functional programming with scala - scala

I've been trying to enhance my knowledge with scala.
I am trying to implement this function recursively but having difficulty.
My main question IS, how can you accept a list in the parameter that accepts either a list or numbers.


depth(x: Any): Int is the signature you want, then pattern match on x to determine if it's a List[_] or not, where _ indicates you don't care what's in the list. (Using Seq[_] would be the more idiomatic Scala type to use, actually.) Note that the example shown is missing a pair of parens, List(1, 2, List(3))... It also assumes that depth(8) == 0 (for example).
A tricky part is that you shouldn't assume that a nested list will either be the first or last element in the "parent" list, i.e., ...List(1,List(2,3),4)... is possible.
A final bit worth mentioning; if you were building a "production" depth method, it would be worth having a Tree abstraction with Node and Leaf concrete types so you can use a better type signature, depth(tree: Tree[_]): Int, to make it explicitly clear when something represents part of the tree structure vs. data in the tree. Using List here is convenient for the exercise, but a bit ambiguous otherwise, since you could have a tree of stuff where some nodes are actually lists.


I will try to answer this by giving a shot on the recursive solution:
def depth(listOrNum: Any): Int = {
def help(y: Any, c: Int): Int = {
y match {
case y: Int => c
case List(curHead, rest # _*) =>
Math.max(help(curHead, c+1), help(rest, c))
case _ => 0
}
}
help(listOrNum, 0)
}


collect is handy here:
def depth(xs: List[Any]): Int =
1 + xs.collect{case xs: List[_] => depth(xs)}
.foldLeft(0)(_ max _)
P.S. I agree with Dean's comments about the type List[Any] being a poor way to represent trees. List[Any] is a type that should never appear in ordinary Scala code, so I'm sad to see it used in an exercise intended for beginners.


If you are insisting on using for comprehension, I can provide implementation that works with it.
First you define two useful classes
import scala.collection.generic.CanBuildFrom
import scala.collection.mutable.Builder
class Folder[T](init : T, step : (T,T) => T) extends Builder[T,T] {
private[this] var state = init
override def += (elem : T) = {
state = step(state, elem)
this
}
override def clear() {
state = init
}
override def result() : T = state
}
class CanBuildFolder[F,T](init : T, step : (T,T) => T) extends CanBuildFrom[F,T,T] {
override def apply() : Builder[T,T] = new Folder(init, step)
override def apply(from : F) : Builder[T,T] = new Folder(init, step)
}
than you can use them with the for comprehension
import scala.math.max
object Test {
val example = List(1, List(2, 3), List( List(4, 5), 6, List(7, List(List(8), 9))))
implicit val maxFolder = new CanBuildFolder[List[Any], Int](0, max)
def depth(source : List[Any]) : Int =
for (x <- source) yield x match {
case l : List[Any] => depth(l) + 1
case _ => 1
}
assert(depth(example) == 5)
}

Related

Implementing value equality of functions

How to override equals to check value equivalence of functions in specific cases? For example, say we have the following f and g functions
val f = (x: Int) => "worf" + x
val g = (x: Int) => "worf" + x
How could we make assert(f == g) pass?
I tried extending Function1 and implemented equality via generator like so
trait Function1Equals extends (Int => String) {
override def equals(obj: Any): Boolean = {
val b = obj.asInstanceOf[Function1Equals]
(1 to 100).forall { _ =>
val input = scala.util.Random.nextInt
apply(input) == b(input)
}
}
}
implicit def functionEquality(f: Int => String): Function1Equals = (x: Int) => f(x)
but could not get implicit conversion to work on == perhaps due to this. Scalactics's TripleEquals comes close
import org.scalactic.TripleEquals._
import org.scalactic.Equality
implicit val functionEquality = new Equality[Int => String] {
override def areEqual(a: Int => String, b: Any): Boolean =
b match {
case p: (Int => String) =>
(1 to 100).forall { _ =>
val input = scala.util.Random.nextInt
a(input) == p(input)
}
case _ => false
}
}
val f = (x: Int) => "worf" + x
val g = (x: Int) => "worf" + x
val h = (x: Int) => "picard" + x
assert(f === g) // pass
assert(f === h) // fail
How would you go about implementing equality of functions, preferably using regular ==?

First of all, function equality is not a simple topic (spoiler: it cannot be implemented correctly; see e.g. this question and the corresponding answer), but let's assume that your method of "asserting same output for a hundred random inputs" is good enough.
The problem with overriding == is that it's already implemented for Function1 instances. So you have two options:
define a custom trait (your approach) and use ==
define a typeclass with operation isEqual and implement it for Function1
Both options have trade-offs.
In the first case, instead of using standard Scala Function1 trait, you have to wrap each function into your custom trait instead. You did that, but then you tried to implement an implicit conversion that will do the conversion from standard Function1 to Function1Equals for you "behind the scenes". But as you realised yourself, that cannot work. Why? Because there already exists a method == for Function1 instances, so there's no reason for the compiler to kick off the implicit conversion. You have to wrap each Function1 instance into your custom wrapper so that the overridden == gets called.
Here's the example code:
trait MyFunction extends Function1[Int, String] {
override def apply(a: Int): String
override def equals(obj: Any) = {
val b = obj.asInstanceOf[MyFunction]
(1 to 100).forall { _ =>
val input = scala.util.Random.nextInt
apply(input) == b(input)
}
}
}
val f = new MyFunction {
override def apply(x: Int) = "worf" + x
}
val g = new MyFunction {
override def apply(x: Int) = "worf" + x
}
val h = new MyFunction {
override def apply(x: Int) = "picard" + x
}
assert(f == g) // pass
assert(f == h) // fail
Your second option is to keep working with standard Function1 instances, but to use a custom method for equality comparison. This can be easily implemented with a typeclass approach:
define a generic trait MyEquals[A] which will have the needed method (let's call it isEqual)
define an implicit value which implements that trait for Function1[Int, String]
define a helper implicit class which will provide the method isEqual for some value of type A as long as there exists an implicit implementation of MyEquals[A] (and we made sure in the previous step that there is one for MyEquals[Function1[Int, String]])
Then the code looks like this:
trait MyEquals[A] {
def isEqual(a1: A, a2: A): Boolean
}
implicit val function1EqualsIntString = new MyEquals[Int => String] {
def isEqual(f1: Int => String, f2: Int => String) =
(1 to 100).forall { _ =>
val input = scala.util.Random.nextInt
f1(input) == f2(input)
}
}
implicit class MyEqualsOps[A: MyEquals](a1: A) {
def isEqual(a2: A) = implicitly[MyEquals[A]].isEqual(a1, a2)
}
val f = (x: Int) => "worf" + x
val g = (x: Int) => "worf" + x
val h = (x: Int) => "picard" + x
assert(f isEqual g) // pass
assert(f isEqual h) // fail
But as I said, keeping the advantages of first approach (using ==) and second approach (using standard Function1 trait) is not possible. I would argue however that using == isn't even an advantage. Read on to find out why.
This is a good demonstration of why typeclasses are useful and more powerful than inheritance. Instead of inheriting == from some superclass object and overriding it, which is problematic for types we cannot modify (such as Function1), there should instead be a typeclass (let's call it Equal) which provides the equality method for a lot of types.
So if an implicit instance of Equal[Function1] doesn't already exist in the scope, we simply provide our own (like we did in my second snippet) and the compiler will use it. On the other hand, if an implicit instance of Equal[Function1] already does exist somewhere (e.g. in the standard library), it changes nothing for us - we still simply need to provide our own, and it will "override" the existing one.
And now the best part: such typeclass already exists in both scalaz and cats. It is called Equal and Eq respectively, and they both named their equality comparison method ===. This is why I said earlier that I wouldn't even consider being able to use == as an advantage. Who needs == anyway? :) Using scalaz or cats in your codebase consistently would mean that you would rely on === instead of == everywhere, and your life would be simple(r).
But don't count on function equality; that whole requirement is weird and not good. I answered your question pretending that it's fine in order to provide some insights, but the best answer would have been - don't rely on function equality at all.

How to extract unique elements from a list of classes in Scala

I have a list of case classes and the instances are the same or similar each other. I need to filter out this list from the "duplicates". In Scala, is there anything like this (pseudo code):
myList.unique ((obj1,obj2) => verifySimilitude(obj1,obj2))
def verifySimilitude(obj1:Foo, obj2:Foo):Boolean = // some logic to verify that objects are the same or at least similar
?
It is pretty much a "cartesian" product so I am wondering what it could be a good solution (keeping the code simple) to solve it.

There is no such built-in function, but it's easy to create your own. For the sake of the example, I'm assuming Foo is simple String and verifySimilitude compares first characters of two strings.
type Foo = String
def verifySimilitude(obj1: Foo, obj2: Foo): Boolean = obj1.headOption == obj2.headOption
val myList = List("aa", "bb", "cc", "a", "b", "c", "d")
myList.foldLeft(List[String]()) {
case (accum, el) => if (accum.exists(verifySimilitude(el, _))) accum else el :: accum
}.reverse
Result:
res0: List[String] = List(aa, bb, cc, d)
Alternative (more efficient) solution would be to create wrapper class that implements equals and hashCode according to your verifySimilitude behavior. Reusing the example above, this will look like:
class SimWrapper(val v:String) {
override def equals(other: Any): Boolean = other match {
case that: SimWrapper => that.v.headOption == v.headOption
case _ => false
}
override def hashCode(): Int = v.headOption.hashCode()
}
myList.map(new SimWrapper(_)).distinct.map(_.v)
With the same result:
res1: List[String] = List(aa, bb, cc, d)
Second approach is more efficient (O(N) comparing to O(N2)), but it also has limited applications, as it makes sense only when you can define reasonably uniform hashCode for particular verifySimilitude.

How does Scala deal with recursive return types?

In OCaml there's this thing called 'rectype' which allows recursive return-types. To illustrate what I mean by that here's a method with such a type:
def foo(n: Int)(i: Int): ??? = {
val m = n + i
(foo(m), m)
}
The question is; what do you put in ???'s place? Looking at the code you'd think it's something like:
Int => Int => (Int => (Int => (Int => (Int => ... , Int)
Why? Because the type of foo(m) is Int => (Int => rep, Int) where rep in the tuple is the repeated structure.
Is there a way to do this?

Sure, Scala has recursive types (but perhaps not the kind you're looking for). Take List, for example (abridged to relevant parts):
sealed abstract class List[+A] ...
final case class ::[B](head: B, tl: List[B]) extends List[B] ...
object Nil extends List[Nothing] ...
List(1, 2, 3) is recursively defined from multiple lists using cons ::.
1 :: 2 :: 3 :: Nil
Or without infix notation:
::(1, ::(2, ::(3, Nil)))
I suppose you could represent the type this way. But notice you have to define the type yourself:
sealed abstract class Inf[A]
case class Func[A](_1: A => Inf[A], _2: A) extends Inf[A] with Product2[A => Inf[A], A]
object Identity extends Inf[Nothing]
def foo(n: Int)(i: Int): Inf[Int] = {
val m = n + i
Func(foo(m) _, m)
}
Or a little more specifically:
def foo(n: Int)(i: Int): Func[Int] = {
val m = n + i
Func(foo(m) _, m)
}
scala> val f = foo(5)(3)
f: Func[Int] = Func(<function1>,8)
scala> f._1(10)
res8: Inf[Int] = Func(<function1>,18)

In your particular case, the return type would depend on the two input values n and i. Both of these are unknown at compile time (Scala is statically typed!), which means the compiler wouldn't know the static return type. This is obviously bad for numerous reasons.
In general, you can neither define recursive types, nor can you utilize type inference for recursive methods.

Tail recursion: internal "loop" function or default values for accumulators

I know of at least two styles to writing tail recursive functions. Take a sum function for example:
def sum1(xs: List[Int]): Int = {
def loop(xs: List[Int], acc: Int): Int = xs match {
case Nil => acc
case x :: xs1 => loop(xs1, acc + x)
}
loop(xs, 0)
}
vs
def sum2(xs: List[Int], acc: Int = 0): Int = xs match {
case Nil => acc
case x :: xs1 => sum2(xs1, x + acc)
}
I've noticed the first style (internal loop function) much more commonly than the second. Is there any reason to prefer it or is the difference just a matter of style?

There a couple of reasons to prefer the first notation.
Firstly, you define clearly to your reader what's the internal implementation from the external one.
Secondly, in your example the seed value is a pretty simple one that you can put straight as a default argument, but your seed value may be a very complicated-to-compute object that requires a longer init than default. Should this init for example require to be done asynchronously, you definitely want to put it out of your default value and manage with Futures or w/e.
Lastly, as Didier mentioned, the type of sum1 is a function from List[Int] -> Int (which makes sense), while the type of sum2 is a function from (List[Int], Int) -> Int which is less meaningful. Also, this implies that it's easier to pass sum1 around than sum2. For example, if you have an object that encapsulates a list of Int's and you want to provide synthesizer functions over it you can do (pseudocode, i dont have a repl to write it properly now):
class MyFancyList[T](val seed: List[T]) = {
type SyntFunction = (List[T] => Any)
var functions = Set[SyntFunction]
def addFunction(f: SyntFunction) = functions += f
def computeAll = {
for {
f <- functions
}
yield {
f(seed)
}
}
}
And you can do:
def concatStrings(list:List[Int]) = {
val listOfStrings = for {
n <- list
}
yield {
n+""
}
listOfStrings.mkString
}
val x = MyFancyList(List(1, 2, 3))
x.addFunction(sum1)
x.addFunction(concatStrings)
x.computeAll == List(6, "123")
but you can't add sum2 (not as easily at least)

Hidden features of Scala

Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
What are the hidden features of Scala that every Scala developer should be aware of?
One hidden feature per answer, please.

Okay, I had to add one more. Every Regex object in Scala has an extractor (see answer from oxbox_lakes above) that gives you access to the match groups. So you can do something like:
// Regex to split a date in the format Y/M/D.
val regex = "(\\d+)/(\\d+)/(\\d+)".r
val regex(year, month, day) = "2010/1/13"
The second line looks confusing if you're not used to using pattern matching and extractors. Whenever you define a val or var, what comes after the keyword is not simply an identifier but rather a pattern. That's why this works:
val (a, b, c) = (1, 3.14159, "Hello, world")
The right hand expression creates a Tuple3[Int, Double, String] which can match the pattern (a, b, c).
Most of the time your patterns use extractors that are members of singleton objects. For example, if you write a pattern like
Some(value)
then you're implicitly calling the extractor Some.unapply.
But you can also use class instances in patterns, and that is what's happening here. The val regex is an instance of Regex, and when you use it in a pattern, you're implicitly calling regex.unapplySeq (unapply versus unapplySeq is beyond the scope of this answer), which extracts the match groups into a Seq[String], the elements of which are assigned in order to the variables year, month, and day.

Structural type definitions - i.e. a type described by what methods it supports. For example:
object Closer {
def using(closeable: { def close(): Unit }, f: => Unit) {
try {
f
} finally { closeable.close }
}
}
Notice that the type of the parameter closeable is not defined other than it has a close method

Type-Constructor Polymorphism (a.k.a. higher-kinded types)
Without this feature you can, for example, express the idea of mapping a function over a list to return another list, or mapping a function over a tree to return another tree. But you can't express this idea generally without higher kinds.
With higher kinds, you can capture the idea of any type that's parameterised with another type. A type constructor that takes one parameter is said to be of kind (*->*). For example, List. A type constructor that returns another type constructor is said to be of kind (*->*->*). For example, Function1. But in Scala, we have higher kinds, so we can have type constructors that are parameterised with other type constructors. So they're of kinds like ((*->*)->*).
For example:
trait Functor[F[_]] {
def fmap[A, B](f: A => B, fa: F[A]): F[B]
}
Now, if you have a Functor[List], you can map over lists. If you have a Functor[Tree], you can map over trees. But more importantly, if you have Functor[A] for any A of kind (*->*), you can map a function over A.

Extractors which allow you to replace messy if-elseif-else style code with patterns. I know that these are not exactly hidden but I've been using Scala for a few months without really understanding the power of them. For (a long) example I can replace:
val code: String = ...
val ps: ProductService = ...
var p: Product = null
if (code.endsWith("=")) {
p = ps.findCash(code.substring(0, 3)) //e.g. USD=, GBP= etc
}
else if (code.endsWith(".FWD")) {
//e.g. GBP20090625.FWD
p = ps.findForward(code.substring(0,3), code.substring(3, 9))
}
else {
p = ps.lookupProductByRic(code)
}
With this, which is much clearer in my opinion
implicit val ps: ProductService = ...
val p = code match {
case SyntheticCodes.Cash(c) => c
case SyntheticCodes.Forward(f) => f
case _ => ps.lookupProductByRic(code)
}
I have to do a bit of legwork in the background...
object SyntheticCodes {
// Synthetic Code for a CashProduct
object Cash extends (CashProduct => String) {
def apply(p: CashProduct) = p.currency.name + "="
//EXTRACTOR
def unapply(s: String)(implicit ps: ProductService): Option[CashProduct] = {
if (s.endsWith("=")
Some(ps.findCash(s.substring(0,3)))
else None
}
}
//Synthetic Code for a ForwardProduct
object Forward extends (ForwardProduct => String) {
def apply(p: ForwardProduct) = p.currency.name + p.date.toString + ".FWD"
//EXTRACTOR
def unapply(s: String)(implicit ps: ProductService): Option[ForwardProduct] = {
if (s.endsWith(".FWD")
Some(ps.findForward(s.substring(0,3), s.substring(3, 9))
else None
}
}
But the legwork is worth it for the fact that it separates a piece of business logic into a sensible place. I can implement my Product.getCode methods as follows..
class CashProduct {
def getCode = SyntheticCodes.Cash(this)
}
class ForwardProduct {
def getCode = SyntheticCodes.Forward(this)
}

Manifests which are a sort of way at getting the type information at runtime, as if Scala had reified types.

In scala 2.8 you can have tail-recursive methods by using the package scala.util.control.TailCalls (in fact it's trampolining).
An example:
def u(n:Int):TailRec[Int] = {
if (n==0) done(1)
else tailcall(v(n/2))
}
def v(n:Int):TailRec[Int] = {
if (n==0) done(5)
else tailcall(u(n-1))
}
val l=for(n<-0 to 5) yield (n,u(n).result,v(n).result)
println(l)

Case classes automatically mixin the Product trait, providing untyped, indexed access to the fields without any reflection:
case class Person(name: String, age: Int)
val p = Person("Aaron", 28)
val name = p.productElement(0) // name = "Aaron": Any
val age = p.productElement(1) // age = 28: Any
val fields = p.productIterator.toList // fields = List[Any]("Aaron", 28)
This feature also provides a simplified way to alter the output of the toString method:
case class Person(name: String, age: Int) {
override def productPrefix = "person: "
}
// prints "person: (Aaron,28)" instead of "Person(Aaron, 28)"
println(Person("Aaron", 28))

It's not exactly hidden, but certainly a under advertised feature: scalac -Xprint.
As a illustration of the use consider the following source:
class A { "xx".r }
Compiling this with scalac -Xprint:typer outputs:
package <empty> {
class A extends java.lang.Object with ScalaObject {
def this(): A = {
A.super.this();
()
};
scala.this.Predef.augmentString("xx").r
}
}
Notice scala.this.Predef.augmentString("xx").r, which is a the application of the implicit def augmentString present in Predef.scala.
scalac -Xprint:<phase> will print the syntax tree after some compiler phase. To see the available phases use scalac -Xshow-phases.
This is a great way to learn what is going on behind the scenes.
Try with
case class X(a:Int,b:String)
using the typer phase to really feel how useful it is.

You can define your own control structures. It's really just functions and objects and some syntactic sugar, but they look and behave like the real thing.
For example, the following code defines dont {...} unless (cond) and dont {...} until (cond):
def dont(code: => Unit) = new DontCommand(code)
class DontCommand(code: => Unit) {
def unless(condition: => Boolean) =
if (condition) code
def until(condition: => Boolean) = {
while (!condition) {}
code
}
}
Now you can do the following:
/* This will only get executed if the condition is true */
dont {
println("Yep, 2 really is greater than 1.")
} unless (2 > 1)
/* Just a helper function */
var number = 0;
def nextNumber() = {
number += 1
println(number)
number
}
/* This will not be printed until the condition is met. */
dont {
println("Done counting to 5!")
} until (nextNumber() == 5)

#switch annotation in Scala 2.8:
An annotation to be applied to a match
expression. If present, the compiler
will verify that the match has been
compiled to a tableswitch or
lookupswitch, and issue an error if it
instead compiles into a series of
conditional expressions.
Example:
scala> val n = 3
n: Int = 3
scala> import annotation.switch
import annotation.switch
scala> val s = (n: #switch) match {
| case 3 => "Three"
| case _ => "NoThree"
| }
<console>:6: error: could not emit switch for #switch annotated match
val s = (n: #switch) match {

Dunno if this is really hidden, but I find it quite nice.
Typeconstructors that take 2 type parameters can be written in infix notation
object Main {
class FooBar[A, B]
def main(args: Array[String]): Unit = {
var x: FooBar[Int, BigInt] = null
var y: Int FooBar BigInt = null
}
}

Scala 2.8 introduced default and named arguments, which made possible the addition of a new "copy" method that Scala adds to case classes. If you define this:
case class Foo(a: Int, b: Int, c: Int, ... z:Int)
and you want to create a new Foo that's like an existing Foo, only with a different "n" value, then you can just say:
foo.copy(n = 3)

in scala 2.8 you can add #specialized to your generic classes/methods. This will create special versions of the class for primitive types (extending AnyVal) and save the cost of un-necessary boxing/unboxing :
class Foo[#specialized T]...
You can select a subset of AnyVals :
class Foo[#specialized(Int,Boolean) T]...

Extending the language. I always wanted to do something like this in Java (couldn't). But in Scala I can have:
def timed[T](thunk: => T) = {
val t1 = System.nanoTime
val ret = thunk
val time = System.nanoTime - t1
println("Executed in: " + time/1000000.0 + " millisec")
ret
}
and then write:
val numbers = List(12, 42, 3, 11, 6, 3, 77, 44)
val sorted = timed { // "timed" is a new "keyword"!
numbers.sortWith(_<_)
}
println(sorted)
and get
Executed in: 6.410311 millisec
List(3, 3, 6, 11, 12, 42, 44, 77)

You can designate a call-by-name parameter (EDITED: this is different then a lazy parameter!) to a function and it will not be evaluated until used by the function (EDIT: in fact, it will be reevaluated every time it is used). See this faq for details
class Bar(i:Int) {
println("constructing bar " + i)
override def toString():String = {
"bar with value: " + i
}
}
// NOTE the => in the method declaration. It indicates a lazy paramter
def foo(x: => Bar) = {
println("foo called")
println("bar: " + x)
}
foo(new Bar(22))
/*
prints the following:
foo called
constructing bar 22
bar with value: 22
*/

You can use locally to introduce a local block without causing semicolon inference issues.
Usage:
scala> case class Dog(name: String) {
| def bark() {
| println("Bow Vow")
| }
| }
defined class Dog
scala> val d = Dog("Barnie")
d: Dog = Dog(Barnie)
scala> locally {
| import d._
| bark()
| bark()
| }
Bow Vow
Bow Vow
locally is defined in "Predef.scala" as:
#inline def locally[T](x: T): T = x
Being inline, it does not impose any additional overhead.

Early Initialization:
trait AbstractT2 {
println("In AbstractT2:")
val value: Int
val inverse = 1.0/value
println("AbstractT2: value = "+value+", inverse = "+inverse)
}
val c2c = new {
// Only initializations are allowed in pre-init. blocks.
// println("In c2c:")
val value = 10
} with AbstractT2
println("c2c.value = "+c2c.value+", inverse = "+c2c.inverse)
Output:
In AbstractT2:
AbstractT2: value = 10, inverse = 0.1
c2c.value = 10, inverse = 0.1
We instantiate an anonymous inner
class, initializing the value field
in the block, before the with
AbstractT2 clause. This guarantees
that value is initialized before the
body of AbstractT2 is executed, as
shown when you run the script.

You can compose structural types with the 'with' keyword
object Main {
type A = {def foo: Unit}
type B = {def bar: Unit}
type C = A with B
class myA {
def foo: Unit = println("myA.foo")
}
class myB {
def bar: Unit = println("myB.bar")
}
class myC extends myB {
def foo: Unit = println("myC.foo")
}
def main(args: Array[String]): Unit = {
val a: A = new myA
a.foo
val b: C = new myC
b.bar
b.foo
}
}

placeholder syntax for anonymous functions
From The Scala Language Specification:
SimpleExpr1 ::= '_'
An expression (of syntactic category Expr) may contain embedded underscore symbols _ at places where identifiers are legal. Such an expression represents an anonymous function where subsequent occurrences of underscores denote successive parameters.
From Scala Language Changes:
_ + 1 x => x + 1
_ * _ (x1, x2) => x1 * x2
(_: Int) * 2 (x: Int) => x * 2
if (_) x else y z => if (z) x else y
_.map(f) x => x.map(f)
_.map(_ + 1) x => x.map(y => y + 1)
Using this you could do something like:
def filesEnding(query: String) =
filesMatching(_.endsWith(query))

Implicit definitions, particularly conversions.
For example, assume a function which will format an input string to fit to a size, by replacing the middle of it with "...":
def sizeBoundedString(s: String, n: Int): String = {
if (n < 5 && n < s.length) throw new IllegalArgumentException
if (s.length > n) {
val trailLength = ((n - 3) / 2) min 3
val headLength = n - 3 - trailLength
s.substring(0, headLength)+"..."+s.substring(s.length - trailLength, s.length)
} else s
}
You can use that with any String, and, of course, use the toString method to convert anything. But you could also write it like this:
def sizeBoundedString[T](s: T, n: Int)(implicit toStr: T => String): String = {
if (n < 5 && n < s.length) throw new IllegalArgumentException
if (s.length > n) {
val trailLength = ((n - 3) / 2) min 3
val headLength = n - 3 - trailLength
s.substring(0, headLength)+"..."+s.substring(s.length - trailLength, s.length)
} else s
}
And then, you could pass classes of other types by doing this:
implicit def double2String(d: Double) = d.toString
Now you can call that function passing a double:
sizeBoundedString(12345.12345D, 8)
The last argument is implicit, and is being passed automatically because of the implicit de declaration. Furthermore, "s" is being treated like a String inside sizeBoundedString because there is an implicit conversion from it to String.
Implicits of this type are better defined for uncommon types to avoid unexpected conversions. You can also explictly pass a conversion, and it will still be implicitly used inside sizeBoundedString:
sizeBoundedString(1234567890L, 8)((l : Long) => l.toString)
You can also have multiple implicit arguments, but then you must either pass all of them, or not pass any of them. There is also a shortcut syntax for implicit conversions:
def sizeBoundedString[T <% String](s: T, n: Int): String = {
if (n < 5 && n < s.length) throw new IllegalArgumentException
if (s.length > n) {
val trailLength = ((n - 3) / 2) min 3
val headLength = n - 3 - trailLength
s.substring(0, headLength)+"..."+s.substring(s.length - trailLength, s.length)
} else s
}
This is used exactly the same way.
Implicits can have any value. They can be used, for instance, to hide library information. Take the following example, for instance:
case class Daemon(name: String) {
def log(msg: String) = println(name+": "+msg)
}
object DefaultDaemon extends Daemon("Default")
trait Logger {
private var logd: Option[Daemon] = None
implicit def daemon: Daemon = logd getOrElse DefaultDaemon
def logTo(daemon: Daemon) =
if (logd == None) logd = Some(daemon)
else throw new IllegalArgumentException
def log(msg: String)(implicit daemon: Daemon) = daemon.log(msg)
}
class X extends Logger {
logTo(Daemon("X Daemon"))
def f = {
log("f called")
println("Stuff")
}
def g = {
log("g called")(DefaultDaemon)
}
}
class Y extends Logger {
def f = {
log("f called")
println("Stuff")
}
}
In this example, calling "f" in an Y object will send the log to the default daemon, and on an instance of X to the Daemon X daemon. But calling g on an instance of X will send the log to the explicitly given DefaultDaemon.
While this simple example can be re-written with overload and private state, implicits do not require private state, and can be brought into context with imports.

Maybe not too hidden, but I think this is useful:
#scala.reflect.BeanProperty
var firstName:String = _
This will automatically generate a getter and setter for the field that matches bean convention.
Further description at developerworks

Implicit arguments in closures.
A function argument can be marked as implicit just as with methods. Within the scope of the body of the function the implicit parameter is visible and eligible for implicit resolution:
trait Foo { def bar }
trait Base {
def callBar(implicit foo: Foo) = foo.bar
}
object Test extends Base {
val f: Foo => Unit = { implicit foo =>
callBar
}
def test = f(new Foo {
def bar = println("Hello")
})
}

Build infinite data structures with Scala's Streams :
http://www.codecommit.com/blog/scala/infinite-lists-for-the-finitely-patient

Result types are dependent on implicit resolution. This can give you a form of multiple dispatch:
scala> trait PerformFunc[A,B] { def perform(a : A) : B }
defined trait PerformFunc
scala> implicit val stringToInt = new PerformFunc[String,Int] {
def perform(a : String) = 5
}
stringToInt: java.lang.Object with PerformFunc[String,Int] = $anon$1#13ccf137
scala> implicit val intToDouble = new PerformFunc[Int,Double] {
def perform(a : Int) = 1.0
}
intToDouble: java.lang.Object with PerformFunc[Int,Double] = $anon$1#74e551a4
scala> def foo[A, B](x : A)(implicit z : PerformFunc[A,B]) : B = z.perform(x)
foo: [A,B](x: A)(implicit z: PerformFunc[A,B])B
scala> foo("HAI")
res16: Int = 5
scala> foo(1)
res17: Double = 1.0

Scala's equivalent of Java double brace initializer.
Scala allows you to create an anonymous subclass with the body of the class (the constructor) containing statements to initialize the instance of that class.
This pattern is very useful when building component-based user interfaces (for example Swing , Vaadin) as it allows to create UI components and declare their properties more concisely.
See http://spot.colorado.edu/~reids/papers/how-scala-experience-improved-our-java-development-reid-2011.pdf for more information.
Here is an example of creating a Vaadin button:
val button = new Button("Click me"){
setWidth("20px")
setDescription("Click on this")
setIcon(new ThemeResource("icons/ok.png"))
}

Excluding members from import statements
Suppose you want to use a Logger that contains a println and a printerr method, but you only want to use the one for error messages, and keep the good old Predef.println for standard output. You could do this:
val logger = new Logger(...)
import logger.printerr
but if logger also contains another twelve methods that you would like to import and use, it becomes inconvenient to list them. You could instead try:
import logger.{println => donotuseprintlnt, _}
but this still "pollutes" the list of imported members. Enter the über-powerful wildcard:
import logger.{println => _, _}
and that will do just the right thing™.

require method (defined in Predef) that allow you to define additional function constraints that would be checked during run-time. Imagine that you developing yet another twitter client and you need to limit tweet length up to 140 symbols. Moreover you can't post empty tweet.
def post(tweet: String) = {
require(tweet.length < 140 && tweet.length > 0)
println(tweet)
}
Now calling post with inappropriate length argument will cause an exception:
scala> post("that's ok")
that's ok
scala> post("")
java.lang.IllegalArgumentException: requirement failed
at scala.Predef$.require(Predef.scala:145)
at .post(<console>:8)
scala> post("way to looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong tweet")
java.lang.IllegalArgumentException: requirement failed
at scala.Predef$.require(Predef.scala:145)
at .post(<console>:8)
You can write multiple requirements or even add description to each:
def post(tweet: String) = {
require(tweet.length > 0, "too short message")
require(tweet.length < 140, "too long message")
println(tweet)
}
Now exceptions are verbose:
scala> post("")
java.lang.IllegalArgumentException: requirement failed: too short message
at scala.Predef$.require(Predef.scala:157)
at .post(<console>:8)
One more example is here.
Bonus
You can perform an action every time requirement fails:
scala> var errorcount = 0
errorcount: Int = 0
def post(tweet: String) = {
require(tweet.length > 0, {errorcount+=1})
println(tweet)
}
scala> errorcount
res14: Int = 0
scala> post("")
java.lang.IllegalArgumentException: requirement failed: ()
at scala.Predef$.require(Predef.scala:157)
at .post(<console>:9)
...
scala> errorcount
res16: Int = 1

Traits with abstract override methods are a feature in Scala that is as not widely advertised as many others. The intend of methods with the abstract override modifier is to do some operations and delegating the call to super. Then these traits have to be mixed-in with concrete implementations of their abstract override methods.
trait A {
def a(s : String) : String
}
trait TimingA extends A {
abstract override def a(s : String) = {
val start = System.currentTimeMillis
val result = super.a(s)
val dur = System.currentTimeMillis-start
println("Executed a in %s ms".format(dur))
result
}
}
trait ParameterPrintingA extends A {
abstract override def a(s : String) = {
println("Called a with s=%s".format(s))
super.a(s)
}
}
trait ImplementingA extends A {
def a(s: String) = s.reverse
}
scala> val a = new ImplementingA with TimingA with ParameterPrintingA
scala> a.a("a lotta as")
Called a with s=a lotta as
Executed a in 0 ms
res4: String = sa attol a
While my example is really not much more than a poor mans AOP, I used these Stackable Traits much to my liking to build Scala interpreter instances with predefined imports, custom bindings and classpathes. The Stackable Traits made it possible to create my factory along the lines of new InterpreterFactory with JsonLibs with LuceneLibs and then have useful imports and scope varibles for the users scripts.