Haskell's Kind System - A Primer

A primer on Type Level programming. My Presentation of the excellent article at https://diogocastro.com/blog/2018/10/17/haskells-kind-system-a-primer/

Transcript

1. Haskell's Kind System A primer https://diogocastro.com/blog/2018/10/17/haskells-kind-system-a-primer Berlin - Haskell Meetup 1 Nov 2018 © Tommaso Piazza, 2018 - https://github.com/blender 1
2. Types We all have seen types & values before © Tommaso Piazza, 2018 - https://github.com/blender 2
3. Types We all have seen types & values before — :t True © Tommaso Piazza, 2018 - https://github.com/blender 2
4. Types We all have seen types & values before — :t True — Bool ✅ © Tommaso Piazza, 2018 - https://github.com/blender 2
5. Types We all have seen types & values before — :t True — Bool ✅ — :t "Hello" © Tommaso Piazza, 2018 - https://github.com/blender 2
6. Types We all have seen types & values before — :t True — Bool ✅ — :t "Hello" — String ✅ © Tommaso Piazza, 2018 - https://github.com/blender 2
7. Types We all have seen types & values before — :t True — Bool ✅ — :t "Hello" — String ✅ — :t (+) © Tommaso Piazza, 2018 - https://github.com/blender 2
8. Types We all have seen types & values before — :t True — Bool ✅ — :t "Hello" — String ✅ — :t (+) — Num a => a -> a -> a ✅ © Tommaso Piazza, 2018 - https://github.com/blender 2
9. Kinds are to types as types are to values © Tommaso Piazza, 2018 - https://github.com/blender 3
10. Kinds are to types as types are to values All inhabited types have kind * © Tommaso Piazza, 2018 - https://github.com/blender 4
11. Kinds are to types as types are to values All inhabited types have kind * — :k Bool © Tommaso Piazza, 2018 - https://github.com/blender 4
12. Kinds are to types as types are to values All inhabited types have kind * — :k Bool — * © Tommaso Piazza, 2018 - https://github.com/blender 4
13. Kinds are to types as types are to values All inhabited types have kind * — :k Bool — * — :k String © Tommaso Piazza, 2018 - https://github.com/blender 4
14. Kinds are to types as types are to values All inhabited types have kind * — :k Bool — * — :k String — * © Tommaso Piazza, 2018 - https://github.com/blender 4
15. Kinds are to types as types are to values All inhabited types have kind * — :k Bool — * — :k String — * — :k [Int] © Tommaso Piazza, 2018 - https://github.com/blender 4
16. Kinds are to types as types are to values All inhabited types have kind * — :k Bool — * — :k String — * — :k [Int] — * © Tommaso Piazza, 2018 - https://github.com/blender 4
17. Not all types are inhabited © Tommaso Piazza, 2018 - https://github.com/blender 5
18. Not all types are inhabited — Just 1 :: Maybe © Tommaso Piazza, 2018 - https://github.com/blender 5
19. Not all types are inhabited — Just 1 :: Maybe — ❌ Expecting one more argument to ‘Maybe’ © Tommaso Piazza, 2018 - https://github.com/blender 5
20. Not all types are inhabited — Just 1 :: Maybe — ❌ Expecting one more argument to ‘Maybe’ — Right 1 :: Either © Tommaso Piazza, 2018 - https://github.com/blender 5
21. Not all types are inhabited — Just 1 :: Maybe — ❌ Expecting one more argument to ‘Maybe’ — Right 1 :: Either — ❌ Expecting two more arguments to ‘Either’ © Tommaso Piazza, 2018 - https://github.com/blender 5
22. Not all types are inhabited — Just 1 :: Maybe — ❌ Expecting one more argument to ‘Maybe’ — Right 1 :: Either — ❌ Expecting two more arguments to ‘Either’ — What are Either and Maybe ? © Tommaso Piazza, 2018 - https://github.com/blender 5
23. Constructors Let's talk about Data Constructors data Person = MkPerson { name :: String, age :: Int } deriving Show © Tommaso Piazza, 2018 - https://github.com/blender 6
24. Constructors Let's talk about Data Constructors data Person = MkPerson { name :: String, age :: Int } deriving Show — 2 Arguments © Tommaso Piazza, 2018 - https://github.com/blender 6
25. Constructors Let's talk about Data Constructors data Person = MkPerson { name :: String, age :: Int } deriving Show — 2 Arguments — MkPerson :: String -> Int -> Person © Tommaso Piazza, 2018 - https://github.com/blender 6
26. Constructors Let's talk about Data Constructors data Person = MkPerson { name :: String, age :: Int } deriving Show — 2 Arguments — MkPerson :: String -> Int -> Person — :t MKPerson "Tommaso" © Tommaso Piazza, 2018 - https://github.com/blender 6
27. Constructors Let's talk about Data Constructors data Person = MkPerson { name :: String, age :: Int } deriving Show — 2 Arguments — MkPerson :: String -> Int -> Person — :t MKPerson "Tommaso" — MKPerson "Tommaso" :: Int -> Person © Tommaso Piazza, 2018 - https://github.com/blender 6
28. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor © Tommaso Piazza, 2018 - https://github.com/blender 7
29. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int © Tommaso Piazza, 2018 - https://github.com/blender 7
30. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int — * © Tommaso Piazza, 2018 - https://github.com/blender 7
31. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int — * — :k Either String © Tommaso Piazza, 2018 - https://github.com/blender 7
32. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int — * — :k Either String — * -> * © Tommaso Piazza, 2018 - https://github.com/blender 7
33. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int — * — :k Either String — * -> * — :k Either © Tommaso Piazza, 2018 - https://github.com/blender 7
34. Constructors (2) Type Constrcutors data Either a b = Left a | Right b -- *_____▾_____* -- Type Constructor — :k Either String Int — * — :k Either String — * -> * — :k Either — * -> * © Tommaso Piazza, 2018 - https://github.com/blender 7
35. Kind Signatures Just as you can write type signatures y :: String -> IO () y = putStrLn You can write kind signatures data List a = Cons a (List a) | Nil {-# LANGUAGE KindSignatures #-} data List (a :: *) = Cons a (List a) | Nil © Tommaso Piazza, 2018 - https://github.com/blender 8
36. HOFs Higher order functions take functions are paramters map :: (a -> b) -> [a] -> [b] © Tommaso Piazza, 2018 - https://github.com/blender 9
37. HKTs Higher kinded types take type constuctors of kind * -> * as parameters {-# LANGUAGE KindSignatures #-} data NonEmpty (f :: * -> *) (a :: *) = MkNonEmpty { head :: a, tail :: f a } type NonEmptyList = NonEmpty [] let nonEmptyListOfInts = MkNonEmpty 1 [] :: NonEmptyList Int © Tommaso Piazza, 2018 - https://github.com/blender 10
38. Not everything is a ⭐ © Tommaso Piazza, 2018 - https://github.com/blender 11
39. Not everything is a ⭐ — :k Show © Tommaso Piazza, 2018 - https://github.com/blender 11
40. Not everything is a ⭐ — :k Show — Show :: * -> Constraint © Tommaso Piazza, 2018 - https://github.com/blender 11
41. Not everything is a ⭐ — :k Show — Show :: * -> Constraint — :k Functor © Tommaso Piazza, 2018 - https://github.com/blender 11
42. Not everything is a ⭐ — :k Show — Show :: * -> Constraint — :k Functor — Functor :: (* -> *) -> Constraint © Tommaso Piazza, 2018 - https://github.com/blender 11
43. Not everything is a ⭐ — :k Show — Show :: * -> Constraint — :k Functor — Functor :: (* -> *) -> Constraint — EverythingOnThisSide m => m IsAConstraint © Tommaso Piazza, 2018 - https://github.com/blender 11
44. Constraints ! Use the Constraint kind by enabling {-# LANGUAGE ConstraintKinds #-} © Tommaso Piazza, 2018 - https://github.com/blender 12
45. Using Constraints Data.Set has no Functor instance class Functor (f :: * -> *) where fmap :: (a -> b) -> f a -> f b Data.Set.map :: Ord b => (a -> b) -> Set a -> Set b -- *___ ▾ ___* -- ! © Tommaso Piazza, 2018 - https://github.com/blender 13
46. Police Data.Set.map :: Ord b => (a -> b) -> Set a -> Set b -- *___ ▾ ___* * ▾ * * ▾ * -- ! f f © Tommaso Piazza, 2018 - https://github.com/blender 14
47. Police Data.Set.map :: Ord b => (a -> b) -> Set a -> Set b -- *___ ▾ ___* * ▾ * * ▾ * -- ! f f class GFunctor ! (f :: * -> *) where fmap :: ! b => (a -> b) -> f a -> f b © Tommaso Piazza, 2018 - https://github.com/blender 15
48. Police Data.Set.map :: Ord b => (a -> b) -> Set a -> Set b -- *___ ▾ ___* * ▾ * * ▾ * -- ! f f class GFunctor ! (f :: * -> *) where fmap :: ! b => (a -> b) -> f a -> f b class GFunctor (c :: * -> Constraint) (f :: * -> *) | f -> c where gfmap :: c b => (a -> b) -> (f a -> f b) © Tommaso Piazza, 2018 - https://github.com/blender 16
49. !"# {-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE KindSignatures #-} {-# LANGUAGE FunctionalDependencies #-} import Data.Kind (Constraint) import qualified Data.Set as Set import qualified Data.List as List class GFunctor (c :: * -> Constraint) (f :: * -> *) | f -> c where gfmap :: c b => (a -> b) -> (f a -> f b) instance GFunctor Ord Set.Set where gfmap = Set.map © Tommaso Piazza, 2018 - https://github.com/blender 17
50. No ! no problem {-# LANGUAGE FlexibleInstances #-} class EmptyConstraint a instance EmptyConstraint a © Tommaso Piazza, 2018 - https://github.com/blender 18
51. No ! no problem {-# LANGUAGE FlexibleInstances #-} class EmptyConstraint a instance EmptyConstraint a instance GFunctor EmptyConstraint [] where gfmap = List.map © Tommaso Piazza, 2018 - https://github.com/blender 19
52. Promotions A data type like data ConnectionStatus = Open | Closed © Tommaso Piazza, 2018 - https://github.com/blender 20
53. Promotions A data type like data ConnectionStatus = Open | Closed Can be promoted to a kind {-# LANGUAGE DataKinds #-} data ConnectionStatus = Open | Closed © Tommaso Piazza, 2018 - https://github.com/blender 21
54. DataKinds © Tommaso Piazza, 2018 - https://github.com/blender 22
55. DataKinds {-# LANGUAGE DataKinds #-} Creates a kind ConnectionStatus and two types 'Open and 'Closed © Tommaso Piazza, 2018 - https://github.com/blender 23
56. DataKinds {-# LANGUAGE DataKinds #-} Creates a kind ConnectionStatus and two types 'Open and 'Closed — :t Open © Tommaso Piazza, 2018 - https://github.com/blender 23
57. DataKinds {-# LANGUAGE DataKinds #-} Creates a kind ConnectionStatus and two types 'Open and 'Closed — :t Open — Open :: ConnectionStatus © Tommaso Piazza, 2018 - https://github.com/blender 23
58. DataKinds {-# LANGUAGE DataKinds #-} Creates a kind ConnectionStatus and two types 'Open and 'Closed — :t Open — Open :: ConnectionStatus — :k Open (or :k 'Open ) © Tommaso Piazza, 2018 - https://github.com/blender 23
59. DataKinds {-# LANGUAGE DataKinds #-} Creates a kind ConnectionStatus and two types 'Open and 'Closed — :t Open — Open :: ConnectionStatus — :k Open (or :k 'Open ) — Open :: ConnectionStatus © Tommaso Piazza, 2018 - https://github.com/blender 23
60. Type level connections data Connection (s :: ConnectionStatus) = MkConnection { connectionId :: String } open :: IO (Connection Open) open = return $ MkConnection "someId" close :: Connection Open -> IO (Connection Closed) close (MkConnection c) = return $ MkConnection (c ++ " is now closed") © Tommaso Piazza, 2018 - https://github.com/blender 24
61. Strings as types Kind Symbol fro GHC.TypeList newtype Money (currency :: Symbol) = Money Rational fivePence :: Money "GBP" fivePence = Money (5 % 100) © Tommaso Piazza, 2018 - https://github.com/blender 25
62. Strings as types Kind Symbol newtype Money (currency :: Symbol) = Money Rational fivePence :: Money "GBP" fivePence = Money (5 % 100) twoEuros :: Money "EUR" twoEuros = Money 2 add :: Money c -> Money c -> Money c add (Money x) (Money y) = Money (x + y) add fivePence fivePence Money (1 % 10) add fivePence twoEuros <interactive>:8:15: error: • Couldn't match type ‘"EUR"’ with ‘"GBP"’ © Tommaso Piazza, 2018 - https://github.com/blender 26
63. 1,2,3... as types Kind Nat {-# LANGUAGE KindSignatures, DataKinds #-} import GHC.TypeLits (Symbol, Nat) newtype Discrete (currency :: Symbol) (scale :: (Nat, Nat)) = Discrete Integer oneDollar :: Discrete "USD" '(1, 1) oneDollar = Discrete 1 oneDollarThirtyCents :: Discrete "USD" '(100, 1) oneDollarThirtyCents = Discrete 130 © Tommaso Piazza, 2018 - https://github.com/blender 27
64. Be Kind Thanks! https://diogocastro.com/blog/2018/10/17/haskells-kind- system-a-primer © Tommaso Piazza, 2018 - https://github.com/blender 28
65. I need help! https://github.com/blender/Rome — Writte in Haskell — Used by Mozilla and others — Tons of room for improvement © Tommaso Piazza, 2018 - https://github.com/blender 29