functional scala i

Mario Gleichmann JUG Frankfurt / Main

Functional Scaλa

Functional Programming with Scala

25.08.2010

Java User Group Frankfurt / MainMario Gleichmann

Mario Gleichmann JUG Frankfurt / Main2

Introduction

Mario Gleichmann

site: www.mg-informatik.de

blog: 'brain driven development'

gleichmann.wordpress.com

mail: [email protected]

http://www.mg-informatik.de/


What is Functional Programming ?

Imperative Style

int sum = 0;

for( int i=1; i<=10; i++ ){

sum = sum + i;}



Imperative Style

int sum = 0;

for( int i=1; i<=10; i++ ){

sum = sum + i;}

Instruction based

Computation method is variable assignment



Functional Style

val sum = fold( 1 to 10, _+_ )



Functional Style

val sum = fold( 1 to 10, add )



Functional Style

val sum = fold( 1 to 10, add )

Expression based

Computation method is function application

fcn


What makes a Function ?

Function Literals

( x :Int, y :Int ) => x + y

Fcn val



val add = ( x :Int, y :Int ) => x + y

Function Values

Elm




Function name Argument list Function expression

Elements

Tp




Function Types

Type of add : ( Int , Int ) => Int

Obj




Note : In Scala, everything is an Object

val add = new Function2[ Int, Int, Int ] {

def apply( x :Int, y: Int ) : Int = x + y }

xplct Tp dcl



val add : ( Int, Int ) => Int = ( x :Int, y :Int ) => x + y

Function Types

Explicit Type Declaration

Shrt



val add : ( Int, Int ) => Int = _ + _

Argument Shortcuts

First Parameter Second Parameter

Argument List omitted !

app




Function Application

...

add( 3, 8 ) >> 11


App obj





...

add( 3, 8 ) >> 11

add.apply( 3, 8 ) >> 11

Mthd



object Math{ ... def mult( x :Int, y :Int ) : Int = x * y

...}

Methods

Elm



object Math{

def mult( x :Int, y :Int ) : Int = x * y

}

Elements

Result Type

Method name Argument list Method body

Tpe



def mult( x :Int, y :Int ) : Int = x * y

Method Types

Type of mult : ( Int , Int ) Int

clsrs


Closures

var limit = 18 val isAdult = ( age :Int ) => age >= limit

Type of isAdult : Int => Boolean

Bnd var


Closures


Bound variable

Fre var


Closures


Free variable

Opn Trm


Closures


Open TermsFree variable

'Open term'

Cls ovr


Closures


'Closing over'

Clsd trm


Closures


'Closed term'

appl


Closures


val isGermanAdult = isAdult( 20 ) >> true

Lim chng


Closures



limit = 21

val isUnitesStatesAdult = isAdult( 20 )

Dym bnd


Closures



limit = 21

val isUnitesStatesAdult = isAdult( 20 ) >> false

'Dynamic' bound

Dta Tp


Data types

data Natural = Zero | Succ( Natural )

'Constructors''Constructors'

smp


Data types

data Natural = Zero | Succ( Natural )

val zero = Zero

val one = Succ( Zero )

val four = Succ( Succ ( Succ ( Succ ( Zero ) ) ) )

Int


Data types

data Integer = … , -3, -2, -1, 0, 1, 2, 3, ...

val zero = 0

val one = 1

val four = 4

Fib pttn


Operating on data types

Pattern Matching

fibonacci( 0 ) → 0

fibonacci( 1 ) → 1

fibonacci( n ) → fibonacci( n – 1 ) + fibonacci( n – 2 )

Ptt mtc



Pattern Matching

val fib : Int => Int = ( i :Int ) => i match {

case 0 => 0

case 1 => 1

case n => fib( n - 1 ) + fib( n - 2 )}

othw



Pattern Matching

val fib : Int => Int = ( i :Int ) => i match {

case 0 => 0

case 1 => 1

case _ => fib( i - 1 ) + fib( i - 2 )}

'otherwise'

Lst


Algebraic Datatypes

data List a = Nil | Cons a ( List a )

Cnstr


Algebraic Datatypes

Value Constructors

data List[T] = Nil | T :: List[T]

'Constructors''Constructors'

smp


Algebraic Datatypes

Value Construction


val emptyList = Nil

smp


Algebraic Datatypes

Value Construction


val emptyList = Nil

val anotherList = 5 :: 4 :: 3 :: 2 :: 1 :: Nil

Rght assoc


Algebraic Datatypes

Value Construction


val emptyList = Nil

val anotherList = 5 :: ( 4 :: ( 3 :: ( 2 :: (1 :: Nil ) ) ) )

Smp tl


Operating on algebraic data types

Pattern Matching

def tail [T] ( list :List[T] ) = list match { case Nil => Nil case x :: xs => xs}

Type of tail: [T] ( List[T] ) List[T]

De con



Pattern Matching

def tail [T] ( list :List[T] ) = list match { case Nil => Nil case x :: xs => xs}

'De-Construction'

Dnt cr



Pattern Matching

val length : List[ _ ] => Int = _ match { case Nil => 0 case _ :: xs => 1 + length( xs )}

Type of length: ( List[ _ ] ) => Int

'some head' (don't care)

Grd



Pattern Matching

def insert[ T <% Ordered[ T ] ] ( elem :T, list :List[T] ) : List[T] =

list match { case Nil => elem :: Nil case x :: xs if elem <= x => elem :: x :: xs case x :: xs => x :: insert( elem, xs ) }

Guard

Smp Tr


Algebraic Datatypes

data Tree = Empty | Leaf Int | Node Int Tree Tree

Example - Tree

Cs clss


Algebraic Datatypes

data Tree = Empty | Leaf Int | Node Int Tree Tree

abstract case class Tree() case object Empty extends Tree case class Leaf( value: Int ) extends Tree

case class Node( value: Int, left :Tree, right: Tree ) extends Tree

Example - Tree

insrt


Algebraic Datatypes

Buildin' an unbalanced, ordered Tree

val insert :( Int, Tree ) => Tree = ( elem :Int, tree :Tree ) => tree match { case Empty => Leaf( elem ) case Node( x, left, right ) if elem < x => Node( x, insert( elem, left ), right ) case Node( x, left, right ) if elem >= x => Node( x, left, insert( elem, right ) ) case Leaf( x ) if elem < x => Node( x, Leaf( elem ), Empty ) case leaf @ Leaf( x ) if elem >= x => Node( elem, leaf, Empty ) }

dpth


Algebraic Datatypes

Pattern Matching

val depth :Tree => Int = _ match { case Empty => 0 case Leaf( _ ) => 1 case Node( _, left, right ) => 1 + max( depth( left ), depth( right ) )}

Prt isb


Partial Functions

case class Isbn( groupNr :Int, publisherNr :Int, titleNr :Int )

val publisherRegionDE = ( isbn :Isbn ) => isbn match { case Isbn( 3, pubNr, _ ) => "D" + ( pubNr.toString charAt 0 )}

…

publisherRegionDE( Isbn( 3, 677873, 8823 ) ) ) >> “D6“

unmtch


Partial Functions



…

publisherRegionDE( Isbn( 0, 677873, 8823 ) ) ) >>?Mtch err


Partial Functions



…

publisherRegionDE( Isbn( 0, 677873, 8823 ) ) ) >> MatchError

Prt fnc


Partial Functions

type =>?[-A, +B] = PartialFunction[A, B]

val publisherRegionDE : Isbn =>? String = { case Isbn( 3, pubNr, _ ) => "D" + ( pubNr.toString charAt 0 )}

…

publisherRegionDE.isDefinedAt( Isbn( 0, 677873, 8823 ) ) ) >> false

chn


Partial Functions

val publisherRegionUS : Isbn =>? String = { case Isbn( 0, pubNr, _ ) => …

case Isbn( 1, pubNr, _ ) => ...}

... val allKnownPubs = publisherRegionDE orElse publisherRegionUS

...allKnownPubs( Isbn( 0, 677873, 8823 ) ) >> “WY“

Partial Function Chaining

cmprn


Comprehensions

Set Comprehensions (Mathematics)

{ x2 | x ∈ { 1 .. 5 } }

>> Set : { 1, 4, 9, 16, 25 }

Smp scla


Comprehensions

val pow :(Int,Int) => Int = ( base :Int, exp :Int ) =>

if( exp == 0 ) 1 else base * pow( base, exp - 1 )

…val squares = for( x <- ( 1 to 5 ) ) yield pow( x, 2 )

Range ...

grn


Comprehensions

val pow :(Int,Int) => Int = ( base :Int, exp :Int ) =>

if( exp == 0 ) 1 else base * pow( base, exp - 1 )

…val squares = for( x <- ( 1 to 5 ) ) yield pow( x, 2 )

>> Seq( 1, 4, 9, 16, 25 )

… as Generator

Mltp gen


Comprehensions

val pairs = for( x <- (1 to 3 ); y <- ( 1 to x ) ) yield (y,x)

>> Seq( (1,1), (1,2), (2,2), (1,3), (2,3), (3,3) )

Tuple2

Multiple Generators

Smp fltn


Comprehensions

val flatten = ( xss :List[ List[Int] ] ) =>

for( xs <- xss; x <- xs ) yield x

...flatten( List( List(1,2), List( 5,6,8 ), List( 21,23,24 ) ) )

>> List(1, 2, 5, 6, 8, 21, 23, 24)

Example – Flatten a List of Lists

Smp int fact


Comprehensions

val factors = ( n :Int ) => for( x <- ( 1 to n ) if n % x == 0 ) yield x ...

factors( 15 )

>> Seq( 1, 3, 5, 15 )

Example – All factors of an Integer

Guard

def prm


Comprehensions


val prime = ( n :Int ) => factors( n ).toList == List( 1, n )

Example – Test 'prime' on Integer

def prms


Comprehensions


val prime = ( n :Int ) => factors( n ).toList == List( 1, n )

…

val primes = (n :Int) => for( x <- (1 to n) if prime( x ) ) yield x

Example – All primes up to an Integer

Hgh rdr Fcn


Higher Order Functions

val filterEvenValues = ( xs :List[Int] ) => {

for( x <- xs; if x % 2 == 0 ) yield x }

Lcl fcn



val filterEvenValues = ( xs :List[Int] ) => {

val isEven = ( i :Int ) => i % 2 == 0

for( x <- xs; if isEven( x ) ) yield x }

Local Functions

Local Function Definition

Smp od



val filterOddValues = ( xs :List[Int] ) => {

val isOdd = ( i :Int ) => i % 2 == 1

for( x <- xs; if isOdd( x ) ) yield x }

rfctg



val filterOddValues = ( xs :List[Int] ) => {

val isOdd : Int => Boolean = _ % 2 == 1

for( x <- xs; if isOdd( x ) ) yield x }

Refactoring ...

bstrcn



val filter = ( predicate: Int => Boolean , xs :List[Int] ) => {

for( x <- xs; if predicate( x ) ) yield x }

… via Abstraction

Fcn Tp



Functions as values

Accepting a Function as Argument

Type of filter: ( Int => Boolean, List[Int] ) => List[Int]

val filter = ( predicate: Int => Boolean , xs :List[Int] ) => {

for( x <- xs; if predicate( x ) ) yield x }

smp



val even : Int => Boolean = _ % 2 == 0val odd : Int => Boolean = _ % 2 == 1val prime : Int => Boolean = …...

val candidates = List( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 )

val evenValues = filter( even, candidates ) val oddValues = filter( odd, candidates )val primes = filter( prime, candidates )

Examples

Mthd crcn



def isPositive( x : Int ) : Boolean = x > 0

val candidates = List( -3, -2, -1, 0, 1, 2, 3 )

val positiveValues = filter( isPositive, candidates )

Coercion

vs






( Int ) : Boolean vs. ( Int ) => Boolean

?Coercion

mplct crcn






Implicit Coercion to ( Int ) => Boolean

!Coercion

xplct crcn



val isPositiveFunc : Int => Boolean = isPositive


val positiveValues = filter( isPositiveFunc, candidates )

Coercion

Explicit Coercion to ( Int ) => Boolean

lmbd xpr


Anonymous Functions

val isNegative = ( x :Int ) => x < 0

filter( isNegative, candidates )

nsrt


Anonymous Functions


filter( ( x :Int ) => x < 0, candidates )

'Lambda' Expression

TP infr


Anonymous Functions


filter( x => x < 0, candidates )

Type of Argument inferred

Shortcuts


shrtct


Anonymous Functions


filter( _ < 0, candidates )

First Argument

Shortcuts

Smp rsc ctrl


Example 1 - Resource Control

Reader reader = new BufferedReader( ... );

try{

System.out.println( reader.readLine() );}finally{

reader.close();}

Mrk rc cnt



Reader reader = new BufferedReader( ... );

try{

System.out.println( reader.readLine() );}finally{

reader.close();}

Resource Control !

Ln pttn



Loan Pattern

using ( new BufferedReader( ... ) ,

reader => println( reader.readLine() );)

fst arg



Loan Pattern



1st Argument: Resource under control

scnd arg



Loan Pattern



2nd Argument: Anonymous Function, using Resource

def fcn



Loan Pattern

val using = ( reader: Reader , block: Reader => Unit ) => {

try{block( reader )

}finally{

reader.close}

}

Smp lggn


Example 2 - Logging

val log = ( logger :Logger, level :LogLevel ) => {

val canLog = logger.canLog( level )

( msg :String ) => if( canLog ) logger.log( level, msg )}

Type of log: ( Logger, LogLevel ) => ( String => Unit )

Returning a Function

Fcn appl


Example 2 - Logging

…val info = log( myErrorLogger , INFO )val fatal = log( myErrorLogger , FATAL )...info( “...“ ) ...fatal( “failure occured ...“ + “...“ + ... )

Expensive operation 'for nothing'



( msg :String ) => if( canLog ) logger.log( level, msg )}

cndn evln


Example 2 - Logging



( x: () => String ) => if( canLog ) logger.log( level, x() )}

Type of log: ( Logger, LogLevel ) => ( () => String ) => Unit

Accepting a Function ... … conditional evaluation

appl


Example 2 - Logging



( x: () => String ) => if( isLog ) logger.log( level, x() )}

…

val fatal = log( myErrorLogger , FATAL )...

...fatal( () => “failure occured ...“ + “...“ + ... )

won't be evaluated at all

blplt


Example 2 - Logging



( x: () => String ) => if( isLog ) logger.log( level, x() )}

…

val fatal = log( myErrorLogger , FATAL )...

...fatal( () => “failure occured ...“ + “...“ + ... )

Annoying boilerplate

cll b nme


Example 2 - Logging


val canLog = logger.isLog( level )

def logMsg(x : => String) = if( canLog ) logger.log( level, x )

logMsg _} By-Name Parameter

appl


Example 2 - Logging


val isLog = logger.canLog( level )

def logMsg(x : => String) = if( canLog ) logger.log( level, x )

logMsg _}

…val fatal = log( myErrorLogger , FATAL )...

fatal( “failure occured ...“ + “...“ + ... )

Smp cstm cntl


Example 3 – Custom Control Structures

def loop( body: => Unit ) : LoopUnlessCond =

new LoopUnlessCond( body )

protected class LoopUnlessCond( body: => Unit ) {

def unless( cond: => Boolean ) { body if ( !cond ) unless( cond ) }}

appl



var i = 10

loop { println( "i = " + i )

i - = 1 } unless ( i == 0 )

obj instc



var i = 10

loop { println( "i = " + i )

i - = 1 } unless ( i == 0 )

Instance of LoopUnlessCond

prt appl


Partial Application

val isPrime = (x :Int) => ( 2 to x/2 ).forall( x % _ != 0 )

Type of isPrime: Int => Boolean

def prms wthn


Partial Application


val primesWithin = ( xs :List[Int] ) => filter( isPrime , xs )

Delegation


fxd var


Partial Application


val primesWithin = ( xs :List[Int] ) => filter( isPrime , xs )

Delegation

variablefixed

appl nappl


Partial Application


val primesWithin = filter( isPrime, _ :List[Int] )

New from Old ...

unappliedapplied

Fcn Tp


Partial Application


val primesWithin = filter( isPrime, _ :List[Int] )

New from Old ...

Type of primesWithin: List[Int] => List[Int]

Crrng


Currying

val filter = ( pred: Int => Boolean , xs :List[Int] ) => {

for( x <- xs; if pred( x ) ) yield x }

Type of filter: ( Int => Boolean , List[Int] ) => List[Int]

Crrd fcn


Currying

'Higher Order Lambda Closures' ...

val filter = ( pred: Int => Boolean ) => ( xs :List[Int] ) => {


Crrd fcn Tp


Currying




Type of filter: ( Int => Boolean ) => List[Int] => List[Int]

sngl arg


Currying




Curried FunctionCurried Function


xpln


Currying





A function ... accepting one (Function) Arg

... resulting in another function

lmbd xpr


Currying





... is defined as a Lambda expession

cls ovr


Currying





... closes over to Arguments (Scope) of surrounding Function 'filter'

Smp prms wthn


Example 1 – Extract primes



val primesWithin = filter( isPrime )

Fcn Tp






Type of primesWithin: List[Int] => List[Int]

appl






...primesWithin( List( 3, 4, 5, 6, 7 ) ) >> List( 3, 5, 7 )

Smp rc mgmt


Example 2 – Ressource Management

val initQuery = (dataSource :DataSource) => (query :String) => ( extractor :ResultSet => Unit ) => { try{ val conn = dataSource.getConnection val stmt = conn.createStatement val resultSet = stmt.executeQuery( query ) extractor( resultSet ) } finally{ try{ if( conn != null ) conn.close } finally{ if( stmt != null ) stmt.close } } }

appl


Example 2 – Ressource Management

val dataSource :DataSource = ...;

...val query = initQuery( dataSource )

…

query( "select * from User where age > 18" ) { result :ResultSet =>

while( result.next ) { .... } }

…

query( "select * from Account where balance < 1000" ) { result :ResultSet =>

while( result.next ) { .... } }

smmy


Summary

Scala supports a style of expression based, functional programming,

offering

● Functions and Closures as first class values

● Algebraic Datatypes and Pattern Matching

● Comprehensions

● Higher Order Functions and Lambda Expressions

● Currying


Thank you !


References

Scala Home www.scala-lang.org

Dr. Erik Meijer C9 Lectures – Functional Programming Fundamentalshttp://channel9.msdn.com

Graham Hutton Programming in HaskellCambridge

Odersky, Spoon, Venners Programming in Scalaartima

http://www.scala-lang.org/

http://channel9.msdn.com/

functional scala i

Technology

new function2 int

x y function typestype

function literals x

x y note

mult x

val isadult

object val

functional styleval