## Evaluation Rules

• Call by value: evaluates the function arguments before calling the function
• Call by name: evaluates the function first, and then evaluates the arguments if need be
def example = 2      // evaluated when called
val example = 2      // evaluated immediately
lazy val example = 2 // evaluated once when needed

def square(x: Double)    // call by value
def square(x: => Double) // call by name
def myFct(bindings: Int*) { ... } // bindings is a sequence of int, containing a varying # of arguments

## Higher order functions

These are functions that take a function as a parameter or return functions.

// sum() returns a function that takes two integers and returns an integer
def sum(f: Int => Int): (Int, Int) => Int = {
def sumf(a: Int, b: Int): Int = {...}
sumf
}

// same as above. Its type is (Int => Int) => (Int, Int) => Int
def sum(f: Int => Int)(a: Int, b: Int): Int = { ... }

// Called like this
sum((x: Int) => x * x * x)          // Anonymous function, i.e. does not have a name
sum(x => x * x * x)                 // Same anonymous function with type inferred

def cube(x: Int) => x * x * x
sum(x => x * x * x)(1, 10) // sum of cubes from 1 to 10
sum(cube)(1, 10)           // same as above

## Currying  ★

Converting a function with multiple arguments into a function with a single argument that returns another function.

def f(a: Int, b: Int): Int // uncurried version (type is (Int, Int) => Int)
def f(a: Int)(b: Int): Int // curried version (type is Int => Int => Int)

## Classes

class MyClass(x: Int, y: Int) {           // Defines a new type MyClass with a constructor
require(y > 0, "y must be positive")    // precondition, triggering an IllegalArgumentException if not met
def this (x: Int) = { ... }             // auxiliary constructor
def nb1 = x                             // public method computed every time it is called
def nb2 = y
private def test(a: Int): Int = { ... } // private method
val nb3 = x + y                         // computed only once
override def toString =                 // overridden method
member1 + ", " + member2
}

new MyClass(1, 2) // creates a new object of type

this references the current object, assert(<condition>) issues AssertionError if condition is not met. See scala.Predef for require,assume and assert.

## Operators

myObject myMethod 1 is the same as calling myObject.myMethod(1)    ★

Operator (i.e. function) names can be alphanumeric, symbolic (e.g. x1*+?%&vector_++counter_=)

The precedence of an operator is determined by its first character, with the following increasing order of priority:

(all letters)
|
^
&
< >
= !
:
+ -
* / %
(all other special characters)

The associativity of an operator is determined by its last character: Right-associative if ending with :, Left-associative otherwise.

Note that assignment operators have lowest precedence. (Read Scala Language Specification 2.9 sections 6.12.3, 6.12.4 for more info)

## Class hierarchies

abstract class TopLevel {     // abstract class
def method1(x: Int): Int   // abstract method
def method2(x: Int): Int = { ... }
}

class Level1 extends TopLevel {
def method1(x: Int): Int = { ... }
override def method2(x: Int): Int = { ...} // TopLevel's method2 needs to be explicitly overridden
}

object MyObject extends TopLevel { ... } // defines a singleton object. No other instance can be created

To create an runnable application in Scala:

object Hello {
def main(args: Array[String]) = println("Hello world")
}

or

object Hello extends App {
println("Hello World") }

## Class Organization

• Classes and objects are organized in packages (package myPackage).

• They can be referenced through import statements (import myPackage.MyClassimport myPackage._import myPackage.{MyClass1, MyClass2}import myPackage.{MyClass1 => A})

• They can also be directly referenced in the code with the fully qualified name (new myPackage.MyClass1)

• All members of packages scala and java.lang as well as all members of the object scala.Predef are automatically imported.

• Traits are similar to Java interfaces, except they can have non-abstract members:

trait Planar { ... }
class Square extends Shape with Planar
• General object hierarchy:

• scala.Any base type of all types. Has methods hashCode and toString that can be overloaded
• scala.AnyVal base type of all primitive types. (scala.Doublescala.Float, etc.)
• scala.AnyRef base type of all reference types. (alias of java.lang.Object, supertype of java.lang.Stringscala.List, any user-defined class)
• scala.Null is a subtype of any scala.AnyRef (null is the only instance of type Null), and scala.Nothing is a subtype of any other type without any instance.

## Type Parameters

Similar to C++ templates or Java generics. These can apply to classes, traits or functions.

class MyClass[T](arg1: T) { ... }
new MyClass[Int](1)
new MyClass(1)   // the type is being inferred, i.e. determined based on the value arguments

It is possible to restrict the type being used, e.g.

def myFct[T <: TopLevel](arg: T): T = { ... } // T must derive from TopLevel or be TopLevel
def myFct[T >: Level1](arg: T): T = { ... } // T must be a supertype of Level1 def myFct[T >: Level1 <: Top Level](arg: T): T = { ... }

## Variance

Given A <: B

If C[A] <: C[B]C is covariant

If C[A] >: C[B]C is contravariant

Otherwise C is nonvariant

class C[+A] { ... } // C is covariant: a C[A] variable can hold C[A] and all A's subtypes (the usual inheritance case)   Stack[T] is a subtype of Stack[S] if T is a subtype of S.
class C[-A] { ... } // C is contravariant: a C[A] variable can hold C[A] and all A's parents (contra or against the usual inheritance case, you can store an object in an Int for example). The opposite holds for type parameters that are tagged with a -.
class C[A] { ... } // C is nonvariant
def fun[T <: A](arg:T) // covariant, arg must be of type T or any of it's subclasses
def fun[T >: A](arg:T) // Contravariant, arg must be of type T or any of it's super class
scala> class Covariant[+A]
defined class Covariant

scala> val cv: Covariant[AnyRef] = new Covariant[String]
cv: Covariant[AnyRef] = Covariant@4035acf6

scala> val cv: Covariant[String] = new Covariant[AnyRef]
<console>:6: error: type mismatch;
found   : Covariant[AnyRef]
required: Covariant[String]
val cv: Covariant[String] = new Covariant[AnyRef]
^
scala> class Contravariant[-A]
defined class Contravariant

scala> val cv: Contravariant[String] = new Contravariant[AnyRef]
cv: Contravariant[AnyRef] = Contravariant@49fa7ba

scala> val fail: Contravariant[AnyRef] = new Contravariant[String]
<console>:6: error: type mismatch;
found   : Contravariant[String]
required: Contravariant[AnyRef]
val fail: Contravariant[AnyRef] = new Contravariant[String]
^

For a function, if A2 <: A1 and B1 <: B2, then A1 => B1 <: A2 => B2.

Functions must be contravariant in their argument types and covariant in their result types, e.g.

trait Function1[-T, +U] {
def apply(x: T): U
} // Variance check is OK because T is contravariant and U is covariant

class Array[+T] {
def update(x: T)
} // variance checks fails

Find out more about variance in lecture 4.4 and lecture 4.5

## Pattern Matching

Pattern matching is used for decomposing data structures:

unknownObject match {
case MyClass(n) => ...
case MyClass2(a, b) => ...
}

Here are a few example patterns

(someList: List[T]) match {
case Nil => ...          // empty list
case x :: Nil => ...     // list with only one element
case List(x) => ...      // same as above
case x :: xs => ...      // a list with at least one element. x is bound to the head,
// xs to the tail. xs could be Nil or some other list.
case 1 :: 2 :: cs => ... // lists that starts with 1 and then 2
case (x, y) :: ps => ... // a list where the head element is a pair
}

The last example shows that every pattern consists of sub-patterns: it only matches lists with at least one element, where that element is a pair. x and y are again patterns that could match only specific types.

### Options

Pattern matching can also be used for Option values. Some functions (like Map.get) return a value of type Option[T] which is either a value of type Some[T] or the value None:

val myMap = Map("a" -> 42, "b" -> 43)
def getMapValue(s: String): String = {
myMap get s match {
case Some(nb) => "Value found: " + nb
case None => "No value found"
}
}
getMapValue("a")  // "Value found: 42"
getMapValue("c")  // "No value found"

Most of the times when you write a pattern match on an option value, the same expression can be written more concisely using combinator methods of the Option class. For example, the function getMapValue can be written as follows:

def getMapValue(s: String): String =
myMap.get(s).map("Value found: " + _).getOrElse("No value found")  // nice

### Pattern Matching in Anonymous Functions

Pattern matches are also used quite often in anonymous functions:

val pairs: List[(Char, Int)] = ('a', 2) :: ('b', 3) :: Nil
val chars: List[Char] = pairs.map(p => p match {
case (ch, num) => ch
})

Instead of p => p match { case ... }, you can simply write {case ...}, so the above example becomes more concise:

val chars: List[Char] = pairs map {
case (ch, num) => ch         //ok!
}

## Collections

Scala defines several collection classes:

### Base Classes

• Iterable (collections you can iterate on)
• Seq (ordered sequences)
• Set
• Map (lookup data structure)

### Immutable Collections

• List (linked list, provides fast sequential access)
• Stream (same as List, except that the tail is evaluated only on demand)
• Vector (array-like type, implemented as tree of blocks, provides fast random access)
• Range (ordered sequence of integers with equal spacing)
• String (Java type, implicitly converted to a character sequence, so you can treat every string like a Seq[Char])
• Map (collection that maps keys to values)
• Set (collection without duplicate elements)

### Mutable Collections

• Array (Scala arrays are native JVM arrays at runtime, therefore they are very performant)
• Scala also has mutable maps and sets; these should only be used if there are performance issues with immutable types

### Examples

val fruitList = List("apples", "oranges", "pears")
// Alternative syntax for lists
val fruit = "apples" :: ("oranges" :: ("pears" :: Nil)) // parens optional, :: is right-associative
fruit.tail   // List("oranges", "pears")
val empty = List()
val empty = Nil

val nums = Vector("louis", "frank", "hiromi")
nums(1)                     // element at index 1, returns "frank", complexity O(log(n))
nums.updated(2, "helena")   // new vector with a different string at index 2, complexity O(log(n))

val fruitSet = Set("apple", "banana", "pear", "banana")
fruitSet.size    // returns 3: there are no duplicates, only one banana

val r: Range = 1 until 5 // 1, 2, 3, 4
val s: Range = 1 to 5    // 1, 2, 3, 4, 5
1 to 10 by 3  // 1, 4, 7, 10
6 to 1 by -2  // 6, 4, 2

val s = (1 to 6).toSet
s map (_ + 2) // adds 2 to each element of the set

val s = "Hello World"
s filter (c => c.isUpper) // returns "HW"; strings can be treated as Seq[Char]

// Operations on sequences
val xs = List(...)
xs.length   // number of elements, complexity O(n)
xs.last     // last element (exception if xs is empty), complexity O(n)
xs.init     // all elements of xs but the last (exception if xs is empty), complexity O(n)
xs take n   // first n elements of xs
xs drop n   // the rest of the collection after taking n elements
xs(n)       // the nth element of xs, complexity O(n)
xs ++ ys    // concatenation, complexity O(n)
xs.reverse  // reverse the order, complexity O(n)
xs updated(n, x)  // same list than xs, except at index n where it contains x, complexity O(n)
xs indexOf x      // the index of the first element equal to x (-1 otherwise)
xs contains x     // same as xs indexOf x >= 0
xs filter p       // returns a list of the elements that satisfy the predicate p
xs filterNot p    // filter with negated p
xs partition p    // same as (xs filter p, xs filterNot p), Partitions this sequence in two sequences according to a predicate.
xs takeWhile p    // take the longest prefix consisting of elements that satisfy p
xs dropWhile p    // the remainder of the list after any leading element satisfying p have been removed
xs span p         // same as (xs takeWhile p, xs dropWhile p)

List(x1, ..., xn) reduceLeft op    // (...(x1 op x2) op x3) op ...) op xn
List(x1, ..., xn).foldLeft(z)(op)  // (...( z op x1) op x2) op ...) op xn
List(x1, ..., xn) reduceRight op   // x1 op (... (x{n-1} op xn) ...)
List(x1, ..., xn).foldRight(z)(op) // x1 op (... (    xn op  z) ...)

xs exists p    // true if there is at least one element for which predicate p is true
xs forall p    // true if p(x) is true for all elements
xs zip ys      // returns a list of pairs which groups elements with same index together
xs unzip       // opposite of zip: returns a pair of two lists
xs.flatMap f   // applies the function to all elements and concatenates the result
xs.sum         // sum of elements of the numeric collection
xs.product     // product of elements of the numeric collection
xs.max         // maximum of collection
xs.min         // minimum of collection
xs.flatten     // flattens a collection of collection into a single-level collection
xs groupBy f   // returns a map which points to a list of elements
xs distinct    // sequence of distinct entries (removes duplicates)

x +: xs  // creates a new collection with leading element x
xs :+ x  // creates a new collection with trailing element x

// Operations on maps
val myMap = Map("I" -> 1, "V" -> 5, "X" -> 10)  // create a map
myMap("I")      // => 1
myMap("A")      // => java.util.NoSuchElementException
myMap get "A"   // => None
myMap get "I"   // => Some(1)
myMap.updated("V", 15)  // returns a new map where "V" maps to 15 (entry is updated)
// if the key ("V" here) does not exist, a new entry is added

// Operations on Streams
val xs = Stream(1, 2, 3)
val xs = Stream.cons(1, Stream.cons(2, Stream.empty)) // same as above
(1 to 1000).toStream // => Stream(1, ?)
x #:: xs // Same as Stream.cons(x, xs)
// In the Stream's cons operator, the second parameter (the tail)
// is defined as a "call by name" parameter.
// Note that x::xs always produces a List

## Pairs (similar for larger Tuples)

val pair = ("answer", 42)   // type: (String, Int)
val (label, value) = pair   // label = "answer", value = 42
pair._2 // 42

## Ordering

There is already a class in the standard library that represents orderings: scala.math.Ordering[T] which contains comparison functions such as lt() and gt() for standard types. Types with a single natural ordering should inherit from the trait scala.math.Ordered[T].

import math.Ordering

def msort[T](xs: List[T])(implicit ord: Ordering) = { ...}
msort(fruits)(Ordering.String)
msort(fruits)   // the compiler figures out the right ordering

## For-Comprehensions

A for-comprehension is syntactic sugar for mapflatMap and filter operations on collections.

The general form is for (s) yield e

• s is a sequence of generators and filters
• p <- e is a generator
• if f is a filter
• If there are several generators (equivalent of a nested loop), the last generator varies faster than the first
• You can use { s } instead of ( s ) if you want to use multiple lines without requiring semicolons
• e is an element of the resulting collection

### Example 1

// list all combinations of numbers x and y where x is drawn from
// 1 to M and y is drawn from 1 to N
for (x <- 1 to M; y <- 1 to N)
yield (x,y)

is equivalent to

(1 to M) flatMap (x => (1 to N) map (y => (x, y)))

### Translation Rules

A for-expression looks like a traditional for loop but works differently internally

for (x <- e1) yield e2 is translated to e1.map(x => e2)

for (x <- e1 if f) yield e2 is translated to for (x <- e1.filter(x => f)) yield e2

for (x <- e1; y <- e2) yield e3 is translated to e1.flatMap(x => for (y <- e2) yield e3)

This means you can use a for-comprehension for your own type, as long as you define mapflatMap and filter.

For more, see lecture 6.5.

### Example 2

for {
i <- 1 until n
j <- 1 until i
if isPrime(i + j)
} yield (i, j)

is equivalent to

for (i <- 1 until n; j <- 1 until i if isPrime(i + j))
yield (i, j)

is equivalent to

(1 until n).flatMap(i => (1 until i).filter(j => isPrime(i + j)).map(j => (i, j)))