Presented at Scala Exchange 2014: https://skillsmatter.com/skillscasts/5946-42-rise-of-the-dependent-types

1. @folone @xeno_by
@adriaanm @retronym @extempore2

2. About me:
@folone
likes types*
*same reasons why @propensive does in
his “Batshit crazy algebra with types” talk

3. 12 hours of audio every minute
300 million people every month

4. Stop… Hackertime!

5. 42.type
$ git clone git@github.com:folone/scala.git -b scalaexchange
$ ant publish-local-opt -Dmaven.version.suffix="-typelevel"

6. 1. Ranged

7. 2. Residue

8. 3. Records

9. Consistency

10. Here’s what you
can do in Scala
scala> val x = "panda!"
x: String = panda!
scala> val t: x.type = x
t: x.type = panda!
scala> final val k = "panda!"
k: String("panda!") = panda!

11. Here’s what you
cannot
scala> val t: "panda!".type = "panda!"
<console>:1: error: identifier expected
but string literal found.
val t: "panda!".type = "panda!"
^

12. scala> val t: "panda!".type = "panda!"
t: "panda!".type = panda!
With 42.type

13. scala> val x = 42
x: Int = 42
scala> val t: x.type = 42
<console>:8: error: type mismatch;
found : x.type (with underlying type Int)
required: AnyRef
val t: x.type = 42
^
scala> val workaround = Witness(42)
workaround: shapeless.Witness{type T = Int(42)} = fresh$macro$3$1@35b45d3f
scala> val t: workaround.T = 42
t: workaround.T = 42
Even more

14. scala> val t: 42.type = 42
t: 42.type = 42
scala> val t: 42 = 42
t: 42.type = 42
Or even
Solution with 42.type

15. SimpleType ::= Path ‘.’ type
A singleton type is of the form p.type,
where p is a path pointing to a value
expected to conform to scala.AnyRef.
Before

16. After
| Literal [‘.’ type]
SimpleType ::= Path ‘.’ type

17. History

18. Quiz
Literal-based singleton types in scala have seen
their first implementation in:
2013 2011 2008 2004

19. http://existentialtype.net/2008/07/21/literally-dependent-types/
Quiz
Literal-based singleton types in scala have seen
their first implementation in:
2013 2011 2008 2004

21. State of deptypes Scala
“Scala vs Idris: Dependent
Types, Now and in the Future”*
*Edwin Brady & Miles Sabin, Strange Loop 2013

22. How can we
make it better?
Well, we can try.
Scala + SMT-solver

23. You would do way better to implement the
[typechecking] logic completely externally to the
compiler and use it as a black box from the
compiler, then you might have a chance.

24. scala> import z3.scala._, z3.scala.dsl._
import z3.scala._
import z3.scala.dsl._

25. scala> findAll((x: Val[Int]) => x > 23 && x < 42).toList
res0: List[Int] = List(24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41)

26. ((x: Val[Int]) => x > 23 && x < 42)

27. ((x: Int) => x > 23 && x < 42)

28. ((x: Int) => x > 23 && x < 42).type

29. val magic: ((x: Int) => x > 23 && x < 42).type = 30

30. val magic: ((x: Int) => x > 23 && x < 42).type = 30
val x: 42 = 42 val x: ((x: Int) => x == 42).type = 42

31. val x: 42 = 42 val x: ((x: Int) => x == 42).type = 42
val x: Int = 42 val x: ((x: Int) => true).type = 42
val magic: ((x: Int) => x > 23 && x < 42).type = 30

32. But
<:
((x: Int) => x > 10).type
((x: Int) => x > 23).type
is

33. LiquidTypes

34. Logically qualifiedTypes

35. bit.ly/42_type

36. this thing would not be possible without:
@xeno_by, @adriaanm, @retronym,
and initial impl by @paulp
Scala Z3 bindings: LARA@EPFL
Z3: Microsoft research
slides, illustrations: @killnicole
Credits:

38. Thanks. Questions?
folone@soundcloud.com