Functional Programming with Arrow

Discussion of data types and type classes available in the library called Arrow for Kotlin.

Transcript

1. Functional Programming
   with Λrrow
   Mohit Sarveiya
   

   View Slide

2. View Slide

3. View Slide

4. Functional Programming with Λrrow
   • Data Types
   
   • Optics
   
   • Error Handling
   
   • Type Classes
   
   • Types of Polymorphism
   
   • Ad-hoc Polymorphism
   
   • Type classes proposal for Kotlin
   

   View Slide

5. Optics
   Iso
   Lens
   

   View Slide

6. Optics
   Iso
   Lens
   

   View Slide

7. data class Point2D
   data class Cords
   (val x: Int, val y: Int)
   Isomorphism
   (val x: Int, val y: Int)
   

   View Slide

8. data class Point2D
   data class Cords
   (val x: Int, val y: Int)
   Isomorphism
   (val x: Int, val y: Int)
   

   View Slide

9. data class Point2D
   data class Cords
   (val x: Int, val y: Int)
   Isomorphism
   (val x: Int, val y: Int)
   fun point2DToCords (point2D: Point2D): Cords {
   return Cords(point2D.x, point2D.y)
   }
   

   View Slide

10. data class Point2D
    data class Cords
    (val x: Int, val y: Int)
    Isomorphism
    (val x: Int, val y: Int)
    fun cordsToPoint2D (cord: Cord): Point2D {
    return Point2D(cord.x, cord.y)
    }
    

    View Slide

11. Isomorphism
    point2DToCords: Point2D "-> Cords
    cordsToPoint2D: Cords "-> Point2D
    

    View Slide

12. Isomorphism
    Source:
    Focus:
    f ≇ g = IdA
    g ≇ f = IdS
    f: "->
    g: "->
    S
    A
    S A
    A S
    

    View Slide

13. Isomorphism
    interface Iso {
    /**
    * Get the focus of a [Iso]
    "*/
    fun get(s: S): A
    /**
    * Get the modified focus of a [Iso]
    "*/
    fun reverseGet(b: B): T
    }
    

    View Slide

14. Isomorphism
    val pointIsoCords : Iso =
    Iso(
    get = { point !-> Cords(point.x, point.y) },
    reverseGet = { cords !-> Point2D(cords.x, cords.y) }
    )
    

    View Slide

15. Isomorphism
    val point = Point2D(6, 10)
    val cords: Cords = pointIsoCords.get(point)
    "// Cords(6, 10)
    

    View Slide

16. Isomorphism
    val cords = Cords(6, 10)
    val point2D: Point2D = pointIsoCords.reverseGet(cords)
    "// Point2D(6, 10)
    

    View Slide

17. data class Point2D
    data class Tuple2
    (val x: Int, val y: Int)
    Isomorphism
    (val x: Int, val y: Int)
    

    View Slide

18. data class Tuple2(val a: A, val b: B)
    Isomorphism
    data class Tuple3(val a: A,
    val b: B,
    val c: C)
    data class Tuple4("..)
    

    View Slide

19. val pointIsoTuple: Iso> =
    Iso(
    get = { point !-> point.x toT point.y },
    reverseGet = { tuple !-> Point2D(tuple.a, tuple.b) }
    )
    Isomorphism
    

    View Slide

20. var point2D = Point2D(1, 2)
    val tuple2 = pointIsoTuple.get(point2D)
    "// Tuple2(a=1, b=2)
    val point2D = pointIsoTuple.reverseGet(tuple2)
    "// Point2D(x=1, y=2)
    Isomorphism
    

    View Slide

21. val pointIsoTuple = Iso(
    get = { point !-> Tuple2(point.x, point.y) },
    reverseGet = { tuple !-> Point2D(tuple.a, tuple.b) }
    )
    Generating Isomorphism
    data class Point2D (val x: Int, val y: Int)
    

    View Slide

22. @Retention(SOURCE)
    @Target(CLASS)
    annotation class isos
    Generating Isomorphism
    

    View Slide

23. Generating Isomorphism
    @isos data class Point2D (val x: Int, val y: Int)
    

    View Slide

24. Optics
    Iso
    Lens
    

    View Slide

25. Lens
    Source: S
    Purpose: Set, Get, Copy an immutable data structure
    through functional references.
    

    View Slide

26. Lens
    Lens
    Get : S "-> A
    Set : A "-> (S "-> S)
    

    View Slide

27. Lens
    data class Person(val name: String, val age: Int)
    

    View Slide

28. Lens
    data class Person(val name: String, val age: Int)
    val personNameLens : Lens = Lens(
    get = { person !-> person.name },
    set = { newName !-> {foo !-> foo.copy(name = newName)} }
    )
    

    View Slide

29. Lens
    val person = Person("John Doe", 100)
    val personNameLens : Lens = Lens(
    get = { person !-> person.name },
    set = { newName !-> {foo !-> foo.copy(name = newName)} }
    )
    

    View Slide

30. Lens
    val person = Person("John Doe", 100)
    val newPerson = personNameLens.set(person, "John Doe Jr”)
    // Person(name=John Doe Jr, age=100)
    

    View Slide

31. Lens
    data class Employee(val name: String, val company: Company)
    data class Company(val name: String, val address: Address)
    data class Address(val city: String, val street: Street)
    data class Street(val number: Int, val name: String)
    

    View Slide

32. Lens
    val street = Street(1, "hacker Way”)
    val address = Address("Menlo Park, CA", street)
    val company = Company("Facebook", address)
    val employee = Employee("John Doe", company)
    

    View Slide

33. Lens
    employee.copy(
    company = employee.company.copy(
    address = employee.company.address.copy(
    street = employee.company.address.street.copy(
    name = employee.company.address.street.name.capitalize()
    )
    )
    )
    )
    

    View Slide

34. Lens
    data class Street(val number: Int, val name: String)
    data class Employee(val name: String, val company: Company)
    

    View Slide

35. val company: Company)
    Lens
    data class Employee(val name: String, val company: Company)
    val employeeCompany: Lens =
    Lens(get = { it.company },
    set = { company !->
    { employee !->
    employee.copy(company = company)
    }
    }
    )
    

    View Slide

36. data class Company(val name: String, val address: Address)
    Lens
    val companyAddress: Lens =
    Lens(
    get = { it.address },
    set = { address !->
    { company !->
    company.copy(address = address)
    }
    })
    val address: Address)
    

    View Slide

37. data class Address(val city: String, val street: Street)
    Lens
    val addressStreet: Lens =
    Lens(
    get = { it.street },
    set = { street !-> {
    address !->
    address.copy(street = street)
    }
    })
    val street: Street)
    

    View Slide

38. data class Street(val number: Int, val name: String)
    Lens
    val streetName: Lens = Lens(
    get = { it.name },
    set = { name !-> { street !-> street.copy(name = name) } }
    )
    val name: String)
    

    View Slide

39. Lens
    val employeeStreetName = employeeCompany compose
    companyAddress compose
    addressStreet compose
    streetName
    val employee = employeeStreetName.modify(
    employee,
    String"::capitalize)
    // Employee(name=John Doe, ... name=Hacker Way))))
    

    View Slide

40. val company: Company)
    Generating Lenses
    val employeeCompany: Lens =
    Lens(get = { it.company },
    set = { company !->
    { employee !->
    employee.copy(company = company)
    }
    }
    )
    data class Employee(val name: String, val company: Company)
    

    View Slide

41. Generating Lenses
    @Retention(SOURCE)
    @Target(CLASS)
    annotation class lenses
    

    View Slide

42. Generating Lens
    @lenses
    data class Employee(val name: String,
    val company: Company)
    

    View Slide

43. Error Handling
    Option
    Either
    Try
    

    View Slide

44. Error Handling
    Option
    Either
    Try
    

    View Slide

45. val books : List? = getBooks()
    

    View Slide

46. val books : List? = getBooks()
    books"?.map { ""... }
    books"?.flatMap { ""... }
    books"?.fold(""...)
    

    View Slide

47. val book : Book? = getBookForId(1000)
    

    View Slide

48. val book : Book? = getBookForId(1000)
    book"?.map { ""... }
    book"?.flatMap { ""... }
    book"?.fold(""...)
    

    View Slide

49. Option
    A
    Some None
    

    View Slide

50. sealed class Option {
    object None : Option()
    data class Some(val t: T) : Option()
    }
    

    View Slide

51. val option : Option = getBookForId(1000)
    fun getBookForId(id : Int) : Option {
    val book : Book? = getAllBooksFromDB().find {
    it.id "== id
    }
    return if (book "!= null) {
    Some(book)
    } else {
    None
    }
    }
    

    View Slide

52. val option : Option = getBookForId(1000)
    fun getBookForId(id : Int) : Option {
    val book : Book? = getAllBooksFromDB().find {
    it.id "== id
    }
    }
    return if (book "!= null) {
    Some(book)
    } else {
    None
    }
    

    View Slide

53. val option : Option = getBookForId(1000)
    fun T?.toOption(): Option =
    if (this != null) {
    Some(this)
    } else {
    None
    }
    

    View Slide

54. val option : Option = getBookForId(1000)
    fun getBookForId(id : Int) : Option {
    return getAllBooksFromDB()
    .find { it.id "== id }
    .toOption()
    }
    

    View Slide

55. val option : Option = getBookForId(1000)
    val totalPrice: Option = option.map { book !->
    book.price + tax
    }
    

    View Slide

56. val option : Option = getBookForId(1000)
    val description = option.fold(
    ifEmpty = {
    "No Description"
    },
    some = {
    it.description
    }
    )
    

    View Slide

57. Error Handling
    Option
    Either
    Try
    

    View Slide

58. fun reciprocal(i: Int): Double {
    if (i "== 0)
    throw IllegalArgumentException("Can’t be 0")
    return 1.0 / i
    }
    

    View Slide

59. throw IllegalArgumentException(“Can’t be 0")
    fun reciprocal(i: Int): Double {
    if (i == 0)
    return 1.0 / i
    }
    

    View Slide

60. try {
    val reciprocal = reciprocal(2)
    compute(reciprocal)
    } catch (e: IllegalArgumentException) {
    log("Failed to take reciprocal”)
    }
    

    View Slide

61. Either
    A
    Left Right
    B
    

    View Slide

62. sealed class Either {
    data class Left(val a: A) : Either()
    data class Right(val b: B) : Either()
    }
    

    View Slide

63. fun reciprocal(i: Int): Double {
    if (i == 0)
    throw IllegalArgumentException(“Can’t be 0")
    return 1.0 / i
    }
    

    View Slide

64. fun reciprocal(i: Int): {
    if (i == 0)
    throw IllegalArgumentException(“Can’t be 0")
    return 1.0 / I
    }
    Either
    

    View Slide

65. fun reciprocal(i: Int): {
    return if (i == 0) {
    } else {
    1.0 / i
    }
    }
    Either.left(IllegalArgumentException(“Can’t be 0")
    Either
    

    View Slide

66. fun reciprocal(i: Int): {
    return if (i == 0) {
    } else {
    }
    }
    Either.left(IllegalArgumentException(“Can’t be 0")
    Either
    Either.right(1.0 / i)
    

    View Slide

67. fun reciprocal(i: Int): {
    return if (i == 0) {
    } else {
    }
    }
    Either.left(IllegalArgumentException(“Can’t be 0")
    Either
    Either.right(1.0 / i)
    

    View Slide

68. val either: Either = reciprocal(2)
    

    View Slide

69. val either: Either = reciprocal(2)
    when(either) {
    is Either.Left "-> log("Failed to take reciprocal")
    is Either.Right "-> compute(either.b)
    }
    

    View Slide

70. Error Handling
    Option
    Either
    Try
    

    View Slide

71. fun reciprocal(i: Int): Double {
    if (i == 0)
    throw IllegalArgumentException(“Can’t be 0")
    return 1.0 / i
    }
    External Library
    

    View Slide

72. var reciprocal : Double = try {
    reciprocal(0)
    } catch (e: IllegalArgumentException) {
    1.0
    }
    

    View Slide

73. val reciprocal = Try {
    reciprocal(2)
    }.getOrDefault {
    1.0
    }
    

    View Slide

74. Try {
    reciprocal(0)
    }.fold(
    { t: Throwable !->
    log("Failed to take reciprocal", t)
    },
    { num: Double !->
    compute(num)
    })
    

    View Slide

75. sealed class Try {
    data class Failure(val e: Throwable) : Try()
    data class Success(val value: A) : Try()
    }
    

    View Slide

76. Adhoc Polymorphism & Type Classes
    

    View Slide

77. Type Classes
    Functor, Monad, Monoid, Applicative …
    Type Constructors
    Option, Try, Either, IO, Ior, Reader, State
    

    View Slide

78. Polymorphism
    Ad-hoc Universal
    Overloading Coercion Inclusion Parametric
    

    View Slide

79. Parametric Polymorphism
    fun head(a : List) : A {
    return a[0]
    }
    • Same implementation for all types.
    

    View Slide

80. Ad-hoc Polymorphism
    fun combineAll(a: Matrix, b: Matrix) : Matrix {
    return doMatrixComputation()
    }
    • Same name with different implementation.
    
    • Type Dependent.
    fun combineAll(a: String, b: String) : String {
    return a + b
    }
    

    View Slide

81. Ad-hoc Polymorphism with Type Class
    inline fun combineAll(
    a: F, b: F,
    ev: Monoid = monoidal()
    ): F {
    return ev.combine(a, b)
    }
    • Polymorphism with Type Classes.
    
    • How do I achieve this?
    

    View Slide

82. Define Type Class
    interface Monoid {
    fun combine(a: F, b: F): F
    }
    

    View Slide

83. Define Type Class
    interface Monoid {
    fun combine(a: F, b: F): F
    }
    val monoidMap = mutableMapOf, Monoid"<*">>()
    

    View Slide

84. Define Instances of Type Class
    val monoidMap = mutableMapOf, Monoid"<*">>()
    monoidMap[String"::class.java] = object: Monoid {
    override fun combine(a: String, b: String): String {
    return a + b
    }
    }
    

    View Slide

85. Define Instances of Type Class
    val monoidMap = mutableMapOf, Monoid"<*">>()
    monoidMap[Matrix"::class.java] = object: Monoid {
    override fun combine(a: Matrix, b: Matrix): Matrix {
    return addMatricies(a, b)
    }
    }
    

    View Slide

86. Getting Instances of Type Class
    val monoidMap = mutableMapOf, Monoid"<*">>()
    inline fun monoidal(): Monoid {
    return monoidMap[F"::class.java] as Monoid
    }
    

    View Slide

87. Ad-hoc Polymorphism with Type Class
    inline fun combineAll(
    a: F, b: F,
    ev: Monoid = monoidal()
    ): F {
    return ev.combine(a, b)
    }
    

    View Slide

88. Ad-hoc Polymorphism with Type Class
    inline fun combineAll(
    a: F, b: F,
    ev: Monoid = monoidal()
    ): F {
    return ev.combine(a, b)
    }
    combineAll(matrix, matrix)
    combineAll("Hello", "World")
    

    View Slide

89. Type Classes in Λrrow
    @typeclass
    interface Functor : TC {
    fun map(fa: HK, f: (A) -> B): HK
    }
    

    View Slide

90. Type Classes Instance in Λrrow
    @instance(Option"::class)
    interface OptionFunctorInstance : Functor {
    override fun map(
    fa: OptionKind, f: kotlin.Function1
    ): Option =
    fa.ev().map(f)
    }
    

    View Slide

91. View Slide

92. Type Classes Proposal
    typeclass Monoid {
    fun A.combine(b: A): A
    fun empty(): A
    }
    

    View Slide

93. Type Classes Proposal
    package intext
    instance object IntMonoid : Monoid {
    fun Int.combine(b: Int): Int = this + b
    fun empty(): Int = 0
    }
    

    View Slide

94. Type Classes Proposal
    import intext.IntMonoid
    1.combine(2) "// 3
    Int.empty() "// 0
    

    View Slide

95. Type Classes Proposal
    import intext.IntMonoid
    fun add(a: A, b: A): A given Monoid = a.combine(b)
    add(1, 1) "// compiles
    add("a", "b") "// does not compile: No `String: Monoid`
    

    View Slide

96. Swift Extension Protocols
    extension Int : Monoid {
    static func e() "-> Int {
    return 0
    }
    }
    extension Bool : Monoid {
    static func e() "-> Bool {
    return false
    }
    }
    

    View Slide

97. Suggestions to Learn more!
    

    View Slide

98. View Slide

99. View Slide

100. View Slide

101. View Slide

102. Thank you!
     twitter.com/heyitsmohit

     github.com/msya
     
     

     View Slide