Symmetry, Scala & Software

Refresh Dublin 15 October 2013

Eric Bowman @ebowman

ebowman@gilt.com http://tech.gilt.com

“harmonious and beautiful proportion

and balance”

http://en.wikipedia.org/wiki/Symmetry

http://en.wikipedia.org/wiki/Symmetry

“patterned self-similarity”

Symmetry is changing without changing.

Symmetry in Scala

•Object-Oriented/Functional Hybrid

•Statically Typed

Scala

public class HelloWorld { public static void main(String[] args) { System.out.println("hello, world"); } }

public class HelloWorld { public static void main(String[] args) { System.out.println("hello, world"); } }

object HelloWorld extends App { println("hello, world") } !

println("hello, world")

public class HelloWorld { public static void main(String[] args) { System.out.println("hello, world"); } }

object HelloWorld extends App { println("hello, world") } !

for (int i = 1; i <= 10; i++) { for (int j = 1; j <= 10; j++) { System.out.println(i*j); } } !!

for (int i = 1; i <= 10; i++) { for (int j = 1; j <= 10; j++) { System.out.println(i*j); } } !!

for { i <- 1 to 10 j <- 1 to 10 } println(i * j) !

Future<Integer> f = callService1(); Future<Integer> f2 = callService2(f.get()); System.out.println(f2.get());

Future<Integer> f = callService1(); Future<Integer> f2 = callService2(f.get()); System.out.println(f2.get());

val f = for { x <- callService1() y <- callService2(x) } yield y println(Await.result(f, Duration.Inf)) !

String capitalize(String name) { if (name == null) return null; else return Character.toUpperCase( name.charAt(0)) + name.substring(1); }

String capitalize(String name) { if (name == null) return null; else return Character.toUpperCase( name.charAt(0)) + name.substring(1); }

def capitalize(n: Option[String]): Option[String] = { for (name <- n) yield { name(0).toUpper + name.substring(1) } } !!

String capitalize(String name) { if (name == null) return null; else return Character.toUpperCase( name.charAt(0)) + name.substring(1); }

Future<Integer> f = callService1(); Future<Integer> f2 = callService2(f.get()); System.out.println(f2.get());

for (int i = 1; i <= 10; i++) { for (int j = 1; j <= 10; j++) { System.out.println(i*j); } } !!

for { i <- 1 to 10 j <- 1 to 10 } println(i * j) !

val f = for { x <- callService1() y <- callService2(x) } yield y println(Await.result(f, Duration.Inf)) !!

def capitalize(name: Option[String]): Option[String] = for (n <- name) yield { n(0).toUpper + n.substring(1) } !!

Java

Scala

Refactoring

“By continuously improving the design of code, we make it easier and easier to work with. This is in sharp contrast to what typically happens: little refactoring and a great deal of attention paid to expediently adding new features. If you get into the hygienic habit of refactoring continuously, you'll find that it is easier to extend and maintain code.”

http://en.wikipedia.org/wiki/Code_refactoring

•Abstraction

•Composition/Decomposition

•Name & Location

1. Finite, unchanging list of possible refactorings.

2. Every refactoring is reversible.

3. Every refactoring is deterministic.

4. Refactorings can be combined in any order.

Group Theory

“‘Numbers measure size; groups measure symmetry.”

Groups and Symmetry, Armstrong, Spring-Verlag, 1988, p.1

http://upload.wikimedia.org/wikipedia/commons/5/53/Evariste_galois.jpg

“The most substantial piece of writing in the whole literature of mankind”

http://opinionator.blogs.nytimes.com/2010/05/02/group-think/

http://opinionator.blogs.nytimes.com/2010/05/02/group-think/

“the symmetry group of an object is the group of all isometries under which the

object is invariant with composition as the operation”

http://en.wikipedia.org/wiki/Symmetry_group

“the symmetry group of a program ... is the group of all refactorings under which the

program behaves identically after applying refactorings in any order”

String capitalize(String name) { if (name == null) return null; else return Character.toUpperCase( name.charAt(0)) + name.substring(1); }

Future<Integer> f = callService1(); Future<Integer> f2 = callService2(f.get()); System.out.println(f2.get());

for (int i = 1; i <= 10; i++) { for (int j = 1; j <= 10; j++) { System.out.println(i*j); } } !!

for { i <- 1 to 10 j <- 1 to 10 } println(i * j) !

val f = for { x <- callService1() y <- callService2(x) } yield y println(Await.result(f, Duration.Inf)) !!

def capitalize(name: Option[String]): Option[String] = for (n <- name) yield { n(0).toUpper + n.substring(1) } !!

Java

Scala

Breaking Symmetry

a[i].x += a[i - 1].x; a[i].y += a[i - 1].y;

http://www.metalev.org/2011/04/source-code-symmetry-and-transcendent.html

http://www.metalev.org/2011/04/source-code-symmetry-and-transcendent.html

a(i) += a(i-1)

a[i].x += a[i - 1].x; a[i].y += a[i - 1].y;

http://pages.cs.wisc.edu/~dyer/vsam/images/mona.gif

http://www.leonardodavinci.net/images/gallery/monalisa_detail1.jpg

http://www.saylor.org/site/wp-content/uploads/2012/04/6-mona-lisa.gif

http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/MaryRose-carpentry_tools1.jpg/250px-MaryRose-carpentry_tools1.jpghttp://test.classconnection.s3.amazonaws.com/324/flashcards/95324/png/altarpiece.png

http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/MaryRose-carpentry_tools1.jpg/250px-MaryRose-carpentry_tools1.jpghttp://test.classconnection.s3.amazonaws.com/324/flashcards/95324/png/altarpiece.png

http://upload.wikimedia.org/wikipedia/commons/6/63/Michelangelos_David.jpghttp://amolife.com/image/images/stories/Art&Abstract/most_popular_sculptures%20(7).jpg

http://www.biographyonline.net/artists/images/Much-The_Scream.jpg

http://www.pics24h.com/img/artwork/5-most-famous-paintings/5-most-famous-paintings03.jpg

FinFin

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@ebowmanebowman@gilt.com

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