42.type: Literal-based Singleton types
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The document discusses literal-based singleton types in Scala. Some key points: 1. Literal-based singleton types allow types like "panda!".type and 42.type, treating literals as singleton types. This enables more consistency in Scala type systems. 2. Examples are provided showing how literal-based singleton types can be used for records, residues, and ranged values. 3. The document discusses how literal-based singleton types could improve dependent types in Scala by enabling types like ((x: Int) => x > 23 && x < 42).type. This may allow integration with SMT solvers like Z3 for compile-time checking of dependent types.
![trait Assoc[K] { type V ; val v: V }
defined trait Assoc
!
def mkAssoc[K, V0](k: K,v0: V0):
Assoc[k.type] { type V = V0 } =
new Assoc[k.type] {type V = V0 ; val v = v0}
mkAssoc: [K, V0](k: K, v: V0)Assoc[k.type]{type V = V0}
!
def lookup[K](k: K)
(implicit a: Assoc[k.type]): a.V = a.v
lookup: [K](k: K)(implicit assoc: Assoc[k.type])assoc.V](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-7-320.jpg)
![> implicit def firstAssoc = mkAssoc(1, "Panda!")
firstAssoc: Assoc[1.type]{type V = String}
!
> implicit def ageAssoc = mkAssoc("Age", 3)
ageAssoc: Assoc["Age".type]{type V = Int}
!
> implicit def nmAssoc = mkAssoc(“Name", “Jane”)
nmAssoc: Assoc["Name".type]{type V = String}
scala> lookup(1)
res0: String = Panda!
scala> lookup("Age")
res1: Int = 3
scala> lookup("Name")
res2: String = Jane](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-8-320.jpg)
{
lhs =>
def +(rhs: Residue[N]): Residue[N] =
Residue((lhs.n + rhs.n) % inhabitant[N])
}](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-10-320.jpg)
 + Residue[13](20)
<console>:10: error: type mismatch;
found : Residue[13.type]
required: Residue[15.type]
Residue[15](15) + Residue[13](20)
^
scala> Residue[13](15) + Residue[13](20)
res1: Residue[13.type] = Residue(9)](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-11-320.jpg)
![class Ranged[From <: Int : SingleInhabitant,
To <: Int : SingleInhabitant] {
def sample = {
val rnd = new scala.util.Random
val from = inhabitant[From]
val to = inhabitant[To]
(from + rnd.nextInt(to - from + 1))
}
}](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-13-320.jpg)
![scala> val range = new Ranged[10, 20]
range: Ranged[10.type,20.type] =
Ranged@78c22d25
!
scala> range.sample
res0: Int = 13
!
scala> range.sample
res1: Int = 11](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-14-320.jpg)
![After
SimpleType ::= Path ‘.’ type
| Literal [‘.’ type]](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-23-320.jpg)
![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)](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-28-320.jpg)
![((x: Val[Int]) => x > 23 && x < 42)](https://image.slidesharecdn.com/42-140910141959-phpapp02/85/42-type-Literal-based-Singleton-types-29-320.jpg)
42.type: Literal-based Singleton types
- 1. 42.type: Literal-based singleton types in Scala @folone @xeno_by @retronym @adriaanm @extempore2
- 2. About me: @folone likes types* *same reasons why @propensive does in his “Batshit crazy algebra with types” talk
- 4. Examples
- 5. 1. Records
- 6. val book = ("author" ->> "Benjamin Pierce") :: ("title" ->> "TAPL") :: ("id" ->> 262162091) :: ("price" ->> 44.11) :: HNil ! scala> book("author") // Note the result type res0: String = Benjamin Pierce ! scala> book("id") // Note the result type res1: Int = 262162091
- 7. trait Assoc[K] { type V ; val v: V } defined trait Assoc ! def mkAssoc[K, V0](k: K,v0: V0): Assoc[k.type] { type V = V0 } = new Assoc[k.type] {type V = V0 ; val v = v0} mkAssoc: [K, V0](k: K, v: V0)Assoc[k.type]{type V = V0} ! def lookup[K](k: K) (implicit a: Assoc[k.type]): a.V = a.v lookup: [K](k: K)(implicit assoc: Assoc[k.type])assoc.V
- 8. > implicit def firstAssoc = mkAssoc(1, "Panda!") firstAssoc: Assoc[1.type]{type V = String} ! > implicit def ageAssoc = mkAssoc("Age", 3) ageAssoc: Assoc["Age".type]{type V = Int} ! > implicit def nmAssoc = mkAssoc(“Name", “Jane”) nmAssoc: Assoc["Name".type]{type V = String} scala> lookup(1) res0: String = Panda! scala> lookup("Age") res1: Int = 3 scala> lookup("Name") res2: String = Jane
- 9. 2. Residue
- 10. case class Residue[N <: Int: SingleInhabitant](n: Long){ lhs => def +(rhs: Residue[N]): Residue[N] = Residue((lhs.n + rhs.n) % inhabitant[N]) }
- 11. scala> Residue[15](15) + Residue[13](20) <console>:10: error: type mismatch; found : Residue[13.type] required: Residue[15.type] Residue[15](15) + Residue[13](20) ^ scala> Residue[13](15) + Residue[13](20) res1: Residue[13.type] = Residue(9)
- 12. 3. Ranged
- 13. class Ranged[From <: Int : SingleInhabitant, To <: Int : SingleInhabitant] { def sample = { val rnd = new scala.util.Random val from = inhabitant[From] val to = inhabitant[To] (from + rnd.nextInt(to - from + 1)) } }
- 14. scala> val range = new Ranged[10, 20] range: Ranged[10.type,20.type] = Ranged@78c22d25 ! scala> range.sample res0: Int = 13 ! scala> range.sample res1: Int = 11
- 15. Consistency
- 16. 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!
- 17. 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!" ^
- 18. With 42.type scala> val t: "panda!".type = "panda!" t: "panda!".type = panda!
- 19. Even more 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
- 20. Solution with 42.type scala> val t: 42.type = 42 t: 42.type = 42 ! ! ! scala> val t: 42 = 42 t: 42.type = 42 Or even
- 21. 42: Literal-based singleton types in Scala
- 22. Before 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.
- 23. After SimpleType ::= Path ‘.’ type | Literal [‘.’ type]
- 24. 4.
- 25. State of deptypes Scala “Scala vs Idris: Dependent Types, Now and in the Future”* *Edwin Brady & Miles Sabin, Strange Loop 2013
- 26. How can we make it better? Well, we can try. Scala + Z3
- 27. scala> import z3.scala._, z3.scala.dsl._ import z3.scala._ import z3.scala.dsl._
- 28. 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)
- 29. ((x: Val[Int]) => x > 23 && x < 42)
- 30. ((x: Int) => x > 23 && x < 42)
- 31. ((x: Int) => x > 23 && x < 42).type
- 32. val magic: ((x: Int) => x > 23 && x < 42).type = 30
- 33. val magic: ((x: Int) => x > 23 && x < 42).type = 30 val x: 42 = 42 val x: ((x: Int) => x == 42).type = 42
- 34. val magic: ((x: Int) => x > 23 && x < 42).type = 30 val x: 42 = 42 val x: ((x: Int) => x == 42).type = 42 val x: Int = 42 val x: ((x: Int) => x).type = 42
- 36. bit.ly/42_type
- 37. Credits: this thing would not be possible without: @xeno_by, @retronym, @adriaanm, and initial impl by @paulp Scala Z3 bindings: LARA@EPFL Z3: Microsoft research slides, illustrations: @killnicole
- 39. Thanks. Questions? - Contributing to Scala compiler - Type-level programming - Working/hackertime at SoundCloud Ask me about: