In this article, we see the Optional class in action through two use cases involving java.util.Map instances. The first use case is a very basic one. It shows how to use the Optional class. The second use case is based on a problem I’ve met in a real project. We’ll see if Optional is helpful in this case.

Optional vs. null

Suppose that you want to get a value from a Map. The value is supposed to be located under the key "a", but you aren’t sure. In the case where the key "a" doesn’t exist, the Map implementation is supposed to return null. But, you want to continue with a default value.

Here, you have two solutions. This one

Integer value = map.get("a");
if (value == null) {
    value = DEFAULT;
}
process(value);

And, this one

Integer value = map.get("a");
process(value == null ? DEFAULT : value);

In order to use the Optional class, we need to define a new accessor for Map instances.

public static <K, V> Optional<V> getFrom(Map<K, V> map, K key) {
    V value = map.get(key);
    if (value == null) return Optional.absent();
    else return Optional.of(value);
}

We notice that you can instantiate Optional by different ways: 1/ by a call to Optional.absent() if there is nothing to return (except the Optional instance), 2/ by of call to Optional.of(value) if you want to return a value. It sounds logical that an accessor to Map returns an Optional, because you aren’t sure that the given key exists in the Map instance.

Below is the same program but using Optional class.

process(getFrom(map, "a").or(DEFAULT));

With this code, we don’t see null anymore.

Going further: Optional to the limit

Now, we suppose that we develop a application based on a set of products differentiated by a unique identifier. The products are organized by product identifier, supplier, city, and country. In order to stock these products, imbricated Map are used: the first level uses the country, the second level uses the city, the third level uses the supplier, and the fourth level uses the product identifier to give access to the product. Here is the code you get with no use of Optional class (please, don’t do this at work! Seriously, don’t do this!)

public Product getProductFrom(
  Map<String, Map<String, Map<String, Map<String, Product>>>> productsByCountry,
  String country, String city, String supplier, String code) {

    Map<String, Map<String, Map<String, Product>>> productsByCity = productsByCountry.get(country);
    if (productsByCity != null) {
        Map<String, Map<String, Product>> productsBySupplier = productsByCity.get(city);
        if (productsBySupplier != null) {
            Map<String, Product> productsByCode = productsBySupplier.get(supplier);
            if (productsByCode != null) {
                return productByCode.get(code);
            }
        }
    }
    return null;
}

This doesn’t sounds great, is it?

Now, below is the solution using Optional class.

public Optional<Product> getProductFrom(
  Map<String, Map<String, Map<String, Map<String, Product>>>> productsByCountry,
  String country, String city, String supplier, String code) {

    Optional<Map<String, Map<String, Map<String, Product>>>> productsByCity
        = getFrom(productsByCountry, country);
    if (productsByCity.isPresent()) {
        Optional<Map<String, Map<String, Product>>> productsBySupplier
            = getFrom(productsByCity.get(), city);
        if (productsBySupplier.isPresent()) {
            Optional<Map<String, Product>> productsByCode
                = getFrom(productsBySupplier.get(), supplier);
            if (productsByCode.isPresent()) {
                return getFrom(productByCode.get(), code);
            }
        }
    }
    return Optional.absent();
}

It looks ugly too!

In a view to simplified this implementation, I propose to introduce the notion of monad.

Option(al) monad

A monad is a programming structure with two operations: unit and bind. Applied to the Optional class, unit converts a value into an Optional instance and bind applied to an Optional a function from value to Optional. Below, you’ve there definitions in Java:

public class OptionalMonad {
    public static <T> Optional<T> unit(T value) {
        return Optional.of(value);
    }

    public static <T, U> Optional<U> bind(
            Optional<T> value,
            Function<T, Optional<U>> function) {
        if (value.isPresent()) return function.apply(value.get());
        else return Optional.absent();
    }
}

Notice that bind checks the presence of a value before to apply the function.

Now, to be used by our example in the section above, we need to define a function that will be used as parameter for the bind operator. This function is based on the method getFrom, previously defined, which gives access to a value of a Map from a given key.

public static <K, V> Function<Map<K, V>, Optional<V>> getFromKey(final K key) {
    return new Function<Map<K, V>, Optional<V>>() {
        @Override
        public Optional<V> apply(Map<K, V> map) {
            return getFrom(map, key);
        }
    };
}

Here is the new code

public Optional<Product> getProductFrom(
  Map<String, Map<String, Map<String, Map<String, Product>>>> productsByCountry,
  String country, String city, String supplier, String code) {

    Optional<Map<String, Map<String, Map<String, Product>>>> productsByCity
        = bind(unit(productsByCountry), Maps2.<String, Map<String, Map<String, Map<String, Product>>>>getFromKey(country));
    Optional<Map<String, Map<String, Product>>> productsBySupplier
        = bind(productsByCity, Maps2.<String, Map<String, Map<String, Product>>>getFromKey(city));
    Optional<Map<String, Product>> productsByCode
        = bind(productsBySupplier, Maps2.<String, Map<String, Product>>getFromKey(supplier));
    Optional<Product> product
        = bind(productsByCode, Maps2.<String, Product>getFromKey(code));

    return product;
}

Or more directly

public Optional<Product> getProductFrom(
  Map<String, Map<String, Map<String, Map<String, Product>>>> productsByCountry,
  String country, String city, String supplier, String code) {

  return bind(bind(bind(bind(unit(productsByCountry),
    Maps2.<String, Map<String, Map<String, Map<String, Product>>>>getFromKey(country)),
    Maps2.<String, Map<String, Map<String, Product>>>getFromKey(city)),
    Maps2.<String, Map<String, Product>>getFromKey(supplier)),
    Maps2.<String, Product>getFromKey(code));
}

OK! It’s weird too. We have to ‘fight’ with inline recursive calls of the bind method and also with Java generics. The Java type inference system isn’t sufficiently powerful to guess them. To reduce occurrences of generics in this code, we could have written a specific version of getFromKey method for each part of the given Map: getFromCountry, getFromCity, getFromSupplier, etc. This moves and distributes the complexity of the code in those methods.

public Map<String, Map<String, Map<String, Product>>> getFromCountry(String country) {
  // type inference system knows what to do here
  return Maps2.getFromKey(country);
}

// declaration of the other methods here
// ...

public Optional<Product> getProductFrom(
  Map<String, Map<String, Map<String, Map<String, Product>>>> productsByCountry,
  String country, String city, String supplier, String code) {

  return bind(
    bind(
      bind(
        bind(
          unit(productsByCountry),
          getFromCountry(country)),
          getFromCity(city)),
          getFromSupplier(supplier)),
          getFromCode(code));
}

The positive side lies into the fact that the if imbrications have disappeared and the code is linear. Notice that due to the bind operator, if one of those call to getFromKey method returns an Optional.absent(), then all the following call to bind will also return an Optional.absent().

Is there an happy end for this?

It’s difficult to do something better in Java by using the Optional class (unless you have better solution). By considering another JVM language, you’ve below a solution in Scala.

def getProductFrom(products: Map[String, Map[String, Map[String, Map[String, Product]]]],
                   country: String, city: String, supplier: String, code: String): Option[Product] = {
  for (
    cities <- products.get(country);
    suppliers <- cities.get(city);
    codes <- vendors.get(supplier);
    product <- codes.get(code)
  ) yield product
}

Here, the for structure provides syntactic sugar to do something close to imperative programming. But in fact, each line in this for structure does the same thing as our previous implementations using the bind operator. The get method here acts the same way as our getFrom method by returning an instance of the type Option. The type Option in Sala is equivalent to the type Optional in Guava. So when you call our Scala version of getProductFrom, if all your parameters appears in the Map, it returns a product. But if one of the parameter isn’t present, you get the default value.

In Other JVM languages proposes the safe-navigation or null-safe operator value?.method(), like in Groovy, in Fantom, in Gosu, etc. It checks if the value isn’t null before calling the method.

// get a product or null
product = products?.get(country)?.get(city)?.get(supplier)?.get(code)

For the kind of problems presented in this post, the null-safe operator does a better job than the monad approach. In fact, monads represent a programming structure with a really wider scope. Associated with types other than Optional, you can extend the application field of monads and get the necessary expressivity to explore non-determinism, concurrent programming, handle of errors, etc.

Conclusion

So, we’ve seen the class Optional provided by Guava in two use cases. For the simple case, we’ve seen how Optional helps to make null reference disappears. But for the complex case, we’ve seen that Optional alone provides no real advantage. Optional class can make the approach a little easier if we introduce the notion of Optional monad. Thereby, not only the null references disappear but also the recursive if structure. But, we have to fight with the Java generics. And even after this, the code is still hard to read.

It seems clear that to explore a recursive data structure made of Map with Java, you have to choose between to fight with if statements or to fight with generics. But, Java may be not the good language for this kind of problem. In other hand, you should ask yourself if using such a structure is a judicious choice?

In this post, we see the solutions of the exercises I’ve proposed and some explanation about the functional programming concepts used.

Factorial

Here is a reminder of the behavior of the factorial:

The factorial of a given integer n (or n!) is the product of the integers between 1 and n.

In imperative style, you write the factorial like this:

public static int factorial(int n) {
    int result = 1;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

The recursive solution in Java

The previous implementation of factorial is based explicitly on state manipulation: the variable result is changed successively in the for loop at each iteration. The functional approach dislike particularly the explicit manipulation of a state in the body of a function. Usually, functional programming prohibits the use of loops like for, while, repeat, etc., for this reason. The only way to express a loop is to use recursion (ie. a function that calls itself).

In Mathematics, you express the factorial recursively like this:

0! = 1
n! = n . (n – 1), for n > 0

Or in plain English:

The factorial of 0 is 1 and the factorial of n is the product between n and the factorial of the preceding integer.

The implementation in Java of the recursive factorial is closed to the mathematic definition:

public static int factorial(int n) {
    if (n == 0) return 1;
    else return n * factorial(n - 1);
}

Recursive solution in Guava

Guava proposes a function representation as object. It’s based on the generic interface Function<T, R>. It looks like this very simple implementation:

public interface Function<T, R> {
    R apply(T value);
}

T is the input type and R the returned type of the function. If you create an instance based on the interface Function, you’ve to defined the method apply(), that represents the body of the function. Here’s the implementation of the recursive version of factorial based on Guava:

Function<Integer, Integer> factorial = new Function<Integer, Integer>() {
    @Override public Integer apply(Integer n) {
        if (n == 0) return 1;
        else return n * apply(n - 1);
    }
};

If you want to use this function, you’ve to write this:

Integer result = factorial.apply(5);

The Guava approach has this particularity to allow you to declare recursive and anonymous functions:

Integer result = new Function<Integer, Integer>() {
    @Override public Integer apply(Integer n) {
        if (n == 0) return 1;
        else return n * apply(n - 1);
    }
}.apply(5);

Tail recursion in Java

There’s another way to implement the recursive version of the factorial. This approach consists in having the recursive call executed just before to return from the function. There must have no other instruction to execute between the recursive call and the return instruction. This approach is called tail recursion. The previous implementation isn’t a case of tail recursion, because you have to execute a multiplication between n and the value returned by the recursive call before to exit the function.

In order to implement a tail recursive factorial, we have to introduce a second parameter (named k) to the function. This parameter contains the partial result of the function through the successive recursive calls. Once the stop condition is reached, k contains the final result. Below, you’ve the implementation of the tail recursive factorial:

private static int fact(int n, int k) {
    if (n == 0) return k;
    else return fact(n - 1, n * k);
}

public static int factorial(int n) {
    return fact(n, 1);
}

Notice that for the first call, the parameter k is initialized to 1. This relates to the basis case: when n is 0 then the function should return 1.

Motivation behind the tail recursion

There’s an important difference in behavior between the recursive and the tail recursive implementations. These difference is visible through the the call stack. In the recursive case, the result is built as you come back from recursive calls. Here is the different states of the call stack in recursive version when we call factorial(5):

-> factorial(5)  // first call
  -> factorial(4)
    -> factorial(3)
      -> factorial(2)
        -> factorial(1)
          -> factorial(0)  // here, we've reached the stop condition
          <- 1
        <- 1 = 1 * 1  // all remaining multiplications are executed
      <- 2 = 2 * 1
    <- 6 = 3 * 2
  <- 24 = 4 * 6
<- 120 = 5 * 24  // we have computed the result in the last return

Now, you can see the call stack for the tail recursive implementation for the same call:

-> fact(5, 1)  // first call
  -> fact(4, 5)  // result is built through the successive calls
    -> fact(3, 20)
      -> fact(2, 60)
        -> fact(1, 120)
          -> fact(0, 120)  // here, we've reached the stop condition
          <- 120  // the final result is obtained directly in the last recursive call
        <- 120
      <- 120
    <- 120
  <- 120
<- 120

You can notice that when we’re coming back from the recursive calls here, the same value is returned. Thus, we can easily imagine to optimize the tail recursive implementation. In fact, there two possible optimizations at this level. The first one is call trampolining. It consists in generating some small modification where recursive call is marked bounce and return is marked landing. Then an external fonction is used to emulate the recursive calls based on a while loop.

The second optimization uses a deeper transformation of the source code, where the while loop is directly put inside the function body. For the tail recursive implementation of the factorial function, this second optimization would turn our source code into this:

public static int factorial(int n, int k) {
    while (!(n == 0)) {
        k = n * k;
        n = n - 1;
    }
    return k;
}

These optimizations prevent the deep use of the call stack. Thus, you have no occurrence of stack overflow. But, you might have an infinite loop if you mistype the stop condition. The advantage of the second optimization over the first one and all recursive implementations is that it’s really quick as there’s no use of the call stack. A language like Scala proposes this second optimization by default. A precise look at the produced bytecode shows the transformation of the recursive call into a goto.

These optimizations aren’t present in Java.

Notice that not all recursive functions can be converted to a tail recursive function. This is the case of the function that computes the Fibonnacci series. It based on the jonction of two recursive calls.

public static fib(int n) {
    if (n <= 1) return 1;
    else return fib(n-1) + fib(n-2);
}

Tail recursion in Guava

We’ve seen that the tail recursive implementation of the factorial needs two parameters. But in Guava, you can only define functions that accept a unique argument! So how do we do to transform a function of one argument into a function of two arguments?

There are two possibilities. The first one consists in creating a class that represents a pair of elements. Thus a function that takes two arguments is equivalent to a function that takes a pair of elements. The second possibility consists in using the curryfication. The curryfication is a use case of the higher order functions. With this, a function that takes many arguments is converted into a function that takes the first argument, and return a function that takes the second argument, and so on till we get the last argument. For example, the addition function (add) is typically a function of two arguments (a and b). You can write add in such a way that add takes a and return a function that waits for b. Once you get b, the function is evaluated. The interest of such an approach isn’t to force you to provide all parameters of a function at the same time. For our add function, you can use add directly to execute an addition: add.apply(1).apply(3) == 4. Or you can use add to define the function add_one just by providing the first parameter only: add_one = add.apply(1). Then, you can provide the second parameter when you want through add_one: add_one.apply(3) == 4.

Below is the implementation of tail recursive factorial based on Guava. The signature of this function is Function<Integer, Function<Integer, Integer>>. Here, you’ve to understand:

factorial is a function that takes a first parameter n and returns another function that takes a second parameter k and returns the factorial of n.

public class FactorialFunction implements Function<Integer, Function<Integer, Integer>> {
    @Override
    Function<Integer, Integer> apply(final Integer n) {
        return new Function<Integer, Integer>() {
            @Override
            public Integer apply(Integer k) {
                if (n == 0) return k;
                else return FactorialFunction.this.apply(n - 1).apply(k * n);
            }
        };
    }
}

FactorialFunction fact = new FactorialFunction();
Integer result = fact.apply(5).apply(1); // factorial of 5

Notice the use of FactorialFunction.this in order to use the outer object in the inner one. You have to reference the outer object in order to set all parameters before the recursive call. This forces you to create a named class to represent your factorial function.

Compare this implementation with the implementation below in Haskell, which is tail recursive and curryfied already. They’re both equivalent:

fact n k = if n == 0
  then k
  else fact (n-1) (n*k)

In fact, there are differences in the Guava implementation: it isn’t optimized and you create a new object for each recursive call.

Suppose that you want to declare a type that represents a pair of elements. We don’t know the type of these elements and they may have different types. In Scala, you’ll write something like this:

case class Pair[T1, T2](first: T1, second: T2)

// usage: val myPair = Pair(1, 2)

The implementation in Java below is a (hugely) simplified equivalent to the implementation in Scala:

public class Pair<T1, T2> {
    private T1 first;
    private T2 second;

    public Pair(T1 first, T2 second) {
        this.first = first;
        this.second = second;
    }

    public static <T1, T2> Pair<T1, T2> Pair(T1 first, T2 second) {
        return new Pair(first, second);
    }
}

Here is an example where I design a binary tree structure with the help of the Java version of Pair. Notice that with this approach, I don’t have to use the diamond declaration in the instantiation (ie. Pair<Integer, Pair<String, ...>>). It’s automatically determined by the type inference algorithm.

Pair<Integer, Pair<String, Pair<Boolean, Object>>> tree
  = Pair(1,
      Pair("hello",
        Pair(true, new Object())));

Now, you can say it’s really helpful!

Photo by Ulrich Vachon

We started from a configuration using Cake to manage the project, a text editor, and some unit tests. We’ve worked by pair, changing one member and switching roles time to time.

I must confess that it isn’t something easy to think FP and write a program in Clojure. But the cohesion of the group and the overall will to reach the goal made it easier to finally write a program that succeeded all the tests.

So, after 1 hour and 20 minutes, here’s the result of our dojo :

https://github.com/elefevre/dojo-at-lunch/blob/master/2011-09-21-nombres-premiers/test/prime_numbers/test/core.clj

Till then, there are different APIs that allow the developers to use functional programming with Java and they don’t have to learn a new the language.

My first article on the Xebia’s blog is available in French: http://blog.xebia.fr/2011/06/29/comparaison-dapi-java-de-programmation-fonctionnelle/

Introduction

You want to plan reservations for a room. Here are some reservations:

• From 4-Jan to 7-Jan, occupant: Mr. A
• From 10-Jan to 21-Jan, occupant: Mrs. B
• From 5-Feb to 18-Feb, occupant: Mr. A
• From 20-Feb to 3-Mar, occupant: Mr. C

Suppose that there is no possibility for a reservation to override another one. How do you determine in a programmatic way who is the occupant the 10-Feb? And the 19-Feb?

Algorithm

There are many possibilities to answer to those questions. Basically, one of them is to store the reservations in a set. When searching for an occupant at a given date, you walk through the set, testing each element. You stop when you have a reservation that contains the given date or when there is no more reservation to test. This is a linear search algorithm. In  the worst case, the time complexity is O(n), ie. when you have to test all elements and there is no matching element or the matching element is the last one.

To improve this algorithm, you can also use a binary search algorithm. It consists at each step in dividing the set of elements in two parts and continuing searching in one of those parts. This algorithm needs a set of sorted elements. Its time complexity is O(log(n)) in the worst case. This is better because if you have 7 elements, you will only need 3 tests against 7 for linear search, in the worst case. And if you have 1000 elements, you will only need 10 tests against 1000 for the linear version, in the worst case. However, with the binary search algorithm, you may lost time while sorting elements. Java proposes in classes java.util.Arrays and java.util.Collections the method sort() the uses the merge sort algorithm that guaranties a time complexity of O(n.log(n)). Thus, sorting + binary search is worst than a linear search, that doesn’t need a sorted set of elements. Note that Java SE proposes implementations of the binary search algorithm in the methods java.util.Arrays.binarySearch() and java.util.Collections.binarySearch().

Another approach to the binary search is to generate the corresponding binary tree. Indeed, the binary search algorithm is like a walk through a height-balanced binary tree. At each step of the algorithm, we select the left part (left branch) or right part (right branch) of the subset of elements (the subtree) according to a central element (a node). But the big difference is that if you apply an algorithm like the red-black tree for your binary tree, two aspects are guaranteed:

1. Each time you add an element, it is sorted with the rest of the tree.
2. The tree is height-balanced. It means that its maximal height is O(log(n)).

For such a tree, the operations insert and search cost of time is O(log(n)) each.

The class java.util.TreeMap represents such a height-balancing binary tree and uses the red-black tree algorithm. But what is even more interesting with this class, is that it provides the methods ceilingEntry() and floorEntry(). They return the map entry which key is the closest respectively after and before the given key.

Representation of a reservation

Below is the source code of a simplified class to represent such reservations. This implementation uses guava.

public class Reservation {
    public Date from;
    public Date to;
    public String occupant;

    public Reservation(Date from, Date to, String occupant) {
        this.from = from;
        this.to = to;
        this.occupant = occupant;
    }

    public boolean contains(Date date) {
        return !(from.after(date) || to.before(date));
    }

    @Override
    public String toString() {
        return Objects.toStringHelper(this)
            .add("from", from)
            .add("to", to)
            .add("occupant", occupant)
            .toString();
    }

    @Override
    public int hashCode() {
        return Objects.hashCode(from, to, occupant);
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj) {
            return true;
        }
        if (obj == null || !(obj instanceof Reservation)) {
            return false;
        }
        Reservation reservation = (Reservation) obj;
        return Objects.equals(from, reservation.from)
            && Objects.equals(to, reservation.to)
            && Objects.equals(occupant, reservation.occupant);
    }

}

We declare below all four reservations that you can find in the introduction at the top of the post.

Date from, to;
Calendar calendar = Calendar.getInstance();

calendar.set(2011, 0, 4);
from = calendar.getTime();
calendar.set(2011, 0, 7);
to = calendar.getTime();
Reservation reserv1MrA = new Reservation(from, to, "Mr. A");

calendar.set(2011, 0, 10);
from = calendar.getTime();
calendar.set(2011, 0, 21);
to = calendar.getTime();
Reservation reserv1MrsB = new Reservation(from, to, "Mrs. B");

calendar.set(2011, 1, 5);
from = calendar.getTime();
calendar.set(2011, 1, 18);
to = calendar.getTime();
Reservation reserv2MrA = new Reservation(from, to, "Mr. A");

calendar.set(2011, 1, 20);
from = calendar.getTime();
calendar.set(2011, 2, 3);
to = calendar.getTime();
Reservation reserv1MrC = new Reservation(from, to, "Mr. C");

How to find a reservation from a given date

I group a set of reservations in a class that I’ve called Planning. Once instantiated, you can add reservations (method add()) and you can get a reservation at a given date (method getReservationAt()).

There are two steps to get a reservation close to a date.

1. I first use the method floorEntry(). It gets you the map entry which key is the greatest one less than the given date.
2. Second, I check if the reservation (that is the value of the entry) contains the given date.

public class Planning {
    public final TreeMap<Date, Reservation> reservations;

    public Planning() {
        reservations = new TreeMap<Date, Reservation>();
    }

    public void add(Reservation reservation) {
        reservations.put(reservation.from, reservation);
    }

    public Reservation getReservationAt(Date date) {
        Entry<Date, Reservation> entry = reservations.floorEntry(date);
        if (entry == null) {
            return null;
        }
        Reservation reservation = entry.getValue();
        if (!reservation.contains(date)) {
            return null;
        }
        return reservation;
    }
}

Test

We first store the reservations declared above in a planning.

Planning planning = new Planning();
planning.add(reserv1MrA);
planning.add(reserv1MrsB);
planning.add(reserv2MrA);
planning.add(reserv1MrC);

Now, who has made a reservation the 10-Feb and the 19-Feb? (Here, I use FEST-assert as assertion API.)

Calendar calendar = Calendar.getInstance();

calendar.set(2011, 1, 10);
Date dateOfMrA = calendar.getTime();
assertThat(planning.getReservationAt(dateOfMrA).occupant).isEqualTo("Mr. A");

calendar.set(2011, 1, 19);
Date dateNoReservation = calendar.getTime();
assertThat(planning.getReservationAt(dateNoReservation)).isNull();

public class Point {
    public final int x;
    public final int y;

    public Point(int x, int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public int hashCode() {
        return Objects.hashCode(x, y);
    }

    @Override
    public boolean equals(Object obj) {
        if (obj == null || !(obj instanceof Point)) {
            return false;
        }
        Point point = (Point) obj;
        return x == point.x && y == point.y;
    }
}

Here is the class Rectangle:

public class Rectangle {
    public final Point start;
    public final Point end;

    public Rectangle(Point start, Point end) {
        this.start = start;
        this.end = end;
    }
}

I suppose that start.x < end.x and that start.y < end.y

I define the minimum and the maximum of two points as the point which coordinates are respectively the minimum and the maximum of the coordinates of the given points. For example, the minimum of the points (1, 4) and (3, 2) is (1, 2), and the maximum is (3, 4).

public class Points {
    // it's an utility class
    private Points() { throw new UnsupportedOperationException(); }

    public static Point min(Point p1, Point p2) {
        return new Point(Math.min(p1.x, p2.x), Math.min(p1.y, p2.y));
    }

    public static Point max(Point p1, Point p2) {
        return new Point(Math.max(p1.x, p2.x), Math.max(p1.y, p2.y));
    }
}

Now, I give the method Rectangle.contains() that checks if a point is inside a rectangle. The idea is to use the methods min() and max() between the given point and the rectangle edges as filters: if the computed point is different from the given point, then the given point is not in the rectangle.

import static Points.*;

public class Rectangle {
    // see code above...

    public boolean contains(Point point) {
        return point.equals(max(start, min(end, point)));
    }
}

If a switch-case statement that accepts strings as entries would be a revolution for you, the Scala’s pattern matching says that this is not enough! Indeed, there are other cases where a series of if-else-if statements would be generously transformed into a look-alike switch-case statement. For example, it would be really nice to simplify a series of instanceof and cast included in if-else-if to execute the good process according to the type of a parameter.

In this post, we see the power of the Scala’s pattern matching in different use cases.

Notice that the pattern matching is not something new. It is something that appears already in some other languages like OCaml, Haskell. A kind of pattern matching also exits in Prolog, but it uses a far different mechanism (unification in this case).

Traditional approach

There is an approach to the Scala’s pattern matching that looks similar to the switch-case structure in C and Java: each case entry use an integer or any scalar type. Here is an example:

def toYesOrNo(choice: Int): String = choice match {
    case 1 => "yes"
    case 0 => "no"
    case _ => "error"
  }

So if  you enter toYesOrNo(1), Scala says ”yes”. And if you enter toYesOrNo(2), Scala says “error”. Notice that the symbol _ is used to formulate the default case.You also have to remark that there is no need to use the break statement.

But if you want that Scala says “yes” when you enter toYesOrNo(1), toYesOrNo(2), or toYesOrNo(3), you will write the function like this:

def toYesOrNo(choice: Int): String = choice match {
    case 1 | 2 | 3 => "yes"
    case 0 => "no"
    case _ => "error"
  }

Now, you can use a string for each case entry. Using strings is interesting when you want to parse options of your applications:

def parseArgument(arg: String) = arg match {
    case "-h" | "--help" => displayHelp
    case "-v" | "--version" => displayVerion
    case whatever => unknownArgument(whatever)
  }

So if you enter parseArgument(“-h”) or parseArgument(“–help”), Scala calls the displayHelp function. And if you enter parseArgument(“huh?”), Scala calls unknownArgument(“huh?”).

Notice that I have not used _ for the default case. Instead, I have put an identifier as its value is used in the associated instruction.

Typed pattern

Sometimes in Java, you have to deal with an instance of something that appears like an Object or any high level classes or interfaces. After checking for nullity, you have to use series of if-else statements and instanceof-cast to check the class or the interface that the instance extends or implements, before using it and processing the instance correctly. This the case when you have to override the equals() method in Java. Here is the way Scala sees the thing:

def f(x: Any): String = x match {
    case i:Int => "integer: " + i
    case _:Double => "a double"
    case s:String => "I want to say " + s
  }

• f(1) → “integer: 1″
• f(1.0) → “a double”
• f(“hello”) → “I want to say hello”

Is not it better than a succession of if+instanceof+cast?

This kind of pattern matching is useful to walk through a structure using the composite design pattern. For example, you can use it to explore the DOM of an XML document or the object model of a JSON message.

Functional approach to pattern matching

A side effect of such a matching is that it provides an alternative way to design functions. For example, consider the factorial function. If you choose the recursive version, usually, you would define it like this:

def fact(n: Int): Int =
    if (n == 0) 1
    else n * fact(n - 1)

But you can use Scala’s pattern matching in this case:

def fact(n: Int): Int = n match {
    case 0 => 1
    case n => n * fact(n - 1)
  }

Notice the use of the variable n in this case. It is matched with any value that does not appears in the preceding cases. You have to understand that the n in the last case is not the same as the one used in the function signature. If you wanted to use the parameter n and not a new variable with the same name, you have to delimit the variable name with back-quote in the case definition, like this: `n`

Here is a simple way to build you factorial function in Scala:

def fact(n) = (1 to n).foldLeft(1) { _ * _ }

Pattern matching and collection: the look-alike approach

Pattern matching may be applied to the collections. Below is a function that computes the length of a list without pattern matching:

def length[A](list : List[A]) : Int = {
    if (list.isEmpty) 0
    else 1 + length(list.tail)
  }

Here is the same function with pattern matching:

def length[A](list : List[A]) : Int = list match {
    case _ :: tail => 1 + length(tail)
    case Nil => 0
  }

In this function, there are two cases. The last one checks if the list is empty with the Nil value. The first one checks if there is at least one element is the list. The notation _ :: tail should be understood “a list with whatever head followed by a tail”. Here the tail can be Nil (ie. empty list) or a non-empty list.

To go further, we will use this approach with tuples in order to improve our method parserArgument() above:

  def parseArgument(arg : String, value: Any) = (arg, value) match {
    case ("-l", lang) => setLanguageTo(lang)
    case ("-o" | "--optim", n : Int) if ((0 < n) && (n <= 5)) => setOptimizationLevelTo(n)
    case ("-o" | "--optim", badLevel) => badOptimizationLevel(badLevel)
    case ("-h" | "--help", null) => displayHelp()
    case bad => badArgument(bad)
  }

Notice first the use of the operator | that allows to match alternative forms of arg inside the tuple. Notice also the use of two patterns for options -o and --optim. These patterns are distinguished by the use of a guard condition. The guard conditions help you to get fine tuned pattern matching when pattern matching alone is not enough.

Advanced pattern matching: case class

Case classes are classes with part of their behavior predefined in order to make easier their construction and their use in a pattern. Case classes enables you to manipulate parameterized symbols for example, parsed by a compiler or used by your internal Domain Specific Language (DSL).

The example below shows how to use case classes and pattern matching in order to build simple mathematical expressions, evaluate them, and compute their derivative. First, lets define the symbol to represent expressions: the variable X, constants, addition, multiplication, and the negative operator (for the fun!). Here sealed means that there is no other children of the class Expression outside of the namespace.

  sealed abstract class Expression
  case class X() extends Expression
  case class Const(value : Int) extends Expression
  case class Add(left : Expression, right : Expression) extends Expression
  case class Mult(left : Expression, right : Expression) extends Expression
  case class Neg(expr : Expression) extends Expression

Now, lets define a function to evaluate expressions with a given value for the variable by using pattern matching.

  def eval(expression : Expression, xValue : Int) : Int = expression match {
    case X() => xValue
    case Const(cst) => cst
    case Add(left, right) => eval(left, xValue) + eval(right, xValue)
    case Mult(left, right) => eval(left, xValue) * eval(right, xValue)
    case Neg(expr) => - eval(expr, xValue)
  }

Lets try the eval() function:

val expr = Add(Const(1), Mult(Const(2), Mult(X(), X())))  // 1 + 2 * X*X
assert(eval(expr, 3) == 19)

Now, we define a function that compute the (unreduced) derivative of an expression:

  def deriv(expression : Expression) : Expression = expression match {
    case X() => Const(1)
    case Const(_) => Const(0)
    case Add(left, right) => Add(deriv(left), deriv(right))
    case Mult(left, right) => Add(Mult(deriv(left), right), Mult(left, deriv(right)))
    case Neg(expr) => Neg(deriv(expr))
  }

Lets try the deriv() function:

val df = deriv(expr)

Here is what you get in df:

Add(Const(0),Add(Mult(Const(0),Mult(X(),X())),Mult(Const(2),Add(Mult(Const(1),X()),Mult(X(),Const(1))))))
// = 0 + (0 * X*X + 2 * (1*X + X*1)) = 4 * X

assert(eval(df, 3), 12)

Other advanced pattern matching features

There are some special notations used in the Scala’s pattern matching. Scala allows to put aliases on patterns or on parts of a pattern. The alias is put before the part of the pattern, separated by @. For example, in the expression address @ Address(_, _, "Paris", "France"), we want any addresses in Paris/France, but we do not care about its content after the match is done. So after, we just use the alias address.

There is also a specific notation to match sequences with _*. It matches zero, one or more elements in a sequence to its end.

In Scala, pattern matching does not appears only after a the function match. You can put pattern matching in any closure and also in a catch block.

You can provide your own behavior for pattern matching. This is called extractor. To do so, you have to provide your own implementation of the unapply() method (and/or unapplySeq() for a sequence).

Conclusion

In this post, we have seen different ways to use the pattern matching with Scala. The main advantage of such a feature is to provide an easy way to build alternative structures based the matching of scalar values, strings, collections, but also types and parameterized symbols. For me, pattern matching is one of the sexiest alternatives to if statements! A good use of pattern matching can make your program really readable and helps you to build an internal DSL.

In this report, I use a twitter style composed of “tweets” (small messages) with fake #hashtag to highlight the topic. This style is more easy to use when you only have a smartphone to take notes. The tweets follow almost the chronological order.

Notice that some blocks of tweets are shifted to the right when it covers a more specific topic. Notice also that some of those tweets are in French, indicated by the tag [FR].

The report

Here I go for 2+1/2 weeks in #China. It’s the 3rd time.

Survival kit : #python and #scheme on my smartphone #imageek

Have seen just a part of the Taihu lake from the plane #china

I’ve just seen a giant thermometer on a blast furnace: #Shanghai#Expo 2010 ?

The last time, I’ve taken the maglev from Pudong airport to #Shanghai

Maglev: Magnetic Levitation train, speed=400km/h, so cooool ! (thx Siemens) #shanghai

Tested: there is no access to twitter from china

As tweeter isn’t accessible from china, I’ve noticed my tweets in my phone #imanolife

For my tweets I have my smartphone and a small notepad

Tested: there is no google.cn. google.com is forward to google.com.hk (hong-kong) by default

#China: world leader of “I fixed it” contest

#China is a quarter of a day in advance compared to France. I’m fully awake at 2am :/

Octobre in #Shanghai is like the end of August in Paris

It’s all foggy in #Shanghai and around: pollution or natural?

Shanghai Sculpture Space

At an art gallery at #Shanghai Sculpture Space in Red Town (http://www.sss570.com/)

“1 people 1 dream” said CN olympic games #china

“Be a better you” says Jiaotong University #shanghai

#Shanghai#Expo 2010: “Better City, Better Life”, and sometimes: “Deeper Freindship”

So cool! IT books worth only about 10 EUR… Even those in English from O’Really. And it seems to be legal #imageek #china

Bah! A computer in #Shanghai has the same price than in Europe

Wúxī (无锡) and Tài Hú Lake (太湖)

10-08: today, I visit #Wuxi and #Taihu lake

#Taihu lake: huge lake close to Shanghai: 2h by bus. It’s like a sea without waves

#Taihu lake: an average deep of 2m for more than 2000km² (see http://en.wikipedia.org/wiki/Taihu_Lake)

Poor #Taihu lake: a green alga on its surface gives the impression that someone has poured some paint

Auchan Carrefour Citroën Peugeot Ikea Mercedes Lamborghini etc.: am I in #China?

#China is one of the only country where you can see cars from all around the world

Chinese people are musicians: they like to play with the horn of their car #IWantToSleep#china

#Shanghai at night is outstanding: the buildings are covered with thousand of dancing lights

There’s even a building that displays a giant TV screen on its front #imahick #shanghai

The top of some buildings have a specific decoration: a crown, a palace entrance, an observatory, etc. #shanghai

There's a building top that looks like a golden mansion #shanghai

[FR] En #Chine, pas d’hypocrisie : on peut vraiment voir les fonctionnaires dormir à leur guichet lol

Bah! 17h and the night is falling already #shanghai

Liked: there’s a countdown for each traffic light, for cars, for pedestrians, for the red light and the green light #china

Good idea: on most of the street name signs, names are written in Chinese and in Pinyin/English #china

Good idea: on the street name sign, you know if you are on the east/west/north/south/middle side of the street and you know where are the other sides #china

Commerce is everywhere you can put an eye on. But concurrency is very hard #china

Today is 10-10-10… Binary for 42. OMG! what does means? #imageek

Today is 10-10-10… Doesn’t mean anything for #China :/

Zhūjiājiǎo (朱家角)

10-10: today, I visit #ZhuJiaJiao #china

There are very nice small villages (eg. #ZhuJiaJiao) with water channels like in Venice #shanghai

#ZhuJiaJiao is a city close to Shanghai: 1h by bus

If you don’t like touristic cities full of commerces like Mont-Saint-Michel, don’t come at #ZhuJiaJiao

There is a smell in the air of a mix of a sweet and/or fatty steamed foods #ZhuJiaJiao

Shanghai places and history

Some places in #Shanghai: The Bund, NanJing lu and People Square, HuaiHai lu, XuJiaHui, PuDong

#Shanghai is word with two syllables, so 2 Chinese characters: shang (上) = on, hai (海)= the sea

#Shanghai is mainly divided in 2 parts by the HuangPu river

#Shanghai was originally a village of fishers

During the 19th century, the main foreign countries has settled their concession around the Bund (west side of the HuangPu) #shanghai

Located in the south part of the city, the French concession has grown to the west #shanghai

We can find HuaiHai lu that was originally called Avenue Joffre #shanghai

#Shanghai is one of the most European cities in China. Here, I feel somewhat at home, compared to Beijing

Or is it the most New-Yorker of the European cities? #shanghai

Guìlín (桂林)

10-11: today I go to #Guilin for 3 days. It is full of beautiful landscape. 2h from Shanghai by plane

#Guilin is located in the Guangxi Zhuang region in the south of China (http://en.wikipedia.org/wiki/Guilin)

Going to test a domestic flight with Juneyao Airlines to go to #Guilin

OH! Changing the boarding gate two times, plane is late due to air flow (1h). WTF! #china

Inside the plane at last! Seems to be a small airbus (A320). The inside is nice #china

[FR] La nourriture à bord est acceptable pour une bouche française. #chine

[FR] ”Mini french bread” est une hérésie: ici, c’est un pain au lait assez sucré #chine

Tested: green clementine – it’s good and it leaves virtually no smell on your fingers #china

Has landed. The atmosphere is full of humidity #guilin

even bikes can drive on motorway! #guilin

people are poor. “There is nothing except tourism and past. #Guilin is like a beautiful woman with dirty clothes” said the guide

#Guilin landscape appears on 20 yuan bills, it also appears in Star Wars and Doom video game

Visiting by boat on the Li river (Li jiang in Chinese). Destination: Yangshou (http://wikitravel.org/en/Yangshuo). #Guilin landscape is really beautiful!

Li river: the water is almost clear and absolutly not deep #guilin

there’s a mountain with 9 horses naturally inscribed on. You can also see faces. Chinese people have a very strong imagination #guilin

now on board of a sort of raft made of 10 bamboo sticks. Never been so closed from water on a boat. #guilin

the water of the river is good, I would like to swin #guilin

The river is 6m deep max #guilin

Result: have crossed some small waterfalls and my bottom is a little wet – nice for the rest, it’s almost quiet #guilin

#Guilin altitude: about 200m

Yangshou: has seen an entertainment named “Impression Liu Sanjie”. Made by the famous Chinese movie director Zhang Yimou. Actors come from local villages. It was really beautiful #guilin

Yangshou: an American asked where I come from. I needed time not to answer “faguo” (法国)

Yangshou: There’s a street with a heavy crowd at night. It’s full of night bars with some individuals that dances in front #guilin

[FR] En France, 13 = malheur. En #Chine, 13 ne veut rien dire. Par contre, 8 = bonheur, 4 = mort/serpent/malheur

The small safe in the hotel is not sealed. It is lightweight and can be put in a large suitcase. Seriously WTF? #china

Chinese ancient imperial examination system has 7 levels #china

Have to pass an exam. 2′ to write the answers in Chinese with an old Chinese pencil. It’s really hard to write “I don’t know”! #guilin#china

Chinese exam: every student is behind a desk in a small cell. Students can’t cheat on each other #guilin#china

Have to go in a Japanese restaurant to drink a safe beer (Asahi). The food in the restaurant is really good and different compared the Japanese restaurant in France #guilin

#China really miss something important: cheese :p

taken in photos with 3 women from Shanghai wearing traditional clothes of #Guilin

have drunken some beer from #Guilin. It’s water with a taste of beer :/ QsingTao is better

/me made some adv. about France: good wines, perfums and cheeses  #FTW #guilin

end of trip in #Guilin. Good journey. Forgot everything about my French life except my language

plane from Guilin to Shanghai is one hour late too, due to air traffic congestion #china

#Shanghai at 3am is unrecognizable: the buildings have disappeared in the dark. The taxis have invaded the streets.  They lookout for the lost costumer

The taxis wait the customers even at the bus stop or at the restaurant exit #shanghai

My little Chinese guidebook confuses men’s/ladies’ restroom (to know the difference can save your life!)

It’s possible to hear some repeated explosions of firecrackers to wish happiness. This leaves some traces of red paper in the street #china

Shanghai Expo 2010 (中国2010年上海世界博览会)

Inside #Shanghai#Expo 2010 for one day

Space Home Pavilion: nothing to do here #shanghai#expo

Some interesting sculptures a the Shanghai shipyard pavilion #shanghai#expo

Pavilion of Future: giant books, light games, playing with senses… imagine the cities of tomorrow: exiting #shanghai#expo

have to cross the river. Too many people waiting for the ferry or the bus #shanghai#expo

Know what? The pavilions of North Korea and of Iran are neighbours #shanghai#expo

France Pavilion: Chinese faces, metalic roses on water, nice looking Citroën berlin car, vertical green elements #shanghai#expo

France Pavilion: has seen Léon, our French mascot #shanghai#expo

France Pavilion: “la ville sensuelle”, romantism with lounge music, time to time: Eiffel tower #shanghai#expo

France Pavilion: I’ve the feeling that this was an expo about Paris #shanghai#expo

Belgian fries (at Léon de Bruxelles) and waffles sold next to the Belgian/EU pavillon (no beer?) #shanghai#expo

Spain Pavilion: this one is really sensual with those women dancing flamengo! #shanghai#expo

Spain Pavilion: Picasso, horses that cross a room: yes! #shanghai#expo

Spain Pavilion: babies on curtains: nice! Giant baby at the end: o_O #shanghai#expo

UK Pavilion: only the transparent structure is interesting #shanghai#expo

Italy Pavilion: really like this one. Full of good surprises #shanghai#expo

Italy Pavilion: Ferrari, pasta, wine, many kind of art #shanghai#expo

Italy Pavilion: Italy, you have to remember that the ground floor is numbered 1 in China, not 0 #shanghai#expo

Luxembourg Pavilion: not so good #shanghai#expo

Would like to visit those pavilion: Algeria, Peru, China, China’s Petroleum #shanghai#expo

[FR] Il est vendu en #Chine des modèles de Peugeot 307 et 408 et de Citroën qu’on ne verra jamais en France

[FR] La Peugeot 206 n’a pas changé en dehors d’une inscription en chinois #chine

In #China, superstitions have also a long life

24°C in #Shanghai. The air is muggy

Jewelry made of jade is very popular #china

Wrong good idea: switch on the light in the hallway by hitting the floor with your foot #IWantToSleep #china

In #China, you don’t eat a yoghurt, you drink it… through a straw!

[FR] Viens de voir la photo de la famille présidentielle sur fond du pavillon français dans petit journal shanghaien #shanghai#expo

[FR] Carla y montre la mascotte française : Léon, un petit chat aux couleurs française #shanghai#expo

The Dream in the Red Chamber (Hóng Lóu Mèng - 红楼梦)

Grand View Garden (Dàguānyuán – 大观园) is a touristic place with a garden, a mansion, and a pagoda on a island. It’s a little frequent: it’s nice

#Daguanyuan represents the place where the story of “The Dream in the Red Chamber” (Le Rêve dans le Pavillon Rouge in French) would have held

“The Dream in the Red Chamber” is one the four important novels in the Chinese literature

#Daguanyuan is a place that is often used as a movie set. Each movie is an opportunity to restore the mansion

Many portals for building entrances in #China are folding, mounted on wheels and automated

Seen: Asian people in Tibetan dresses, dancing on a Tibetan music in front of a Tibetan restaurant #shanghai

Restaurant in China

The chic restaurant is located in a tower. You can ask for a private lounge (there a many) #china

In a Chinese restaurant, you usually find a large round table with a lazy Susan made of glass #china

Dishes arrive with the same rhythm. They are put on the lazy Susan. Everyone around the table helps oneself as he wants #china

A pair of chopsticks, a spoon made of porcelain, a bowl for the rice and the soup, a bowl for the tea, a small plate: here are your weapons to eat in #China

Just notice that china with a small ‘c’ means porcelain in English!

Seen: someone has dropped (not done on purpose) a bottle in a gutter. 5min later, an old man on a bike collected it in a view to sell it #shanghai

There’s no need for a street cleaning company, because poor people work on them already #shanghai

Bah! Spitting is a common practice #china

Have to back soon: it’s forecast 22°C in #Shanghai. In Paris, 7°C with a strike maybe Why should I come back?

I spent 2 weeks and a half in October wearing t-shirts and sunglasses #notashamed

I really forgot lots of thing about my French life. That’s what I call a good trip

Python is simple, so becoming a Python programmer is simple too!

How to learn to program in Python?

The answer is simple! Go to the address http://www.python.org/doc/ and click on the Tutorial link.

Once you have done with the tutorial, you will not be a strong Python programmer. In fact, at the end, you will be able to put most of your ideas into a Python script. It helps if you have experienced programming with another language and if you have some knowledge in object-oriented programming (OOP) — the last is optional. But, above all, it is necessary to have a sufficient open mind.

How to be a better Python programmer?

The answer is simple! Practice Python and read the source code of the files in the Python standard library ($PYTHONPATH/Lib).

Do not fear that kind of code, it will not bite you! By doing this, you will learn some patterns and some idioms used in Python. The bulk of the source code in the standard library is sufficiently clear.

How to become a strong Python programmer?

The answer is simple! Read the PEPs (Python Enhancement Proposals) starting from this one http://www.python.org/dev/peps/ and use google.

Here the goal is to explore what is unknown by most of the programmer or by other language. Do you know what is a generator or a decorator? Can the list comprehension make my life as a developer better? And what about the database API? The answers are in the PEPs and google.

For example, to learn more about Python’s decorators, take a look at http://www.python.org/dev/peps/pep-0318/.

Is this enough?

The answer is simple! Absolutely not!

All the answers here should be considered as starting points. After that, there are many things to explore. But, you have to do the same thing you would do with another language to improve your skill: explore forums, listen to conferences, answer to questions, and contribute.

To Infinity And Beyond

$ python -c "import this"
The Zen of Python, by Tim Peters

Beautiful is better than ugly.
Explicit is better than implicit.
Simple is better than complex.
Complex is better than complicated.
Flat is better than nested.
Sparse is better than dense.
Readability counts.
Special cases aren't special enough to break the rules.
Although practicality beats purity.
Errors should never pass silently.
Unless explicitly silenced.
In the face of ambiguity, refuse the temptation to guess.
There should be one-- and preferably only one --obvious way to do it.
Although that way may not be obvious at first unless you're Dutch.
Now is better than never.
Although never is often better than *right* now.
If the implementation is hard to explain, it's a bad idea.
If the implementation is easy to explain, it may be a good idea.
Namespaces are one honking great idea -- let's do more of those!