The document discusses functional programming concepts like higher-order functions, function composition, currying, and lazy evaluation. It provides examples of implementing strategies like converting between units using functions and creating streams of prime numbers lazily to avoid stack overflows. Tail call optimization is mentioned as a way to avoid stack overflows with recursive functions.

1. trampolines, monoids
& other functional
amenities
This is NOT your
father's
by Mario Fusco
mario.fusco@gmail.com
twitter: @mariofusco
Laziness,

2. public static <T> void sort(List<T> list,
Comparator<? super T> c)
Essence of Functional Programming
Data and behaviors are the same thing!
Data
Behaviors
Collections.sort(persons,
(p1, p2) -> p1.getAge() – p2.getAge())

3. Higher-order functions
Are they so mind-blowing?

4. Higher-order functions
Are they so mind-blowing?
… but one of the most influent sw engineering
book is almost completely dedicated to them

5. Command
Template Method
Functions are more general and higher level abstractions
Factory
Strategy

6. public interface Converter {
double convert(double value);
}
public class AbstractConverter implements Converter {
public double convert(double value) {
return value * getConversionRate();
}
public abstract double getConversionRate();
}
public class Mi2KmConverter extends AbstractConverter {
public double getConversionRate() { return 1.609; }
}
public class Ou2GrConverter extends AbstractConverter {
public double getConversionRate() { return 28.345; }
}
A strategy pattern Converter

7. public List<Double> convertValues(List<Double> values,
Converter converter) {
List<Double> convertedValues = new ArrayList<Double>();
for (double value : values) {
convertedValues.add(converter.convert(value));
}
return convertedValues;
}
List<Double> values = Arrays.asList(10, 20, 50);
List<Double> convertedDistances =
convertValues(values, new Mi2KmConverter());
List<Double> convertedWeights =
convertValues(values, new Ou2GrConverter());
Using the Converter

8. A functional Converter
public class Converter implements
ExtendedBiFunction<Double, Double, Double> {
@Override
public Double apply(Double conversionRate, Double value) {
return conversionRate * value;
}
}
@FunctionalInterface
public interface ExtendedBiFunction<T, U, R> extends
BiFunction<T, U, R> {
default Function<U, R> curry1(T t) {
return u -> apply(t, u);
}
default Function<T, R> curry2(U u) {
return t -> apply(t, u);
}
}

9. Currying
Converter converter = new Converter();
double tenMilesInKm = converter.apply(1.609, 10.0);
Function<Double, Double> mi2kmConverter = converter.curry1(1.609);
double tenMilesInKm = mi2kmConverter.apply(10.0);
Converter
value
rate
result
Mi2km
Converter
value
rate=1.609
result
List<Double> values = Stream.of(10, 20, 50)
.map(new Converter().curry1(1.609))
.collect(toList())

10. Function Composition
Celsius  Fahrenheit : F = C * 9/5 + 32
Converter
value
rate=9/5

11. Function Composition
Celsius  Fahrenheit : F = C * 9/5 + 32
Converter
value
rate=9/5
andThen
n -> n+32
result

12. Function Composition
Celsius  Fahrenheit : F = C * 9/5 + 32
Converter
value
rate=9/5
andThen
n -> n+32
result
Celsius2FarenheitConverter
Function<Double, Double> c2fConverter =
new Converter().curry1(9.0/5)
.andThen(n -> n + 32);

13. More Function Composition
@FunctionalInterface
public interface ExtendedBiFunction<T, U, R> extends
BiFunction<T, U, R> {
default <V> ExtendedBiFunction<V, U, R>
compose1(Function<? super V, ? extends T> before) {
return (v, u) -> apply(before.apply(v), u);
}
default <V> ExtendedBiFunction<T, V, R>
compose2(Function<? super V, ? extends U> before) {
return (t, v) -> apply(t, before.apply(v));
}
}
default <V> Function<V, R>
compose(Function<? super V, ? extends T> before) {
return (V v) -> apply(before.apply(v));
}

14. More Function Composition
Fahrenheit  Celsius : C = (F - 32) * 5/9
Converter
rate=5/9
result

15. More Function Composition
Fahrenheit  Celsius : C = (F - 32) * 5/9
Converter
rate=5/9
value
n -> n-32
result
compose2

16. More Function Composition
Fahrenheit  Celsius : C = (F - 32) * 5/9
Converter
rate=5/9
value
n -> n-32
result
Farenheit2CelsiusConverter
Function<Double, Double> f2cConverter =
new Converter().compose2((Double n) -> n - 32)
.curry1(5.0/9);
Functions are building blocks to create other functions
compose2

17. Monoids
A monoid is a triple (T, ∗, z) such that ∗ is an associative binary operation on T, and z ∈ T has the property that for all
x ∈ T it holds that x∗z = z∗x = x.
interface Monoid<T> {
T append(T a, T b);
T zero();
}
class Appender implements Monoid<String> {
public String append(String a, String b) { return a + b; }
public String zero() { return ""; }
}
class Multiplier implements Monoid<Integer> {
public Integer append(Integer a, Integer b) { return a * b; }
public Integer zero() { return 1; }
}

18. Endomorphisms & Monoids
interface Endomorphism<A> extends Function<A, A> { }
interface EndoMonoid<A> extends Monoid<Endomorphism<A>> {
@Override
default Endomorphism<A> append(Endomorphism<A> f1,
Endomorphism<A> f2) {
return ???
}
@Override
default Endomorphism<A> zero() {
return ???
}
}

19. Endomorphisms & Monoids
interface Endomorphism<A> extends Function<A, A> { }
interface EndoMonoid<A> extends Monoid<Endomorphism<A>> {
@Override
default Endomorphism<A> append(Endomorphism<A> f1,
Endomorphism<A> f2) {
return ???
}
@Override
default Endomorphism<A> zero() {
return ???
}
}
f1.andThen(f2);
Function.identity();

20. public class SalaryCalculator {
// B = basic + 20%
public double plusAllowance(double d) { return d * 1.2; }
// C = B + 10%
public double plusBonus(double d) { return d * 1.1; }
// D = C - 30%
public double plusTax(double d) { return d * 0.7; }
// E = D - 10%
public double plusSurcharge(double d) { return d * 0.9; }
public double calculate(double basic, boolean[] flags) {
double salary = basic;
if (flags[0]) salary = plusAllowance(salary);
if (flags[1]) salary = plusBonus(salary);
if (flags[2]) salary = plusTax(salary);
if (flags[3]) salary = plusSurcharge(salary);
return salary;
}
}
SalaryCalculator

21. public class FluentEndoMonoid<A> implements EndoMonoid<A> {
private final Endomorphism<A> endo;
public FluentEndoMonoid(Endomorphism<A> endo) { this.endo = endo; }
public FluentEndoMonoid(Endomorphism<A> endo, boolean b) {
this.endo = b ? endo : zero();
}
public FluentEndoMonoid<A> add(Endomorphism<A> other) {
return new FluentEndoMonoid<A>(append(endo, other));
}
public FluentEndoMonoid<A> add(Endomorphism<A> other, boolean b) {
return add(b ? other : zero());
}
public Endomorphism<A> get() { return endo; }
public static <A> FluentEndoMonoid<A> endo(Endomorphism<A> f, boolean b) {
return new FluentEndoMonoid<A>(f, b);
}
}
FluentEndoMonoid

22. public class SalaryCalculator {
public double calculate(double basic, boolean [] flags) {
return getCalculator(bs).apply(basic);
}
public Endomorphism<Double> getCalculator(boolean[] flags) {
return endo(this::plusAllowance, flags[0])
.add(this::plusBonus, flags[1])
.add(this::plusTax, flags[2])
.add(this::plusSurcharge, flags[3])
.get();
}
}
Endomorphism<Double> f = salaryCalc.getCalculator(true, false, false, true);
double aliceNet = f.apply(alice.getIncome());
double brianNet = f.apply(brian.getIncome());
Functional SalaryCalculator
You can calculate a single salary …
… but also obtain a calculator for a given combination of flags (Factory)

23. Lazy Evaluation
Lazy evaluation (or call-by-name) is an evaluation strategy which delays the evaluation of an expression until its value is needed
I know what to do. Wake me up when you really need it

24. Creating a Stream of prime numbers
public static IntStream primes(int n) {
return IntStream.iterate(2, i -> i + 1)
.filter(n –> isPrime(n))
.limit(n);
}
public static boolean isPrime(int candidate) {
int candidateRoot = (int) Math.sqrt((double) candidate);
return IntStream.rangeClosed(2, candidateRoot)
.noneMatch(i -> candidate % i == 0);
}

25. Creating a Stream of prime numbers
public static IntStream primes(int n) {
return IntStream.iterate(2, i -> i + 1)
.filter(n –> isPrime(n))
.limit(n);
}
public static boolean isPrime(int candidate) {
int candidateRoot = (int) Math.sqrt((double) candidate);
return IntStream.rangeClosed(2, candidateRoot)
.noneMatch(i -> candidate % i == 0);
}
It iterates through every number every time to see if it can be exactly divided by a candidate number, but it would be enough to only test numbers that have been already classified as prime

26. Recursively creating a Stream of primes
static Intstream numbers() {
return IntStream.iterate(2, n -> n + 1);
}
static int head(IntStream numbers) {
return numbers.findFirst().getAsInt();
}
static IntStream tail(IntStream numbers) {
return numbers.skip(1);
}
static IntStream primes(IntStream numbers) {
int head = head(numbers);
return IntStream.concat(
IntStream.of(head),
primes(tail(numbers).filter(n -> n % head != 0))
);
}

27. Recursively creating a Stream of primes
static Intstream numbers() {
return IntStream.iterate(2, n -> n + 1);
}
static int head(IntStream numbers) {
return numbers.findFirst().getAsInt();
}
static IntStream tail(IntStream numbers) {
return numbers.skip(1);
}
static IntStream primes(IntStream numbers) {
int head = head(numbers);
return IntStream.concat(
IntStream.of(head),
primes(tail(numbers).filter(n -> n % head != 0))
);
}
Cannot invoke 2 terminal operations on the same Streams
Problems?
No lazy evaluation in Java leads to an endless recursion

28. Lazy evaluation in Scala
def numbers(n: Int): Stream[Int] = n #:: numbers(n+1)
def primes(numbers: Stream[Int]): Stream[Int] =
numbers.head #::
primes(numbers.tail filter (n -> n % numbers.head != 0))
lazy concatenation
In Scala the #:: method (lazy concatenation) returns immediately and the elements are evaluated only when needed

29. interface HeadTailList<T> {
T head();
LazyList<T> tail();
default boolean isEmpty() { return true; }
}
Implementing a lazy list in Java
class LazyList<T> implements HeadTailList<T> {
private final T head;
private final Supplier<MyList<T>> tail;
public LazyList(T head,
Supplier<HeadTailList<T>> tail) {
this.head = head;
this.tail = tail;
}
public T head() { return head; }
public HeadTailList<T> tail() { return tail.get(); }
public boolean isEmpty() { return false; }
}

30. … and its lazy filter
public HeadTailList<T> filter(Predicate<T> p) {
return isEmpty() ?
this :
p.test(head()) ?
new LazyList<>(head(), () -> tail().filter(p)) :
tail().filter(p);
}
2
3
4
5
6
7
8
9
2
3
5
7

31. Back to generating primes
static HeadTailList<Integer> primes(HeadTailList<Integer> numbers) {
return new LazyList<>(
numbers.head(),
() -> primes(numbers.tail()
.filter(n -> n % numbers.head() != 0)));
}
static LazyList<Integer> from(int n) {
return new LazyList<Integer>(n, () -> from(n+1));
}
LazyList<Integer> numbers = from(2);
int two = primes(numbers).head();
int three = primes(numbers).tail().head();
int five = primes(numbers).tail().tail().head();

32. Printing primes
static <T> void printAll(HeadTailList<T> list) {
while (!list.isEmpty()){
System.out.println(list.head());
list = list.tail();
}
}
printAll(primes(from(2)));
static <T> void printAll(HeadTailList<T> list) {
if (list.isEmpty()) return;
System.out.println(list.head());
printAll(list.tail());
}
printAll(primes(from(2)));

33. Iteration vs. Recursion
External Iteration public int sumAll(int n) { int result = 0; for (int i = 0; i <= n; i++) { result += i; } return result; }
Recursion public int sumAll(int n) { return n == 0 ? 0 : n + sumAll(n - 1); }
Internal Iteration public static int sumAll(int n) { return IntStream.rangeClosed(0, n).sum(); }

34. public class PalindromePredicate implements Predicate<String> {
@Override public boolean test(String s) {
return isPalindrome(s, 0, s.length()-1);
}
private boolean isPalindrome(String s, int start, int end) {
while (start < end && !isLetter(s.charAt(start))) start++;
while (start < end && !isLetter(s.charAt(end))) end--;
if (start >= end) return true;
if (toLowerCase(s.charAt(start)) !=
toLowerCase(s.charAt(end))) return false;
return isPalindrome(s, start+1, end-1);
}
}
Another Recursive Example
Tail Rescursive Call

35. What's the problem?
List<String> sentences = asList( "Dammit, I’m mad!",
"Rise to vote, sir!",
"Never odd or even",
"Never odd and even",
"Was it a car or a cat I saw?",
"Was it a car or a dog I saw?",
VERY_LONG_PALINDROME );
sentences.stream()
.filter(new PalindromePredicate())
.forEach(System.out::println);
Exception in thread "main" java.lang.StackOverflowError at java.lang.Character.getType(Character.java:6924) at java.lang.Character.isLetter(Character.java:5798) at java.lang.Character.isLetter(Character.java:5761) at org.javaz.trampoline.PalindromePredicate.isPalindrome(PalindromePredicate.java:17) at org.javaz.trampoline.PalindromePredicate.isPalindrome(PalindromePredicate.java:21) at org.javaz.trampoline.PalindromePredicate.isPalindrome(PalindromePredicate.java:21) at org.javaz.trampoline.PalindromePredicate.isPalindrome(PalindromePredicate.java:21) ……..

36. Tail Call Optimization
int func_a(int data) { data = do_this(data); return do_that(data); }
... | executing inside func_a()
push EIP | push current instruction pointer on stack
push data | push variable 'data' on the stack
jmp do_this | call do_this() by jumping to its address
... | executing inside do_this()
push EIP | push current instruction pointer on stack
push data | push variable 'data' on the stack
jmp do_that | call do_that() by jumping to its address
... | executing inside do_that()
pop data | prepare to return value of 'data'
pop EIP | return to do_this()
pop data | prepare to return value of 'data'
pop EIP | return to func_a()
pop data | prepare to return value of 'data'
pop EIP | return to func_a() caller
...

37. Tail Call Optimization
int func_a(int data) {
data = do_this(data);
return do_that(data);
}
... | executing inside func_a()
push EIP | push current instruction pointer on stack
push data | push variable 'data' on the stack
jmp do_this | call do_this() by jumping to its address
... | executing inside do_this()
push EIP | push current instruction pointer on stack
push data | push variable 'data' on the stack
jmp do_that | call do_that() by jumping to its address
... | executing inside do_that()
pop data | prepare to return value of 'data'
pop EIP | return to do_this()
pop data | prepare to return value of 'data'
pop EIP | return to func_a()
pop data | prepare to return value of 'data'
pop EIP | return to func_a() caller
...
caller
avoid putting instruction on stack

38. from Recursion to Tail Recursion
Recursion public int sumAll(int n) { return n == 0 ? 0 : n + sumAll(n - 1); }
Tail Recursion public int sumAll(int n) { return sumAll(n, 0); } private int sumAll(int n, int acc) { return n == 0 ? acc : sumAll(n – 1, acc + n); }

39. Tail Recursion in Scala
def isPalindrome(s: String): Boolean = isPalindrome(s, 0, s.length-1)
@tailrec
def isPalindrome(s: String, start: Int, end: Int): Boolean = {
val pos1 = nextLetter(s, start, end)
val pos2 = prevLetter(s, start, end)
if (pos1 >= pos2) return true
if (toLowerCase(s.charAt(pos1)) !=
toLowerCase(s.charAt(pos2))) return false
isPalindrome(s, pos1+1, pos2-1)
}
def nextLetter(s: String, start: Int, end: Int): Int =
if (start > end || isLetter(s.charAt(start))) start
else nextLetter(s, start+1, end)
def prevLetter(s: String, start: Int, end: Int): Int =
if (start > end || isLetter(s.charAt(end))) end
else prevLetter(s, start, end-1)

40. Tail Recursion in Java?
Scala (and many other functional languages) automatically perform tail call optimization at compile time
@tailrec annotation ensures the compiler will optimize a tail recursive function (i.e. you will get a compilation failure if you use it on a function that is not really tail recursive)
Java compiler doesn't perform any tail call optimization (and very likely won't do it in a near future)
How can we overcome this limitation and have StackOverflowError-free functions also in Java tail recursive methods?

41. Trampolines to the rescue
A trampoline is an iteration applying a list of functions. Each function returns the next function for the loop to run.
Func1
return
apply
Func2
return
apply
Func3
return
apply
FuncN
apply
…
result
return

42. Implementing the TailCall …
@FunctionalInterface public interface TailCall<T> { TailCall<T> apply(); default boolean isComplete() { return false; } default T result() { throw new UnsupportedOperationException(); } default T invoke() { return Stream.iterate(this, TailCall::apply) .filter(TailCall::isComplete) .findFirst() .get() .result(); } // ... missing terminal TailCall }

43. … and the terminal TailCall
public static <T> TailCall<T> done(final T value) {
return new TailCall<T>() {
@Override
public boolean isComplete() { return true; }
@Override
public T result() { return value; }
@Override
public TailCall<T> apply() {
throw new UnsupportedOperationException();
}
};
}

44. Using the Trampoline
public class PalindromePredicate implements Predicate<String> {
@Override public boolean test(String s) {
return isPalindrome(s, 0, s.length()-1).invoke();
}
private TailCall<Boolean> isPalindrome(String s, int start,
int end) {
while (start < end && !isLetter(s.charAt(start))) start++;
while (end > start && !isLetter(s.charAt(end))) end--;
if (start >= end) return done(true);
if (toLowerCase(s.charAt(start)) !=
toLowerCase(s.charAt(end))) return done(false);
int newStart = start + 1;
int newEnd = end - 1;
return () -> isPalindrome(s, newStart, newEnd);
}
}

46. Mario Fusco Red Hat – Senior Software Engineer
mario.fusco@gmail.com twitter: @mariofusco
Q
A
Thanks … Questions?