What the f is a monad?

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What the ƒ is a Monad?
artist: Heni Sandoval

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Why this talk?

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Why should you care?
• Functional Programming is the new black
• Scala, C#, Clojure, Haskell, “JavaScript”, Java 8 etc..
• Java community is lagging behind
• C# introduced Lambdas in 2007 (C# 3.0)…
• Little knowledge of theoretical foundations
• Functor, applicative, monad etc..
• Perhaps Java is heading more towards FP, better be prepared

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Why should you care?
• Write “better” code
• Strong typing -> robust and expressive code
• Readability -> small functions that do less
• Immutability -> easier to reason the flow
• Reusable functions -> leaner code
• Simple when familiar

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What I want to do today?
• There are a lot of very good practical talks about FP
• A Pragmatist’s Guide to Functional Geekery by Michał Płachta
• g ∘ f patterns by Mario Fusco
• I want
• To give you insight into the underlying theory
• Simplify the theory so you remember
• To interest you to go and look for more
• Help you understand future readings about Monad

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Notations - Function Types
parseInt :: String -> int
public int parseInt(String i)
•f :: A -> B
A B
f
f
f Add :: int -> int -> int
public int add(int x, int y)

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Notations - Function Composition
f :: A -> B
g :: B -> C
g o f :: A -> C
o :: (A->B)->(B->C)->(A->C)
Function composition
A B C
f
f
g
g
g o f
g o f

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Higher Order Function
//first-order function
public int timesTwo(int i){
return i * 2;
}
//higher-order function
public Function<Integer, Integer> multiplyBy(int n){
return x -> x * n;
}
//higher-order function
public Function<Integer, Integer> twice(Function<Integer, Integer> f){
return i -> f.andThen(f).apply(i);
}

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Pure Functional
Programming

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Pure Functional Programming
• Programs composed of “pure” functions =>
• No side effects
• Can be “memoized” i.e. always return the same (i.e. it’s a map)
• Side effects are1
Modifying a variable
Modifying a data structure in place
Setting a field on an object
Throwing an exception or halting with an error
Printing to the console or reading user input
Reading from or writing to a file
Drawing on the screen
• Declarative style instead of imperative -> What not How1Chapter 1 of “Functional Programming”, Paul Chiusano & Runar Bjarnason

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•exceptions = partial function
A B
f
f
f
The partial
function is a
lie

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• How to make a useful program?
• => Minimise and control side effects
Side
effects
Pure
functions
Input Output
Database

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Functor
Optional<Integer> intOption = Optional.of(42);
Function<Integer, String> toStr = i -> i.toString();
Optional<String> strOption = intOption.map(toStr);
CompletableFuture<Integer> intFuture = completedFuture(42)
CompletableFuture<String> strFuture = intFuture.thenApply(f)
List<Integer> numbers = List.of(1, 2, 3);
List<String> strings =
numbers.stream().map(toStr).collect(Collectors.toList());

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Functor
• The function that creates the lifted function is called map
map (g)
F :: A -> F[A]
g :: A -> B
map :: (A -> B) -> F[A] -> F[B]
map(g) :: F[A] -> F[B]
g
F
F

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Functor
g
1 2 {}
1 2 {}
Some< >
map (g)
Empty<>
map (g)
map (g)
Optional< >
Some< > Empty<>

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Functor
• Functor Summary
• Container for types
• map “lifts” functions
• Lifted functions change the content of the box, not the box
• Structure is unchanged

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Functor
Definition
functor ≈ map

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Monad
• From Bartosz Milewski’s blog post on Monad
• Can you guess what this object is?
• Fixing CO2 scrubbers on board of Apollo 13
• Wart treatment
• Fixing Apple’s iPhone 4 dropped call issue
• Making a prom dress
• Building a suspension bridge

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Use case
input="126,3", output:126/3 = 42
public (String, String) split(String s){
return s.split(",")
}
public (double, double) parse((String, String) p){
return (parseDouble(p._1), parseDouble(p._2))
}
public double divide ((double, double) numbers){
return numbers._1 / numbers._2
}

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Use case
split
parse
divide

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split
parse
divide
divide ∘ parse ∘ split
Use case

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• Exceptions -> Partial functions
• We modify functions to return “embellished” results
f f
Use case
Wrapper

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Optional<T> Either<L, R>
Optional.of(“OK”)
Optional.empty()
Either.left(new Exception(“…”))
Either.right(“OK”)
Exception handling
Use case

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Asynchronous process
public String sayHello(){
return "Hello";
}
Use case
public CompletableFuture<String> sayHello(){
return CompletableFuture.supplyAsync(() -> {
return "Hello";
})
}

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Logging
public Pair<Integer, String> getMagicNumber(){
final StringBuilder builder = new StringBuilder();
builder.append("About to compute the numbern");
final int magicNumber = 126/3;
builder.append(“Finished computing the numbern");
return Pair.of(magicNumber, builder.toString());
}
Use case

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Environment
public Function<Properties, String> buildUrl(){
return properties -> {
final String host = properties.getProperty("host");
final String port = properties.getProperty("port");
return String.format("http://%s:%s", host, port);
}
}
Use case

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public Optional<(String,String)> split(String s)
public Optional<(double, double)> parse((String, String) p)
public Optional<double> divide ((double, double) numbers)
Let’s try with Optional
Use case

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Use case
public Optional<Double> myProgram(String s){
final Optional<(String,String)> split = split(s);
if(split.isPresent()){
final Optional<(double, double)> parse = parse(split.get());
if(parse.isPresent()){
final Optional<Double> result = divide(parse.get());
if(result.isPresent()){
return result.get();
}
}
}
return Optional.empty();
}

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split
parse
divide
Use case

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split
parse
divide
????
Use case

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f :: A -> M[B]
g :: B -> M[C]
g >=> f :: A -> M[C]
• How can we compose wrapped result types??
g
f
g >=> f
Use case

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f :: A -> M[B]
g :: B -> M[C]
map(g) o f :: A -> M[M[C]]
g >=> f :: A -> M[C]
Can we use a Functor??
map (g)
f
map (g) o f
We need something that can do M[M[T]] -> M[T]
g
Use case

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Monad
map g
f
flatten
flatten
flatten o map (g) o f
f :: A -> M[B]
g :: B -> M[C]
g >=> f :: A -> M[C]
g >=> f = flatten o map (g) o f
g

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Functor
Definition
Monad ≈ Functor + flatten

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Monad
flatmap (g) = flatten o map (g)
M :: A -> M[A]
f :: A -> M[B]
map ::(A -> B) -> M[A] -> M[B]
flatmap ::(A -> M[B]) -> M[A] -> M[B]
g >=> f = x -> flatmap(g)(f(x))
flatten
g
map g

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Monad
g >=> f = x -> flatmap(g)(f(x))
g >=> f = flatmap g f
>=> ≈ flatmap
add : int -> int -> int
a + b = add a b
+ ≈ add

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Monad
split
parse
divide
divide >=> parse >=> split

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Functor
Definition
monad ≈ flatmap

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Monad
• Exception handling
• Optional
• Either
• Asynchronous process
• CompletableFuture
• Logging
• Environment

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Monad
public static <T> CompletableFuture<T> completedFuture(T value)
public static <T> Optional<T> of(T value)
public static <T> Stream<T> of(T e)
flatmap ::(A -> M[B]) -> M[A] -> M[B]
pure :: A -> M[A]

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Monad
• Definition
• Functor + flatten
• flatmap
• Advantages
• Manage and control side effects
• Program with side effect as if they were not here
• Monad makes partial functions total
• Composes functions with side effects with flatmap

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Monad
public Optional<Double> myProgram(String s){
final Optional<(String,String)> split = split(s);
if(split.isPresent()){
final Optional<(double, double)> parse = parse(split.get());
if(parse.isPresent()){
final Optional<Double> result = divide(parse.get());
if(result.isPresent()){
return result.get();
}
}
}
return Optional.empty();
}

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Monad
public Optional<Double> myProgram(String s) {
return split(s)
.flatMap(split -> parse(split))
.flatMap(parse -> divide(parse));
}

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Monad
def split(s: String): Option[(String, String)] = ???
def parse(p: (String, String)): Option[(Double, Double)] = ???
def divide(n: (Double, Double)): Option[Double] = ???
def myProgram(s: String): Option[Double] = {
for {
split <- split(s)
parse <- parse(split)
divide <- divide(parse)
} yield divide
}

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Monad
Unmanaged SE Managed SE
Composable
Non composable
Monad

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Key takeaways
4. Monad allows composition of wrapper data types
g >=> f
3. Pick Monads for Embellished/wrapper types to manage side effects
1. Functor ≈ map
2. Monad ≈ flatmap

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Before you go
• Be pragmatic
• Keep an eye out

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What the ƒ is a monad?

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Sources
• Bartosz Milewski, “Category Theory for programmers”
• Video lectures
• Blog posts
• “Functional Programming” by Paul Chiusano & Runar Bjarnason
(ISBN 9781617290657)
• Pattern matching with Brian Goetz - 2017 JVMLS
• The art of Simplicity by Venkat Subramaniam (vJUG24 Key note)

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Thank you
• Thank you @BartoszMilewski
• Thank you @GeorgianaElenaL
• Thank you @JulienTruffaut

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Questions
?
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What the f is a monad?

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