To run the presentation just load the file presentation/algebraic-abstractions.html in a browser.
Note: Chrome by default doesn't allow accessing local files. If you still want to use chrome — start chrome with --allow-file-access-from-files
This repository holds the presentation and the code for a talk given at a Scala UG Berlin talk on Algebraic Abstractions. The presentation is in the folder named presentation, algebraic-abstractions.html and a set of quotes on Abstractions can be seen in quotes.html also in the same folder.
This is also an sbt project with the source under src/main/scala. The source is organized into type-classes representing the various abstractions. Sums includes the sum used as a vehicle to introduce the various abstractions.
An sbt console session (REPL session) might look like this
% sbt
> console
[info] Starting scala interpreter...
[info]
import SemigroupOps._
import EqualOps._
import Sums._
import Foldable._
import Monoid._
import org.scalacheck.Test
Welcome to Scala 2.11.8 (Java HotSpot(TM) 64-Bit Server VM, Java 1.8.0_51).
Type in expressions for evaluation. Or try :help.
scala> SemigroupProps.laws[Int].check()
+ semigroup.associativity: OK, passed 100 tests.
scala> val dp = Test.Parameters.default
dp: org.scalacheck.Test.Parameters = Parameters
scala> SemigroupProps.laws[Int].check(dp.withMinSuccessfulTests(1000000))
+ semigroup.associativity: OK, passed 1000000 tests.
scala> sum(List(List(1,2,3), List(3,4,5)))
res0: List[Int] = List(1, 2, 3, 3, 4, 5)
scala> SemigroupProps.laws[List[Int]].check()
+ semigroup.associativity: OK, passed 100 tests.
scala> sum(Tree(1,2,3,4))
res1: Int = 10
scala> val jan = Map("€" -> 100, "$" -> 900, "#" -> 300)
jan: scala.collection.immutable.Map[String,Int] = Map(€ -> 100, $ -> 900, # -> 300)
scala> val feb = Map("€" -> 900, "#" -> 500)
feb: scala.collection.immutable.Map[String,Int] = Map(€ -> 900, # -> 500)
scala> sum(List(jan, feb))
res3: scala.collection.immutable.Map[String,Int] = Map(€ -> 1000, # -> 800, $ -> 900)
scala> MonoidProps.laws[Int].check()
+ monoid.associativity: OK, passed 100 tests.
+ monoid.left identity: OK, passed 100 tests.
+ monoid.right identity: OK, passed 100 tests.
scala> sumMap(List('a','b', 'c'))(_.toInt)
res4: Int = 294
scala> val mult = Monoid.lift(1)(Semigroup.lift(_ * _))
mult: goto.Monoid[Int] = goto.Monoid$$anon$2@771786bd
scala> sum(Tree(1,2,3,4,5))(tree,mult)
res5: Int = 120
scala> val faultyIntSG : Semigroup[Int] = Semigroup.lift(_ - _)
faultyIntSG: Semigroup[Int] = Semigroup$$anon$1@56af11b7
scala> SemigroupProps.laws[Int](faultyIntSG, implicitly[Equal[Int]], implicitly[org.scalacheck.Arbitrary[Int]]).check()
! semigroup.associativity: Falsified after 0 passed tests.
> ARG_0: 519846777
> ARG_1: -1
> ARG_2: 2147483647or you can checkout TestRun in src/test directory and run
% sbt
> test:compile
...
> test:runMain TestRun
[info] Running TestRun
[info]
[info] + semigroup.associativity: OK, passed 100 tests.
[info]
[info] + semigroup.associativity: OK, passed 1000000 tests.
[info]
[info] + semigroup.associativity: OK, passed 100 tests.
[info]
[info] + monoid.associativity: OK, passed 100 tests.
[info]
[info] + monoid.left identity: OK, passed 100 tests.
[info]
[info] + monoid.right identity: OK, passed 100 tests.
[info]
[info] ! semigroup.associativity: Falsified after 0 passed tests.
[info] > ARG_0: -476403604
[info] > ARG_1: -1768763504
[info] > ARG_2: 1
[success] Total time: 3 s, completed Apr 3, 2016 3:54:37 PMUse tut.