Variance & Types - Scalabase

What is Variance, the connection between Types & Variance and how Scala supports it?
Deep dive into types of Variances and how they relate to Functions.

Transcript

1. Variance & Types Asjad Baig
2. About Me • Application Developer • Functional Programming ⇔ Category Theory • @AsjadSB
3. Will discuss... • Type Bounds • How to use :: Variance and its type • Liskov Substitution Principle • Function trait connection with Variance • How compiler ensures Variance
4. Types ...
5. Type Bounds 1. A & B both are types 2. A .: B A subtype of B 3. A .: B B subtype of A / A supertype of B
6. Animal Kingdom
7. Type Hierarchy - SCALA
8. Type Hierarchy - SCALA
9. Type Hierarchy - SCALA
10. Type Hierarchy - SCALA
11. Type Hierarchy - Kingdom
12. Type Hierarchy - Kingdom
13. Type Hierarchy - Kingdom
14. Type Hierarchy - Kingdom
15. Lower Bounds • [A .: Bulldog] • Range of possibilities A can have ? • {Dog, Animal, Any, Bulldog}
16. Upper Bounds • [A .: Dog] • Range of possibilities A can have ? • {Dobermann, Greyhound, Bulldog, Nothing, Dog}
17. Multi Bounds • [Animal .: A .: Bulldog] • Range of possibilities A can have ? • {Animal, Dog, Bulldog}
18. Variance Arriving
19. Variance • Scala supports subtyping • Variance refers to how subtyping between more complex types relates to subtyping between their components
20. Variance
21. Types Of Variance • Covariance • Invariance • Contravariance
22. Pre-Condition • C[T] is a parameterized type • A & B are types such that A .: B
23. CoVariance • C[A] .: C[B] • The subtyping relation is preserved in the same direction • Parameterize as C[+ T] (Type Notation) • Most Immutable Scala Collections are Covariant
24. CoVariance
25. ContraVariance • C[A] .> C[B] • The subtyping relation is in the opposite direction • Parameterize as C[- T]
26. ContraVariance
27. Modelling ZooKeeper • class ZooKeeper[-T] • Is there a way to restrict it to just Animals ?
28. Modelling ZooKeeper • class ZooKeeper[-T] • Is there a way to restrict it to just Animals ? • class ZooKeeper[-T .: Animal]
29. ZooKeeper
30. InVariance • C[A] .= C[B] • There’s no relation with the parameterized type • Parameterize as C[ T] • Mutable collections are Invariant
31. Array in Java - Mutable
32. Array in Scala - Invaraint
33. Producer ⇔ Consumer
34. Liskov Substitution Principle
35. How it started • Let functionQ(x) be a property provable about objects x of type B . • Then functionQ(y) should be provable for objects y of type A where A .: B
36. How it started If A .: B, then everything one can to do with a value of type B one should also be able to do with a value of type A. How it’s going • Let functionQ(x) be a property provable about objects x of type B . • Then functionQ(y) should be provable for objects y of type A where A .: B
37. If A .: B, then everything one can to do with a value of type B one should also be able to do with a value of type A. How it’s going
38. How it started • Let functionQ(x) be a property provable about objects x of type B . • Then functionQ(y) should be provable for objects y of type A where A .: B
39. Function Trait • trait Function1[-T, +R] • Contravariant input (Arguments) • Covariant output (Result) • T .> R
40. Function Typing Rule • If we have functions ◦ fn1 = A1 .> B1 ◦ fn2 = A2 .> B2 • A1 .> B1 .: A2 .> B2 (i.e fn1 .: fn2) • Only when :: ◦ B1 .: B2 Covariant in Result Types ◦ A1 .: A2 Contravariant in Argument types
41. Function Typing Rule
42. Function Typing Rule
43. Function Typing Rule
44. Example
45. Function for Elephant • Elephant eats Grass • fn1 :: Animal .> Napier • fn2 :: Elephant .> Grass
46. Function for Elephant
47. Function for Elephant
48. Function Trait • trait Function1[-T, +R] • Similarly, Function2[ -T1, -T2, +R]
49. Function Trait • How N input function should look ?
50. Function Trait • How N input function should look ? • FunctionN[ -Input1,..,-InputN, +Result] • But there’s a limitation here with value N
51. Function Trait • How N input function should look ? • FunctionN[ -Input1,..,-InputN, +Result] • But there’s a limitation here with value N • N = 22
52. Function Trait • How N input function should look ? • FunctionN[ -Input1,..,-InputN, +Result] • But there’s a limitation here with value N • N = 22 • But, in scala3 this limitation is no more!!
53. Scala Compiler Checks • Covariant type params can only appear in method results • Contravariant type param can only appear in method param • Invariant type param can appear anywhere
54. Producer ⇔ Consumer
55. Covariance Example : List
56. List.add()
57. List.add()
58. List.add()
59. List.add()
60. ContraVariance Example
61. ContraVariance Example
62. Inference 1. Scala immutable collection, Producer => Covariant 2. Consumer modelling => Contravariant 3. Mutable Collections => Invariant 4. Thanks to Bounds => i.e. add() operation for Covariant types List 5. FunctionN [ -Input1,..,-InputN , +Result] (scala3)
63. Resources 1. FP Principles EPFL : Coursera 2. Foundations of FP : Julien Truffaut 3. RockTheJVM 4. DevInsideYou
64. Thanks!