pure x = Product (pure x) (pure x)
mf <*> mx = Product (first mf <*> first mx) (second mf <*> second mx)

Applicative Do Notation
Created at Facebook, ApplicativeDo extension allows you to write Applicative
Code in a more familiar fashion, if you come from imperative programming.

{-# LANGUAGE ApplicativeDo #-}
renderPage postId authorId = do
post <- getPost postId
author <- getAuthor authorId
return $ Page post author
ApplicativeDo
@jlgarhdez

Recap

Recap
● Use more applicatives, they DO ROCK!
● Always separate domain modelling from interpretation (with free applicatives)
● Eliminate boilerplate with meta-programming (with static analysis)
● Keep writing your code in do-block style (with ApplicativeDo)
● Have fun!
● Bonus point: Convince your boss to use Haskell!

Bibliography
● Idioms: applicative programming with effects. McBride, Paterson
● The Essence of the Iterator Pattern. Gibbons, Oliveira
● Origami programming. Gibbons
● Static Analysis with Applicatives. Gergő Érdi

Applicative style programming

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