MAP, FILTER, REDUCE: Functional programming simplifies collections

@crichardson
Map(), ﬂatMap() and reduce() are your
new best friends:
Simpler collections, concurrency, and big
data
Chris Richardson
Author of POJOs in Action
Founder of the original CloudFoundry.com
@crichardson
chris@chrisrichardson.net
http://plainoldobjects.com

@crichardson
Presentation goal
How functional programming simpliﬁes
your code
Show that
map(), ﬂatMap() and reduce()
are remarkably versatile functions

@crichardson
About Chris
Founder of a buzzword compliant (stealthy, social, mobile,
big data, machine learning, ...) startup
Consultant helping organizations improve how they
architect and deploy applications using cloud, micro
services, polyglot applications, NoSQL, ...

@crichardson
Agenda
Why functional programming?
Simplifying collection processing
Eliminating NullPointerExceptions
Simplifying concurrency with Futures and Rx Observables
Tackling big data problems with functional programming

@crichardson
What’s functional
programming?

@crichardson
It’s a programming paradigm

@crichardson
It’s a kind of programming
language

@crichardson
Functions as the building
blocks of the application

@crichardson
Functions as ﬁrst class
citizens
Assign functions to variables
Store functions in ﬁelds
Use and write higher-order functions:
Pass functions as arguments
Return functions as values

@crichardson
Avoids mutable state
Use:
Immutable data structures
Single assignment variables
Some functional languages such as Haskell don’t side-effects
There are beneﬁts to immutability
Easier concurrency
More reliable code
But be pragmatic

@crichardson
"the highest goal of
programming-language
design to enable good
ideas to be elegantly
expressed"
http://en.wikipedia.org/wiki/Tony_Hoare

@crichardson
More expressive
More concise
More intuitive - solution matches problem deﬁnition
Elimination of error-prone mutable state
Easy parallelization

@crichardson
An ancient idea that has
recently become popular

@crichardson
Mathematical foundation:
λ-calculus
Introduced by
Alonzo Church in the 1930s

@crichardson
Lisp = an early functional
language invented in 1958
http://en.wikipedia.org/wiki/
Lisp_(programming_language)
1940
1950
1960
1970
1980
1990
2000
2010
garbage collection
dynamic typing
self-hosting compiler
tree data structures
(defun factorial (n)
(if (<= n 1)
1
(* n (factorial (- n 1)))))

@crichardson
My ﬁnal year project in 1985:
Implementing SASL
sieve (p:xs) =
p : sieve [x | x <- xs, rem x p > 0];
primes = sieve [2..]
A list of integers starting with 2
Filter out multiples of p

Mostly an Ivory Tower
technology
Lisp was used for AI
FP languages: Miranda,
ML, Haskell, ...
“Side-eﬀects
kills kittens and
puppies”

@crichardson
http://steve-yegge.blogspot.com/2010/12/haskell-researchers-announce-discovery.html
!*
!*
!*

@crichardson
But today FP is mainstream
Clojure - a dialect of Lisp
A hybrid OO/functional language
A hybrid OO/FP language for .NET
Java 8 has lambda expressions

@crichardson
Java 8 lambda expressions
are functions
x -> x * x
x -> {
for (int i = 2; i < Math.sqrt(x); i = i + 1) {
if (x % i == 0)
return false;
}
return true;
};
(x, y) -> x * x + y * y

@crichardson
Java 8 lambdas are a
shorthand* for an anonymous
inner class
* not exactly. See http://programmers.stackexchange.com/questions/
177879/type-inference-in-java-8

@crichardson
Java 8 functional interfaces
Interface with a single abstract method
e.g. Runnable, Callable, Spring’s TransactionCallback
A lambda expression is an instance of a functional
interface.
You can use a lambda wherever a function interface
“value” is expected
The type of the lambda expression is determined from it’s
context

@crichardson
Example Functional Interface
Function<Integer, Integer> square = x -> x * x;
BiFunction<Integer, Integer, Integer>
sumSquares = (x, y) -> x * x + y * y;
Predicate<Integer> makeIsDivisibleBy(int y) {
return x -> x % y == 0;
}
Predicate<Integer> isEven = makeIsDivisibleBy(2);
Assert.assertTrue(isEven.test(8));
Assert.assertFalse(isEven.test(11));

@crichardson
Example Functional Interface
ExecutorService executor = ...;
final int x = 999
Future<Boolean> outcome = executor.submit(() -> {
for (int i = 2; i < Math.sqrt(x); i = i + 1) {
if (x % i == 0)
return false;
}
return true;
}
This lambda is
a Callable

@crichardson
Lot’s of application code
=
collection processing:
Mapping, ﬁltering, and reducing

@crichardson
Social network example
public class Person {
enum Gender { MALE, FEMALE }
private Name name;
private LocalDate birthday;
private Gender gender;
private Hometown hometown;
private Set<Friend> friends = new HashSet<Friend>();
....
public class Friend {
private Person friend;
private LocalDate becameFriends;
...
}
public class SocialNetwork {
private Set<Person> people;
...

@crichardson
Mapping, ﬁltering, and
reducing
public Set<Hometown> hometownsOfFriends() {
Set<Hometown> result = new HashSet<>();
for (Friend friend : friends) {
result.add(friend.getPerson().getHometown());
}
return result;
}

@crichardson
reducing
public Set<Person> friendOfFriends() {
Set<Person> result = new HashSet();
for (Friend friend : friends)
for (Friend friendOfFriend : friend.getPerson().friends)
if (friendOfFriend.getPerson() != this)
result.add(friendOfFriend.getPerson());
return result;
}

@crichardson
reducing
...
public Set<Person> lonelyPeople() {
Set<Person> result = new HashSet<Person>();
for (Person p : people) {
if (p.getFriends().isEmpty())
result.add(p);
}
return result;
}

@crichardson
reducing
...
public int averageNumberOfFriends() {
int sum = 0;
sum += p.getFriends().size();
}
return sum / people.size();
}

@crichardson
Problems with this style of
programming
Low level
Imperative (how to do it) NOT declarative (what to do)
Verbose
Mutable variables are potentially error prone
Difﬁcult to parallelize

@crichardson
Java 8 streams to the rescue
A sequence of elements
“Wrapper” around a collection
Streams can also be inﬁnite
Provides a functional/lambda-based API for transforming,
ﬁltering and aggregating elements
Much simpler, cleaner code

@crichardson
Using Java 8 streams -
mapping
class Person ..
private Set<Friend> friends = ...;
return friends.stream()
.map(f -> f.getPerson().getHometown())
.collect(Collectors.toSet());
}

@crichardson
The map() function
s1 a b c d e ...
s2 f(a) f(b) f(c) f(d) f(e) ...
s2 = s1.map(f)

@crichardson
...
public Set<Person> peopleWithNoFriends() {
Set<Person> result = new HashSet<Person>();
if (p.getFriends().isEmpty())
result.add(p);
}
return result;
}
ﬁltering
...
public Set<Person> lonelyPeople() {
return people.stream()
.filter(p -> p.getFriends().isEmpty())
}

@crichardson
Using Java 8 streams - friend
of friends V1
class Person ..
Set<Set<Friend>> fof = friends.stream()
.map(friend -> friend.getPerson().friends)
...
}
Using map()
=> Set of Sets :-(
Somehow we need to flatten

@crichardson
mapping
class Person ..
.flatMap(friend -> friend.getPerson().friends.stream())
.map(Friend::getPerson)
.filter(f -> f != this)
}
maps and ﬂattens

@crichardson
The ﬂatMap() function
s1 a b ...
s2 f(a)0 f(a)1 f(b)0 f(b)1 f(b)2 ...
s2 = s1.ﬂatMap(f)

@crichardson
reducing
...
public long averageNumberOfFriends() {
return people.stream()
.map ( p -> p.getFriends().size() )
.reduce(0, (x, y) -> x + y)
/ people.size();
} int x = 0;
for (int y : inputStream)
x = x + y
return x;

@crichardson
The reduce() function
s1 a b c d e ...
x = s1.reduce(initial, f)
f(f(f(f(f(f(initial, a), b), c), d), e), ...)

@crichardson
Newton's method for ﬁnding square
roots
public class SquareRootCalculator {
public double squareRoot(double input, double precision) {
return
Stream.iterate(
new Result(1.0),
current -> refine(current, input, precision))
.filter(r -> r.done)
.findFirst().get().value;
}
private static Result refine(Result current,
double input, double precision) {
double value = current.value;
double newCurrent =
value - (value * value - input) / (2 * value);
boolean done = Math.abs(value - newCurrent) < precision;
return new Result(newCurrent, done);
}
class Result { boolean done; double value; }
Creates an inﬁnite stream:
seed, f(seed), f(f(seed)), .....
Don’t panic!
Streams are lazy

@crichardson
Tony’s $1B mistake
“I call it my billion-dollar mistake.
It was the invention of the null
reference in 1965....But I couldn't
resist the temptation to put in a
null reference, simply because it
was so easy to implement...”
http://qconlondon.com/london-2009/presentation/
Null+References:+The+Billion+Dollar+Mistake

@crichardson
Coding with null pointers
class Person
public Friend longestFriendship() {
Friend result = null;
if (result == null ||
friend.getBecameFriends()
.isBefore(result.getBecameFriends()))
result = friend;
}
return result;
}
Friend oldestFriend = person.longestFriendship();
if (oldestFriend != null) {
...
} else {
...
}
Null check is essential yet
easily forgotten

@crichardson
Java 8 Optional<T>
A wrapper for nullable references
It has two states:
empty throws an exception if you try to get the reference
non-empty contain a non-null reference
Provides methods for:
testing whether it has a value
getting the value
...
Return reference wrapped in an instance of this type instead of null

@crichardson
Coding with optionals
class Person
public Optional<Friend> longestFriendship() {
Friend result = null;
if (result == null ||
friend.getBecameFriends().isBefore(result.getBecameFriends()))
result = friend;
}
return Optional.ofNullable(result);
}
Optional<Friend> oldestFriend = person.longestFriendship();
// Might throw java.util.NoSuchElementException: No value present
// Person dangerous = popularPerson.get();
if (oldestFriend.isPresent) {
...oldestFriend.get()
} else {
...
}

@crichardson
Using Optionals - better
Optional<Friend> oldestFriendship = ...;
Friend whoToCall1 = oldestFriendship.orElse(mother);
Avoid calling isPresent() and get()
Friend whoToCall3 =
oldestFriendship.orElseThrow(
() -> new LonelyPersonException());
Friend whoToCall2 =
oldestFriendship.orElseGet(() -> lazilyFindSomeoneElse());

@crichardson
Using Optional.map()
public Optional<Friend> longestFriendship() {
return ...;
}
public Optional<Long> ageDifferenceWithOldestFriend() {
Optional<Friend> oldestFriend = longestFriendship();
return oldestFriend.map ( of ->
Math.abs(of.getPerson().getAge() - getAge())) );
}
Eliminates messy conditional logic

@crichardson
Using ﬂatMap()
class Person
public Optional<Friend> longestFriendship() {...}
public Optional<Friend> longestFriendshipOfLongestFriend() {
return
longestFriendship()
.flatMap(friend ->
friend.getPerson().longestFriendship());
}
not always a symmetric
relationship. :-)

@crichardson
Let’s imagine you are performing
a CPU intensive operation
class Person ..
.map(f -> cpuIntensiveOperation())
}

@crichardson
class Person ..
return friends.parallelStream()
.map(f -> cpuIntensiveOperation())
}
Parallel streams = simple
concurrency Potentially uses N cores
Nx speed up

@crichardson
Let’s imagine that you are
writing code to display the
products in a user’s wish list

@crichardson
The need for concurrency
Step #1
Web service request to get the user proﬁle including wish
list (list of product Ids)
Step #2
For each productId: web service request to get product info
Sequentially terrible response time
Need fetch productInfo concurrently

@crichardson
Futures are a great
concurrency abstraction
http://en.wikipedia.org/wiki/Futures_and_promises

@crichardson
Worker thread or
event-driven
Main thread
How futures work
Outcome
Future
Client
get
Asynchronous
operation
set
initiates

@crichardson
Beneﬁts
Simple way for two concurrent activities to communicate safely
Abstraction:
Client does not know how the asynchronous operation is
implemented
Easy to implement scatter/gather:
Scatter: Client can invoke multiple asynchronous operations
and gets a Future for each one.
Gather: Get values from the futures

@crichardson
Example wish list service
public interface UserService {
Future<UserProfile> getUserProfile(long userId);
}
public class UserServiceProxy implements UserService {
private ExecutorService executorService;
@Override
public Future<UserProfile> getUserProfile(long userId) {
return executorService.submit(() ->
restfulGet("http://uservice/user/" + userId,
UserProfile.class));
}
...
}
public interface ProductInfoService {
Future<ProductInfo> getProductInfo(long productId);
}

@crichardson
public class WishlistService {
private UserService userService;
private ProductInfoService productInfoService;
public Wishlist getWishlistDetails(long userId) throws Exception {
Future<UserProfile> userProfileFuture = userService.getUserProfile(userId);
UserProfile userProfile = userProfileFuture.get(300, TimeUnit.MILLISECONDS);
Example wish list service
get user
info
List<Future<ProductInfo>> productInfoFutures =
userProfile.getWishListProductIds().stream()
.map(productInfoService::getProductInfo)
.collect(Collectors.toList());
long deadline = System.currentTimeMillis() + 300;
List<ProductInfo> products = new ArrayList<ProductInfo>();
for (Future<ProductInfo> pif : productInfoFutures) {
long timeout = deadline - System.currentTimeMillis();
if (timeout <= 0) throw new TimeoutException(...);
products.add(pif.get(timeout, TimeUnit.MILLISECONDS));
}
...
return new Wishlist(products);
}
asynchronously
get all products
wait for
product
info

@crichardson
It works BUT
Code is very low-level and
messy
And, it’s blocking

@crichardson
Better: Futures with callbacks
no blocking!
def asyncSquare(x : Int)
: Future[Int] = ... x * x...
val f = asyncSquare(25)
Guava ListenableFutures, Spring 4 ListenableFuture
Java 8 CompletableFuture, Scala Futures
f onSuccess {
case x : Int => println(x)
}
f onFailure {
case e : Exception => println("exception thrown")
}
Partial function applied to
successful outcome
Applied to failed outcome

@crichardson
But
callback-based scatter/gather
Messy, tangled code
(aka. callback hell)

@crichardson
Functional futures - map
def asyncPlus(x : Int, y : Int) = ... x + y ...
val future2 = asyncPlus(4, 5).map{ _ * 3 }
assertEquals(27, Await.result(future2, 1 second))
Scala, Java 8 CompletableFuture
Asynchronously transforms
future

@crichardson
Functional futures - ﬂatMap()
val f2 = asyncPlus(5, 8).flatMap { x => asyncSquare(x) }
assertEquals(169, Await.result(f2, 1 second))
Scala, Java 8 CompletableFuture (partially)
Calls asyncSquare() with the eventual
outcome of asyncPlus()

@crichardson
ﬂatMap() is asynchronous
Outcome3f3
Outcome3
f2
f2 = f1 ﬂatMap (someFn)
Outcome1
f1
Implemented using callbacks
someFn(outcome1)

@crichardson
class WishListService(...) {
def getWishList(userId : Long) : Future[WishList] = {
userService.getUserProfile(userId) flatMap { userProfile =>
Scala wishlist service
val futureOfProductsList : Future[List[ProductInfo]] =
Future.sequence(listOfProductFutures)
val timeoutFuture = ...
Future.firstCompletedOf(Seq(wishlist, timeoutFuture))
}
}
val wishlist =
futureOfProductsList.map { products =>
WishList(products) }
val listOfProductFutures : List[Future[ProductInfo]] =
userProfile.wishListProductIds
.map { productInfoService.getProductInfo }

@crichardson
Using Java 8 CompletableFutures
public class UserServiceImpl implements UserService {
@Override
public CompletableFuture<UserInfo> getUserInfo(long userId) {
return CompletableFuture.supplyAsync(
() -> httpGetRequest("http://myuservice/user" + userId,
UserInfo.class));
}
Runs in ExecutorService

@crichardson
Using Java 8 CompletableFutures
public CompletableFuture<Wishlist> getWishlistDetails(long userId) {
return userService.getUserProfile(userId).thenComposeAsync(userProfile -> {
Stream<CompletableFuture<ProductInfo>> s1 =
userProfile.getWishListProductIds()
.stream()
.map(productInfoService::getProductInfo);
Stream<CompletableFuture<List<ProductInfo>>> s2 =
s1.map(fOfPi -> fOfPi.thenApplyAsync(pi -> Arrays.asList(pi)));
CompletableFuture<List<ProductInfo>> productInfos = s2
.reduce((f1, f2) -> f1.thenCombine(f2, ListUtils::union))
.orElse(CompletableFuture.completedFuture(Collections.emptyList()));
return productInfos.thenApply(list -> new Wishlist());
});
}
Java 8 is missing Future.sequence()
ﬂatMap()!
map()!

@crichardson
Introducing Reactive
Extensions (Rx)
The Reactive Extensions (Rx) is a library for composing
asynchronous and event-based programs using
observable sequences and LINQ-style query operators.
Using Rx, developers represent asynchronous data
streams with Observables , query asynchronous
data streams using LINQ operators , and .....
https://rx.codeplex.com/

@crichardson
About RxJava
Reactive Extensions (Rx) for the JVM
Original motivation for Netﬂix was to provide rich Futures
Implemented in Java
Adaptors for Scala, Groovy and Clojure
https://github.com/Netﬂix/RxJava

@crichardson
RxJava core concepts
trait Observable[T] {
def subscribe(observer : Observer[T]) : Subscription
...
}
trait Observer[T] {
def onNext(value : T)
def onCompleted()
def onError(e : Throwable)
}
Notiﬁes
An asynchronous stream of items
Used to
unsubscribe

Comparing Observable to...
Observer pattern - similar but
adds
Observer.onComplete()
Observer.onError()
Iterator pattern - mirror image
Push rather than pull
Futures - similar
Can be used as Futures
But Observables = a stream
of multiple values
Collections and Streams -
similar
Functional API supporting
map(), ﬂatMap(), ...
But Observables are
asynchronous

@crichardson
Fun with observables
val every10Seconds = Observable.interval(10 seconds)
-1 0 1 ...
t=0 t=10 t=20 ...
val oneItem = Observable.items(-1L)
val ticker = oneItem ++ every10Seconds
val subscription = ticker.subscribe { (value: Long) => println("value=" + value) }
...
subscription.unsubscribe()

@crichardson
def getTableStatus(tableName: String) : Observable[DynamoDbStatus]=
Observable { subscriber: Subscriber[DynamoDbMessage] =>
}
Connecting observables to the
outside world
amazonDynamoDBAsyncClient.describeTableAsync(
new DescribeTableRequest(tableName),
new AsyncHandler[DescribeTableRequest, DescribeTableResult] {
override def onSuccess(request: DescribeTableRequest,
result: DescribeTableResult) = {
subscriber.onNext(DynamoDbStatus(result.getTable.getTableStatus))
subscriber.onCompleted()
}
override def onError(exception: Exception) = exception match {
case t: ResourceNotFoundException =>
subscriber.onNext(DynamoDbStatus("NOT_FOUND"))
subscriber.onCompleted()
case _ =>
subscriber.onError(exception)
}
})
}

@crichardson
Transforming observables
val tableStatus = ticker.flatMap { i =>
logger.info("{}th describe table", i + 1)
getTableStatus(name)
}
Status1 Status2 Status3 ...
t=0 t=10 t=20 ...
+ Usual collection methods: map(), filter(), take(), drop(), ...

@crichardson
Calculating rolling average
class AverageTradePriceCalculator {
def calculateAverages(trades: Observable[Trade]):
Observable[AveragePrice] = {
...
}
case class Trade(
symbol : String,
price : Double,
quantity : Int
...
)
case class AveragePrice(
symbol : String,
price : Double,
...)

@crichardson
Calculating average pricesdef calculateAverages(trades: Observable[Trade]): Observable[AveragePrice] = {
trades.groupBy(_.symbol).map { symbolAndTrades =>
val (symbol, tradesForSymbol) = symbolAndTrades
val openingEverySecond =
Observable.items(-1L) ++ Observable.interval(1 seconds)
def closingAfterSixSeconds(opening: Any) =
Observable.interval(6 seconds).take(1)
tradesForSymbol.window(...).map {
windowOfTradesForSymbol =>
windowOfTradesForSymbol.fold((0.0, 0, List[Double]())) { (soFar, trade) =>
val (sum, count, prices) = soFar
(sum + trade.price, count + trade.quantity, trade.price +: prices)
} map { x =>
val (sum, length, prices) = x
AveragePrice(symbol, sum / length, prices)
}
}.flatten
}.flatten
}

@crichardson
Let’s imagine that you want
to count word frequencies

@crichardson
Scala Word Count
val frequency : Map[String, Int] =
Source.fromFile("gettysburgaddress.txt").getLines()
.flatMap { _.split(" ") }.toList
frequency("THE") should be(11)
frequency("LIBERTY") should be(1)
.groupBy(identity)
.mapValues(_.length))
Map
Reduce

@crichardson
But how to scale to a cluster
of machines?

@crichardson
Apache Hadoop
Open-source software for reliable, scalable, distributed computing
Hadoop Distributed File System (HDFS)
Efﬁciently stores very large amounts of data
Files are partitioned and replicated across multiple machines
Hadoop MapReduce
Batch processing system
Provides plumbing for writing distributed jobs
Handles failures
...

@crichardson
Overview of MapReduce
Input
Data
Mapper
Mapper
Mapper
Reducer
Reducer
Reducer
Out
put
Data
Shufﬂe
(K,V)
(K,V)
(K,V)
(K,V)*
(K,V)*
(K,V)*
(K1,V, ....)*
(K2,V, ....)*
(K3,V, ....)*
(K,V)
(K,V)
(K,V)

@crichardson
MapReduce Word count -
mapperclass Map extends Mapper<LongWritable, Text, Text, IntWritable> {
private final static IntWritable one = new IntWritable(1);
private Text word = new Text();
public void map(LongWritable key, Text value, Context context) {
String line = value.toString();
StringTokenizer tokenizer = new StringTokenizer(line);
while (tokenizer.hasMoreTokens()) {
word.set(tokenizer.nextToken());
context.write(word, one);
}
}
}
(“Four”, 1), (“score”, 1), (“and”, 1), (“seven”, 1), ...
Four score and seven years
http://wiki.apache.org/hadoop/WordCount

@crichardson
Hadoop then shufﬂes the
key-value pairs...

@crichardson
MapReduce Word count -
reducer
class Reduce extends Reducer<Text, IntWritable, Text, IntWritable> {
public void reduce(Text key,
Iterable<IntWritable> values, Context context) {
int sum = 0;
for (IntWritable val : values) {
sum += val.get();
}
context.write(key, new IntWritable(sum));
}
}
(“the”, 11)
(“the”, (1, 1, 1, 1, 1, 1, ...))
http://wiki.apache.org/hadoop/WordCount

@crichardson
About MapReduce
Very simple programming abstract yet incredibly powerful
By chaining together multiple map/reduce jobs you can process
very large amounts of data
e.g. Apache Mahout for machine learning
But
Mappers and Reducers = verbose code
Development is challenging, e.g. unit testing is difﬁcult
It’s disk-based, batch processing slow

@crichardson
Scalding: Scala DSL for
MapReduce
class WordCountJob(args : Args) extends Job(args) {
TextLine( args("input") )
.flatMap('line -> 'word) { line : String => tokenize(line) }
.groupBy('word) { _.size }
.write( Tsv( args("output") ) )
def tokenize(text : String) : Array[String] = {
text.toLowerCase.replaceAll("[^a-zA-Z0-9s]", "")
.split("s+")
}
}
https://github.com/twitter/scalding
Expressive and unit testable
Each row is a map of
named ﬁelds

@crichardson
Apache Spark
Part of the Hadoop ecosystem
Key abstraction = Resilient Distributed Datasets (RDD)
Collection that is partitioned across cluster members
Operations are parallelized
Created from either a Scala collection or a Hadoop
supported datasource - HDFS, S3 etc
Can be cached in-memory for super-fast performance
Can be replicated for fault-tolerance
http://spark.apache.org

@crichardson
Spark Word Count
val sc = new SparkContext(...)
sc.textFile(“s3n://mybucket/...”)
.flatMap { _.split(" ")}
.groupBy(identity)
.mapValues(_.length)
.toArray.toMap
}
}
Expressive, unit testable and very fast

@crichardson
Summary
Functional programming enables the elegant expression of
good ideas in a wide variety of domains
map(), ﬂatMap() and reduce() are remarkably versatile
higher-order functions
Use FP and OOP together
Java 8 has taken a good ﬁrst step towards supporting FP

@crichardson
Questions?
@crichardson chris@chrisrichardson.net
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MAP, FILTER, REDUCE: Functional programming simplifies collections

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MAP, FILTER, REDUCE: Functional programming simplifies collections