Co and contra variance: A war of conquest

A non standalone slides for explaining covariance and contravariance.

Transcript

1. CO AND CONTRA VARIANCE: A WAR OF CONQUEST Sebastián Ortega @_sortega
2. JARGON
3. JARGON
4. “ “A monad is just a monoid in the category of endofunctors, what's the problem?” –James Iry, in his blog
5. “ “A monad is just a monoid in the category of endofunctors, what's the problem?” –James Iry, in his blog
6. “By making type constructors covariant or contravariant instead of invariant, more programs will be accepted as well-typed.
7. SOLID PRINCIPLES ➤ Single responsibility principle ➤ Open-closed principle ➤ Liskov substitution principle ➤ Interface-segregation principle ➤ Dependency injection principle
8. SOLID PRINCIPLES ➤ Single responsibility principle ➤ Open-closed principle ➤ Liskov substitution principle ➤ Interface-segregation principle ➤ Dependency injection principle
10. WHAT IT TAKES TO BE A SUBTYPE? “Let Φ(x) be a property provable about objects x of type T. Then Φ(y) should be true for objects y of type S where S is a subtype of T.” – Barbara Liskov
11. SHOW ME SOME CODE
13. WHAT WENT WRONG?
14. “IS A” is about BEING
15. “IS A” is about BEING behaviour
16. “To err is to be human but compilers never forget. –The Rust Book
17. IS ARRAY[VEGETARIANFOOD] A SUBTYPE OF ARRAY[FOOD]? Array[VegetarianFood] Array[Food]
18. IS ARRAY[VEGETARIANFOOD] A SUBTYPE OF ARRAY[FOOD]? NOPE Array[VegetarianFood] Array[Food]
19. WHY?
20. TYPE SYSTEM All programs
21. TYPE SYSTEM All programs Programs that work
22. TYPE SYSTEM All programs Well-typed programs Programs that work
23. TYPE SYSTEM All programs Well-typed programs Programs that work 2 + 2 = 5
24. TYPE SYSTEM All programs Well-typed programs Programs that work 2 + 2 = 5 Region of abysmal pain
25. BETTER TYPE SYSTEM All programs Well-typed programs Programs that work
26. BETTER TYPE SYSTEM All programs Well-typed programs Programs that work
28. WHAT’S IN A CONTRACT?
29. WHAT’S IN A CONTRACT? Precondition OK Compiler friendly Object has been initialized y y Object has some property y n Input arguments have some type y y Input arguments have some property y n Global state has some property n n
30. WHAT’S IN A CONTRACT? Postcondition OK Compiler friendly Returned value has a type y y Returned value has a property y n Object state has a property y n Global state has some property n n
31. WHAT’S IN A CONTRACT? (II)
32. WHAT’S IN A CONTRACT? (II) ➤We must respect the contract
33. WHAT’S IN A CONTRACT? (II) ➤We must respect the contract ➤We can constrain the postconditions
34. WHAT’S IN A CONTRACT? (II) ➤We must respect the contract ➤We can constrain the postconditions ➤We can relax the preconditions
35. def method(arg: ): def method(arg: ): A A’ B B’
36. def method(arg: ): def method(arg: ): A A’ B B’
37. def method(arg: ): def method(arg: ): A A’ B B’
38. LET’S LISTEN TO THE CODE
39. Food VegetarianFood VeganFood
40. Food VegetarianFood VeganFood
41. Food VegetarianFood VeganFood
42. Food VegetarianFood VeganFood
43. Food VegetarianFood VeganFood
44. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood]
45. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood]
46. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood] This is a category!
47. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood] Type ’s are called objects This is a category!
48. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood] Type ’s are called objects ’s are called morphisms This is a category!
49. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood] Type ’s are called objects ’s are called morphisms This is a category! Another category!
50. Food VegetarianFood VeganFood Restaurant[Food] Restaurant[VegetarianFood] Restaurant[VeganFood] Restaurant[_] is covariant Type ’s are called objects ’s are called morphisms This is a category! Another category!
51. Food VegetarianFood VeganFood
52. Food VegetarianFood VeganFood Consumer[Food] Consumer[VegetarianFood] Consumer[VeganFood]
53. Food VegetarianFood VeganFood Consumer[Food] Consumer[VegetarianFood] Consumer[VeganFood]
54. Food VegetarianFood VeganFood Consumer[Food] Consumer[VegetarianFood] Consumer[VeganFood]
55. Food VegetarianFood VeganFood Consumer[Food] Consumer[VegetarianFood] Consumer[VeganFood]
56. Food VegetarianFood VeganFood Consumer[Food] Consumer[VegetarianFood] Consumer[VeganFood] The dual category! Consumer[_] is contravariant
57. Food VegetarianFood VeganFood
58. Food VegetarianFood VeganFood Array[Food] Array[VegetarianFood] Array[VeganFood]
59. Food VegetarianFood VeganFood Array[Food] Array[VegetarianFood] Array[VeganFood]
60. Food VegetarianFood VeganFood Array[Food] Array[VegetarianFood] Array[VeganFood] Array[_] is invariant
61. Food VegetarianFood VeganFood Array[Food] Array[VegetarianFood] Array[VeganFood] Array[_] is invariant
62. “By making type constructors covariant or contravariant instead of invariant, more programs will be accepted as well-typed.
64. Congratulations! You have conquered the provinces of Covariant and Contravariant Functors
65. CO/CONTRA VARIANCE EVERYWHERE! ➤ Collections library: Seq[+A], Iterable[+A] ➤ A=>B desugars to Function1[-A, +B] ➤ PartialFunction[-A, +B]. ➤ PartiallyOrdered[+A] ➤ Scalacheck generators, Gen[+T] ➤ …
66. Q/A
67. Q/A
68. WE ARE HIRING bit.ly/scala_jt
69. ➤ Incomplete and mostly wrong history of programming languages. http://james-iry.blogspot.com.es/2009/05/brief-incomplete-and- mostly-wrong.html ➤ (Liskov, 99) “Behavioral Subtyping Using Invariants and Constraints”, Barbara Liskov & Jeannette Wing ➤ Uncle Bob on LSP . http://www.objectmentor.com/resources/articles/ lsp.pdf ➤ The Rust book. http://doc.rust-lang.org/book/ ➤ Scape from the Ivory Tower, presentation by Simon Peyton Jones. https://yow.eventer.com/events/1004/talks/1054 ➤ Presentation by Philip Walder: “Propositions as types”. https:// www.youtube.com/watch?v=IOiZatlZtGU
70. ➤ Blog post, “Covariance and Contravariance” http:// typeinference.com/typing/2015/10/29/ covariance_and_contravaciance.html ➤ Celular automaton as in “A new kind of science” by Stephen Wolfram. http://wolframscience.com/thebook.html