The document discusses the complexities and modularity of functors and type classes in functional programming, particularly within the context of Scala. It critiques the Haskell functor hierarchy, presenting alternatives provided by the ZIO Prelude library that aim to offer better compositional patterns. The document also highlights design principles and various type classes that facilitate easier and more ergonomic programming practices.

1. SF Scala Meetup - July 30, 2020
John A. De Goes — @jdegoes
Adam Fraser — @adamfraser
Refactoring Functional
Type Classes

2. WHY YOU’RE
HERE
“Let me tell you why you’re here. You’re here
because you know something. What you know
you can’t explain, but you feel it. You’ve felt it
your entire life, that there’s something wrong
with the world. You don’t know what it is, but
it’s there, like a splinter in your mind, driving
you mad. It is this feeling that has brought you
to me. Do you know what I’m talking about?”
— Morpheus, The Matrix

3. TABLE OF
CONTENTS
01
THE LEGEND OF FUNCTOR
The supreme reign of the Haskell functor hierarchy
02
TROUBLE IN FUNCTOR TOWN
Drawbacks of the classic functor hierarchy
03
EASY ALGEBRA
Unlike category theory, you already know algebra
04
TOUR OF ZIO PRELUDE
An algebraic, modular, & Scala-first basis for type classes

4. THE LEGEND
OF FUNCTOR

5. Functor
THE LEGEND
OF FUNCTOR
trait Functor[F[_]] {
def map[A, B](fa: F[A])(f: A => B): F[B]
}

6. Functor -> Apply
THE LEGEND
OF FUNCTOR
trait Apply[F[_]] extends Functor[F] {
def map[A, B](fa: F[A])(f: A => B): F[B]
def ap[A, B](ff: F[A => B])(f: F[A]): F[B]
}

7. Functor -> Apply -> Applicative
THE LEGEND
OF FUNCTOR
trait Applicative[F[_]] extends Apply[F] {
def map[A, B](fa: F[A])(f: A => B): F[B]
def ap[A, B](ff: F[A => B])(f: F[A]): F[B]
def pure[A](a: A): F[A]
}

8. Functor -> Apply -> Applicative -> Monad
THE LEGEND
OF FUNCTOR
trait Monad[F[_]] extends Applicative[F] {
def map[A, B](fa: F[A])(f: A => B): F[B]
def ap[A, B](ff: F[A => B])(f: F[A]): F[B]
def pure[A](a: A): F[A]
def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B]
}
*Bind is skipped.

9. THE LEGEND OF
FUNCTOR
The Ubiquity of Functor in
Functional Programming
● Haskell
● Scala
○ Scalaz
○ Cats
● Kotlin
● Java
● F#
● Idris
● And many others!
9

10. Books Have Been Written About It
THE LEGEND
OF FUNCTOR

11. TROUBLE IN
FUNCTOR TOWN

12. The Curse of Haskellisms
TROUBLE IN
FUNCTOR TOWN
def ap[A, B](
ff: F[A => B], fa: F[A]): F[B]
f :: Int -> Int -> Int -> Int
f <$> arg1 <*> arg2 <*> arg3

13. Set Is Not A “Functor”?
TROUBLE IN
FUNCTOR TOWN
set.map(f).map(g)
set.map(f andThen g)
f g f.andThen(g)
A B C A C

14. The Functor Hierarchy Is A Lie!
TROUBLE IN
FUNCTOR TOWN
Functor in FP
Functor in Math

15. ZIO Config
TROUBLE IN
FUNCTOR TOWN
(string(“server”) |@|
int(“port”))(
Config.apply(_),
Config.unapply(_))

16. ZIO Codec
TROUBLE IN
FUNCTOR TOWN
lazy val js: Codec[Val] =
((spacing, ()) ~>
(obj | arr | str | `true` |
`false` | `null` | num)
<~ ((), spacing))

17. Introspectable Monads
TROUBLE IN
FUNCTOR TOWN for {
bool <- boolParser
value <- if (bool) parserA
else parserB
} yield value

18. Constrained DSLs
TROUBLE IN
FUNCTOR TOWN
def map[A, B](fa: F[A])(f: A => B): F[B]
val fa: F[A] = …
val f : A => B = …
fa.map(a => f(a))
Type B is unconstrainable!

19. Invariance Pain
TROUBLE IN
FUNCTOR TOWN
val functorDog: F[Dog] = …
val functorAnimal: F[Animal] =
functorDog
ERROR!!!

20. Invariance Pain
TROUBLE IN
FUNCTOR TOWN
val functorDog: F[Dog] = …
val functorAnimal: F[Animal] =
functorDog.widen[Animal]

21. Stack-Exploding Strictness
TROUBLE IN
FUNCTOR TOWN
def forever[A](fa: F[A]): F[A] =
fa *> forever(fa)

22. Lawless Type Classes & Operations
TROUBLE IN
FUNCTOR TOWN
Defer
Foldable
Monad#tailRecM
Parallel
NonEmptyParallel
UnorderedFoldable

23. Type Class Proliferation
TROUBLE IN
FUNCTOR TOWN
Align
Alternative
Always
Applicative
ApplicativeError
Apply
Bifoldable
Bifunctor
Bimonad
Bitraverse
CoflatMap
CommutativeApplicative
CommutativeApply
CommutativeFlatMap
CommutativeMonad
Comonad
Contravariant
ContravariantMonoidal
ContravariantSemigroupal
Defer
Distributive
Eval
EvalGroup
EvalMonoid
EvalSemigroup
FlatMap
Foldable
Functor
FunctorFilter
Inject
InjectK
Invariant
InvariantMonoidal
InvariantSemigroupal
Later
Monad
MonadError
MonoidK
NonEmptyParallelNonEmptyR
educible
NonEmptyTraverse
NotNull
Now
Parallel
Reducible
Representable
SemigroupK
Semigroupal
Show
StackSafeMonad
Traverse
TraverseFilter
UnorderedFoldable
UnorderedTraverse

24. Type Class Proliferation
TROUBLE IN
FUNCTOR TOWN
Align
Alternative
Always
Applicative
ApplicativeError
Apply
Bifoldable
Bifunctor
Bimonad
Bitraverse
CoflatMap
CommutativeApplicative
CommutativeApply
CommutativeFlatMap
CommutativeMonad
Comonad
Contravariant
ContravariantMonoidal
ContravariantSemigroupal
Defer
Distributive
Eval
EvalGroup
EvalMonoid
EvalSemigroup
FlatMap
Foldable
Functor
FunctorFilter
Inject
InjectK
Invariant
InvariantMonoidal
InvariantSemigroupal
Later
Monad
MonadError
MonoidK
NonEmptyParallelNonEmptyR
educible
NonEmptyTraverse
NotNull
Now
Parallel
Reducible
Representable
SemigroupK
Semigroupal
Show
StackSafeMonad
Traverse
TraverseFilter
UnorderedFoldable
UnorderedTraverse
*meme from dev.to

25. Maddening Monad Transformers
TROUBLE IN
FUNCTOR TOWN
type MyApp[E, W, S, R, A] =
OptionT[
EitherT[
WriterT[
StateT[
Kleisli[Task, R, *],
S, *],
W, *],
E, *],
*]

26. TROUBLE IN
FUNCTOR TOWN
Is There Another Way?

27. EASY ALGEBRA

28. EASY ALGEBRA
// Set of elements
type Int
// Operations on those elements
def plus(x: Int, y: Int): Int
// Laws about those operations
x + (y + z) == (x + y) + z
x + y == y + x
You Already Know This

29. EASY ALGEBRA
Associativity
// Set of elements
type A
// Operations on those elements
def combine(l: A, r: A): A
// Laws about those operations
a1 <> (a2 <> a3) == (a1 <> a2) <> a3

30. EASY ALGEBRA
Identity
// Set of elements
type A
// Operations on those elements
def combine(l: A, r: A): A
val identity: A
// Laws about those operations
a <> identity == a
identity <> a == a

31. EASY ALGEBRA
Commutativity
// Set of elements
type A
// Operations on those elements
def combine(l: A, r: A): A
// Laws about those operations
a1 <> a2 == a2 <> a1

32. EASY ALGEBRA

33. EASY ALGEBRA
Standard Types
// Associative, commutative, identity
def combine(l: Int, r: Int): Int =
l + r
val identity: Int = 0
// Associative, identity
def combine(l: String, r: String): String =
l + r
val identity: String = “”

34. EASY ALGEBRA
Business Domain Specific Types
final case class Csv(
rows: Vector[Vector[String]],
headers: Map[String, Int]
)
// Associative, identity
def combine(l: Csv, r: Csv): Csv =
???

35. TOUR OF ZIO
PRELUDE
> PRELUDE

36. ZIO Prelude is a small library that brings a
common, useful algebraic abstractions & data
types to Scala developers.
ZIO Prelude is an alternative to libraries like
Scalaz and Cats based on radical ideas that
embrace modularity & subtyping in Scala and
offer new levels of power and ergonomics.
TOUR OF ZIO
PRELUDE

37. TOUR OF ZIO
PRELUDE
Radical Orthogonal Principled
Scala-First Minimal
Pragmatic
Accessible Opinionated
Guiding Design Principles

38. TOUR OF ZIO
PRELUDE Data Structures &
Patterns for
Traversing
List[A], Option[A], ...
Patterns of
Composition for
Types
(A, A) => A
Patterns of
Composition for
Type Constructors
(F[A], F[A]) => F[A]
Three Areas of Focus

39. TOUR OF ZIO
PRELUDE
The Anti-Modularity of the Functor Hierarchy
Functor
Applicative, Monad, etc.
Trouble starts here!

40. TOUR OF ZIO
PRELUDE
The Anti-Modularity of the Functor Hierarchy
Functions Composition
The Classic Functor
Hierarchy

41. TOUR OF ZIO
PRELUDE
The Anti-Modularity of the Functor Hierarchy
trait Monad[F[_]] extends Applicative[F] {
def map[A, B](fa: F[A])(f: A => B): F[B]
def ap[A, B](ff: F[A => B])(f: F[A]): F[B]
def pure[A](a: A): F[A]
def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B]
}

42. TOUR OF ZIO
PRELUDE
Detangling Functions from Composition
trait Monad[F[_]] {
def map[A, B](fa: F[A])(f: A => B): F[B]
def zip[A, B](fa: F[A], fb: F[B]): F[(A, B)]
def any: F[Any]
def flatten[A](fa: F[F[A]]): F[A]
}

43. TOUR OF ZIO
PRELUDE
The Modularity of the ZIO Prelude Hierarchy
Functions Composition
ZIO Prelude
Hierarchy

44. TOUR OF ZIO
PRELUDE
The Modularity of the ZIO Prelude Hierarchy
type Semigroup[A] = Associative[A]
type CommutativeSemigroup[A] = Associative[A] with Commutative[A]
type Monoid[A] = Identity[A]
type CommutativeMonoid[A] = Commutative[A] with Identity[A]
type Group[A] = Identity[A] with Inverse[A]
type AbelianGroup[A] = Commutative[A] with Identity[A] with Inverse[A]

45. TOUR OF ZIO
PRELUDE
The Modularity of the ZIO Prelude Hierarchy
type Functor[F[+_]] = Covariant[F]
type Contravariant[F[-_]] = zio.prelude.Contravariant[F]
type Invariant[F[_]] = zio.prelude.Invariant[F]
type Alternative[F[+_]] = Covariant[F] with IdentityBoth[F] with IdentityEither[F]
type InvariantAlt[F[_]] = Invariant[F] with IdentityBoth[F] with IdentityEither[F]

46. TOUR OF ZIO
PRELUDE
The Modularity of the ZIO Prelude Hierarchy
type InvariantSemigroupal[F[_]] = Invariant[F] with AssociativeBoth[F]
type Semigroupal[F[+_]] = Covariant[F] with AssociativeBoth[F]
type ContravariantSemigroupal[F[-_]] = Contravariant[F] with AssociativeBoth[F]
type SemigroupK[F[_]] = AssociativeEither[F]
type MonoidK[F[_]] = IdentityEither[F]
type ContravariantMonoidal[F[-_]] = Contravariant[F] with IdentityBoth[F]
type InvariantMonoidal[F[_]] = Invariant[F] with IdentityBoth[F]

47. TOUR OF ZIO
PRELUDE
The Modularity of the ZIO Prelude Hierarchy
type FlatMap[F[+_]] = Covariant[F] with AssociativeFlatten[F]
type Monad[F[+_]] = Covariant[F] with IdentityFlatten[F]
type Divide[F[-_]] = Contravariant[F] with AssociativeBoth[F]
type Divisible[F[-_]] = Contravariant[F] with IdentityBoth[F]
type Decidable[F[-_]] = Contravariant[F] with IdentityBoth[F] with IdentityEither[F]
type Apply[F[+_]] = Covariant[F] with AssociativeBoth[F]
type Applicative[F[+_]] = Covariant[F] with IdentityBoth[F]
type InvariantApplicative[F[_]] = Invariant[F] with IdentityBoth[F]

48. TOUR OF ZIO
PRELUDE
trait Associative[A] {
def combine(l: A, r: A): A
}
// a1 <> (a2 <> a3) == (a1 <> a2) <> a3

49. TOUR OF ZIO
PRELUDE
trait Identity[A] extends Associative[A] {
def combine(l: A, r: A): A
def identity: A
}
// a <> identity == a
// identity <> a == a

50. TOUR OF ZIO
PRELUDE
trait Commutative[A] extends Associative[A] {
def combine(l: A, r: A): A
}
// a1 <> a2 == a2 <> a1

51. TOUR OF ZIO
PRELUDE
trait Covariant[F[+_]] {
def map[A, B](f: A => B):
F[A] => F[B]
}
Variance Guarantees Automatic Widening

52. TOUR OF ZIO
PRELUDE
trait Contravariant[F[-_]] {
def contramap[A, B](f: B => A):
F[A] => F[B]
}
Variance Guarantees Automatic Narrowing

53. TOUR OF ZIO
PRELUDE
case class <=>[A, B](
to: A => B, from: B => A)
trait Invariant[F[_]] {
def invmap[A, B](f: A <=> B):
F[A] <=> F[B]
}

54. TOUR OF ZIO
PRELUDE
trait AssociativeBoth[F[_]] {
def combine[A, B](
left : F[A],
right: F[B]): F[(A, B)]
}
// zio1 zip zio2

55. TOUR OF ZIO
PRELUDE
trait AssociativeEither[F[_]] {
def combine[A, B](
left : F[A],
right: F[B]): F[Either[A, B]]
}
// zio1 orElseEither zio2

56. TOUR OF ZIO
PRELUDE
trait AssociativeFlatten[F[+_]] {
def flatten[A](nested: F[F[A]]): F[A]
}
// zio.flatten

57. TOUR OF ZIO
PRELUDE
trait IdentityBoth[F[_]] extends
AssociativeBoth[F] {
def combine[A, B](
left : F[A],
right: F[B]): F[(A, B)]
def any: F[Any]
}
// zio1 zip zio2
// ZIO.unit

58. TOUR OF ZIO
PRELUDE
trait IdentityEither[F[_]] extends
AssociativeBoth[F] {
def combine[A, B](
left : F[A],
right: F[B]): F[Either[A, B]]
def none: F[Nothing]
}
// zio1 orElseEither zio2
// ZIO.halt(Cause.empty)

59. TOUR OF ZIO
PRELUDE
trait IdentityFlatten[F[+_]] extends
AssociativeFlatten[F] {
def flatten[A](nested: F[F[A]]): F[A]
def any: F[Any]
}
// zio.flatten
// ZIO.unit

60. TOUR OF ZIO
PRELUDE
trait CommutativeBoth[F[_]] extends
AssociativeBoth[F] {
def combine[A, B](
left : F[A],
right: F[B]): F[(A, B)]
}
// zio1 zipPar zio2

61. TOUR OF ZIO
PRELUDE
trait CommutativeEither[F[_]] extends
AssociativeEither[F] {
def combine[A, B](
left : F[A],
right: F[B]): F[Either[A, B]]
}
// zio1 raceEither zio2

62. TOUR OF ZIO
PRELUDE
trait Traversable[Data[+_]] {
def foreach[Effect[_]: …, A, B](as: Data[A])(
f: A => Effect[B]): Effect[Data[B]]
}
// requests.foreach { request =>
// handleRequest(request)
// }

63. TOUR OF ZIO
PRELUDE
trait NonEmptyTraversable[Data[+_]] extends
Traversable[Data] {
def foreach1[Effect[_]: …, A, B](as: Data[A])(
f: A => Effect[B]): Effect[Data[B]]
}

64. TOUR OF ZIO
PRELUDE
Debug[-A]
Equal[-A]
Hash[-A]
Ord[-A]
Embracing Declaration-Site Variance
implicit val ordAnimal:
Ord[Animal] = …
if (dog1 <= dog2) {
// WORKS!!!
}

65. TOUR OF ZIO
PRELUDE
NonEmptyList[A]
Validation[E, A]
ZSet[M, A]
Embrace & Extend Scala Collections

66. TOUR OF ZIO
PRELUDE
trait ZPure[-StateIn, +StateOut, -Env, +Err, +Success]
type State[S, +A] = ZPure[S, S, Any, Nothing, A]
type EState[S, +E, +A] = ZPure[S, S, Any, E , A]
No More Monad Transformers
For when you think ZIO is great but just doesn’t have enough type parameters

67. TOUR OF ZIO
PRELUDE
type MyStack[S1, S2, R, E, A] =
Kleisli[
({ type lambda[a] =
EitherT[
({ type lambda[a] =
IndexedStateT[Eval, S1, S2, a]
})#lambda,
E,
a]
})#lambda,
R,
A]
The Alternative

68. TOUR OF ZIO
PRELUDE
// Monad Transformers
def get[S, R, E]: MyStack[S, S, R, E, S] = {
type SState[A] = State[S, A]
type EitherESState[A] = EitherT[SState, E, A]
val eitherT = EitherT.liftF[SState, E, S](State.get)
Kleisli.liftF[EitherESState, R, S](eitherT)
}
// ZPure
def get[S]: State[S, S] =
State.get[S]
Ergonomics

69. TOUR OF ZIO
PRELUDE
Performance

70. TOUR OF ZIO
PRELUDE
Newtypes
object Meter extends Subtype[Int]
type Meter = Meter.Type
object Sum extends SubtypeF
type Sum[A] = Sum.Type[A]
object Natural extends
NewtypeSmart[Int](isGreaterThanEqualTo(0))
type Natural = Natural.Type

71. TOUR OF ZIO
PRELUDE
Ergonomics
List(1, 2, 3, 4, 5).foldMap(Sum(_))
// 15
List(1, 2, 3, 4, 5).foldMap(Prod(_))
// 120

72. ● Documentation
● More Instances
● More Polishing
● Effect Type Classes
● Performance Optimization
● Automatic Derivation for ADTs
● Get Feedback from Real Users
NEXT STEPS

73. SPECIAL THANKS
● Dejan Mijic
● Sken
● Manfred Weber
● Jorge Aliss
● Phil Derome
● Kamal King
● Maxim Schuwalaw
And Salar Rahmanian!

74. THANK YOU!
Does anyone have any questions?
github.com/zio/zio-prelude
Get mentored: patreon.com/jdegoes
Follow us: @jdegoes, @adamfraser