Keynote at Scala eXchange, London, December 2016

1. From DOT to Dotty
Martin Odersky
ScalaX, London, 8 December 2016

2. DOT: Foundations
dotty: Prototype
… for future Scala

3. Why Do Foundations Matter?
• They help ensure properties such as type soundness.
• They serve as a feedback loop for language design.
• They help detect hidden connections between language
features.

4. Why Not Pick Existing
Foundations?
• Because they would lead to variants of existing
languages.
• Foundations are formative!

5. Our Aim
We are looking for a minimal theory that can model
1. type parameterization,
2. modules,
3. objects and classes.
minimal: We do not deal with inheritance here.

6. Our Aim
We are looking for a minimal theory that can model
1. type parameterization,
2. modules,
3. objects and classes.
There were several attempts before, including νObj,
which was proposed as a basis for Scala (ECOOP 2003).
But none of them felt completely canonical or minimal.
Related: 1ML, which can model (1) and (2) by mapping to
System F.

7. Dependent Types
• We will model modules as objects with type members.
• This requires a notion of dependent type - the type
referred to by a type member depends on the owning
value.
• In Scala we restrict dependencies to paths.
• In the calculus presented here we restrict it further to
variables.
Variable x
Path p = x | p.a

8. Dependent Types in Code
We can model heterogeneous maps like this:

9. Dependent Types in Code

10. Dependent Types in Code

11. Foundations: DOT
The DOT calculus is intended to be a minimal foundation of
Scala.
Its type structure is a blueprint for the types used internally
in the compiler.

12. DOT Terms
• Translated to Scala notation, the language covered by
DOT is:
Value v = (x: T) => t Function
new { x: T => d } Object
Definition d = def a = t Method definition
type A = T Type
Term t = v Value
x Variable
t1(t2) Application
t.a Selection
{ val x = t1; t2 } Local definition.

13. DOT Types
The Types covered by DOT are:
Type T = Any Top type
Nothing Bottom type
x.A Selection
(x: T1) => T2 Function
{ def a: T } Method declaration
{ type T >: T1 <: T2 } Type declaration
T1 & T2 Intersection
{ x => T } Recursion

14. DOT Types
The Types covered by DOT are:
Type T = Any Top type
Nothing Bottom type
x.A Selection
(x: T1) => T2 Function
{ def a: T } Method declaration
{ type T >: T1 <: T2 } Type declaration
T1 & T2 Intersection
{ x => T } Recursion
Should Scala have these?

15. DOT Types
The Types covered by DOT are:
Type T = Any Top type
Nothing Bottom type
x.A Selection
(x: T1) => T2 Function
{ def a: T } Method declaration
{ type T >: T1 <: T2 } Type declaration
T1 & T2 Intersection
{ x => T } Recursion
Will replace the
T1 with T2
syntax

16. DOT Types
The Types covered by DOT are:
Type T = Any Top type
Nothing Bottom type
x.A Selection
(x: T1) => T2 Function
{ def a: T } Method declaration
{ type T >: T1 <: T2 } Type declaration
T1 & T2 Intersection
{ x => T } RecursionScala has only refinements
T { d1 … dn}
with this as self reference.

17. DOT Syntax in Greek
Note: terms are in ANF form.
This simplifies some things, but is not essential.

18. Type Assignment

19. Definition Type Assignment

20. Subtyping

21. Expressiveness
Simple as the model is, it is actually quite expressive.
Directly representable:
▶ type parameters
▶ variance
▶ nominal typing
▶ generative modules
▶ self types
▶ ADTs and simple classes
Requires smallish extension:
▶ Classes with inheritance

22. Meta Theory
Simple as the model is, the soundness proof of DOT was
surprisingly hard.
▶ Attempts were made since about 2008.
▶ Previous publications (FOOL 12, OOPSLA 14) report
about (some) advances and (lots of) difficulties.
▶ Essential challenge: Subtyping theories are
programmer-definable.

23. Programmer-Definable Theorems
In Scala and DOT, the subtyping relation is given in part by
user-definable definitions:
type T >: S <: U { T: S .. U }
This makes T a supertype of S and a subtype of U. By
transitivity, S <: U.
So the type definition above proves a subtype relationship
which was potentially not provable before.

24. Bad Bounds
What if the bounds are non-sensical?
Example:
type T >: Any <: Nothing
By the same argument as before, this implies that
Any <: Nothing
Once we have that, again by transitivity we get S <: T for
arbitrary S and T.
That is, the subtyping relations collapses to a single point!
This means that most proof techniques for soundness fail.

25. Dealing with it
Observation: To prove preservation, we need to reason at
the top-level only about environments that arise from an
actual computation
Such environments correspond to run-time stores which
binds variables to values.
And values have guaranteed good bounds because all type
members in definitions are aliases.
By an elaborate argument one can make use of this
observation to show soundness.

26. For Details

27. Consequences for Language Design
• So far: Some soundness issues were known, but it was
not clear how to fix them.
• Can one impose restrictions to guarantee good
bounds?
• Has been tried for a while but was not complete.
• The meta theory taught us a principle to ensure
soundness:
Every prefix p of a type selection p.A must be a
computed value.

28. Things To Avoid
trait BadBounds { type A >: Any <: Nothing }
lazy val x: BadBounds = ???
BadBounds # A
val x: BadBounds = null
Need to drastically restrict types we
can write in a lazy val:
Only concrete types with good bounds
are allowed.Need to drastically restrict types we
can write in a projection:
Only concrete types with good bounds
are allowed.

31. Things To Avoid
trait BadBounds { type A >: Any <: Nothing }
lazy val x: BadBounds = ???
BadBounds # A
val x: BadBounds = null
Need to track null in the type system
(straightforward)
Need to track initialization status
(hard)

32. dotty
dotty is the working name for our new Scala compiler.
• Builds on DOT in its internal data structures.
• Generics get expressed as type members.
• Supports the next iteration(s) of the Scala
programming language.

33. A Whirlwind Tour Of Dotty
Constructs

34. Dropped Features
DelayedInit
Macros
Existential Types
Procedure Syntax
Early Initializers
General Type
Projection
def run() { ... }
Will be rewritten automatically to
def run(): Unit = { ... }
class Foo
extends DelayedInit
class C extends {
val x = e
} with D
Use trait parameters
instead
T # X
- Was shown to be unsound
for general types T.
- Projection C#X from class
types C still available.
(the reflection
based kind)
def m(...) =
macro impl(...)
C[U] forSome { type U }
Wildcards C[_]still supported.

35. Implemented New Features
Multiversal Equality
Intersection Types
Union types
Trait parameters
Function arity
adaptation
pairs.map((x, y) => x + y)
instead of
pairs.map {
case (x, y) => x + y
}
T & U
- replaces T with U
- is commutative
T | U
avoids huge lubs
@static methods and fields
non-blocking lazy vals
trait T(x: Int) { ... }
object O {
@static val x = ...
@static def f() = ...
}
lazy val x = ... // thread-local
@volatile
lazy val x - ... // thread-safe,
// avoids dead-locks
type-safe ==, !=

36. And Further Down the
Road ?
Implicit Function Types
scala.meta
scrap all 22’s
effects

37. Implicit Function Types

38. What Are Implicit Function Types?
and what is “Contextual Abstraction”?

39. “Abstraction”
The ability to name a concept
and use just the name afterward

40. “Contextual”
The context comprises all the inputs that let a program do
its work, including:
• configuration data
• capabilities
• dependency injection
• type class instances

41. Implicit Parameters
• Technique of choice to pass inputs to program parts that
need them.
• Advantage over normal parameters:
No boilerplate code to pass them along the edges of a
call graph.
• But we still need to declare them as parameters
everywhere they are passed!

42. Example: Transaction Handling

43. Example (2)

44. Example (3)

45. Example Run

46. Can We Do Better?
• Problem: Boilerplate code for declaring implicit
parameters
• Repeating this 3x does not look so terrible.
• But in the dotty compiler there are 2641(!) occurrences of
• We’d like to get rid of them.

47. Towards A Solution
Let’s massage the definition of f1 a bit:
f1’s right hand side is now an implicit function value.
What is its type?
So far: Transaction => Int
From now on: implicit Transaction => Int
or, desugared: ImplicitFunction1[Transaction, Int]

48. Inside ImplicitFunction1
ImplicitFunction1 can be thought of being defined as
follows:
Analogously for all other arities.

49. Two Rules for Typing
1. Implicit functions get implicit arguments just like implicit
methods. Given:
f expands to f(a)
2. Implicit functions get created on demand. If the
expected type of b is implicit A => B, then
b expands to implicit _: A => b

50. Revised Example:
But where does current come from?

51. Revised Example (2)

52. Summary
• Implicit function types are a neat way to abstract over
contexts.
• It’s a very powerful feature, because it allows one to
inject implicit values in a scope simply by defining type.
• This opens up a lot of possibilities.
• I expect it will fundamentally affect the kind of Scala code
in the future.

53. When Can I Expect This?
Scala 2.12
Scala 2.13
Scala 3.0
TASTY,
middle end?
stdlib
collections
dotty MVP
dotty 0.x releases
2016
backend, classpath handling
Scala 2.14
2017
2018
This is open source work, depends on community’s contributions.
à Roadmap is tentative, no promises:
“MVP” = minimal
viable
prototype

54. Contributors
Theory (DOT): Nada Amin, Tiark Rompf, Sandro Stucki, Samuel
Grütter. based on previous work by Adriaan Moors, Donna Malayeri,
Geoffrey Washburn, and others.
Implementation (dotty): Many contributors, including
Dmitry Petrashko Nicolas Stucki
Guillaume Martres Sebastien Douraene
Felix Mulder Ondrej Lhotak
Liu Fengyun Vera Salvisberg
Close collaboration with scalac team
Adriaan Moors Seth Tisue
Jason Zaugg Stefan Zeiger
Lukas Rytz

55. Find out more on scala-lang.org/blog

56. Thank You