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Functional Programming
with Λrrow
Mohit Sarveiya
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Functional Programming with Λrrow
• Data Types
• Optics
• Error Handling
• Type Classes
• Types of Polymorphism
• Ad-hoc Polymorphism
• Type classes proposal for Kotlin
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Optics
Iso
Lens
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Optics
Iso
Lens
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data class Point2D
data class Cords
(val x: Int, val y: Int)
Isomorphism
(val x: Int, val y: Int)
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data class Point2D
data class Cords
(val x: Int, val y: Int)
Isomorphism
(val x: Int, val y: Int)
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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)
}
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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)
}
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Isomorphism
point2DToCords: Point2D "-> Cords
cordsToPoint2D: Cords "-> Point2D
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Isomorphism
Source:
Focus:
f ≇ g = IdA
g ≇ f = IdS
f: "->
g: "->
S
A
S A
A S
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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
}
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Isomorphism
val pointIsoCords : Iso =
Iso(
get = { point !-> Cords(point.x, point.y) },
reverseGet = { cords !-> Point2D(cords.x, cords.y) }
)
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Isomorphism
val point = Point2D(6, 10)
val cords: Cords = pointIsoCords.get(point)
"// Cords(6, 10)
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Isomorphism
val cords = Cords(6, 10)
val point2D: Point2D = pointIsoCords.reverseGet(cords)
"// Point2D(6, 10)
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data class Point2D
data class Tuple2
(val x: Int, val y: Int)
Isomorphism
(val x: Int, val y: Int)
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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("..)
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val pointIsoTuple: Iso> =
Iso(
get = { point !-> point.x toT point.y },
reverseGet = { tuple !-> Point2D(tuple.a, tuple.b) }
)
Isomorphism
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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
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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)
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@Retention(SOURCE)
@Target(CLASS)
annotation class isos
Generating Isomorphism
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Generating Isomorphism
@isos data class Point2D (val x: Int, val y: Int)
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Optics
Iso
Lens
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Lens
Source: S
Purpose: Set, Get, Copy an immutable data structure
through functional references.
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Lens
Lens
Get : S "-> A
Set : A "-> (S "-> S)
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Lens
data class Person(val name: String, val age: Int)
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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)} }
)
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Lens
val person = Person("John Doe", 100)
val personNameLens : Lens = Lens(
get = { person !-> person.name },
set = { newName !-> {foo !-> foo.copy(name = newName)} }
)
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Lens
val person = Person("John Doe", 100)
val newPerson = personNameLens.set(person, "John Doe Jr”)
// Person(name=John Doe Jr, age=100)
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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)
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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)
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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()
)
)
)
)
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Lens
data class Street(val number: Int, val name: String)
data class Employee(val name: String, val company: Company)
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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)
}
}
)
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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)
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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)
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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)
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Lens
val employeeStreetName = employeeCompany compose
companyAddress compose
addressStreet compose
streetName
val employee = employeeStreetName.modify(
employee,
String"::capitalize)
// Employee(name=John Doe, ... name=Hacker Way))))
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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)
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Generating Lenses
@Retention(SOURCE)
@Target(CLASS)
annotation class lenses
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Generating Lens
@lenses
data class Employee(val name: String,
val company: Company)
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Error Handling
Option
Either
Try
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Error Handling
Option
Either
Try
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val books : List? = getBooks()
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val books : List? = getBooks()
books"?.map { ""... }
books"?.flatMap { ""... }
books"?.fold(""...)
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val book : Book? = getBookForId(1000)
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val book : Book? = getBookForId(1000)
book"?.map { ""... }
book"?.flatMap { ""... }
book"?.fold(""...)
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Option
A
Some None
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sealed class Option {
object None : Option()
data class Some(val t: T) : Option()
}
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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
}
}
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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
}
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val option : Option = getBookForId(1000)
fun T?.toOption(): Option =
if (this != null) {
Some(this)
} else {
None
}
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val option : Option = getBookForId(1000)
fun getBookForId(id : Int) : Option {
return getAllBooksFromDB()
.find { it.id "== id }
.toOption()
}
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val option : Option = getBookForId(1000)
val totalPrice: Option = option.map { book !->
book.price + tax
}
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val option : Option = getBookForId(1000)
val description = option.fold(
ifEmpty = {
"No Description"
},
some = {
it.description
}
)
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Error Handling
Option
Either
Try
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fun reciprocal(i: Int): Double {
if (i "== 0)
throw IllegalArgumentException("Can’t be 0")
return 1.0 / i
}
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throw IllegalArgumentException(“Can’t be 0")
fun reciprocal(i: Int): Double {
if (i == 0)
return 1.0 / i
}
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try {
val reciprocal = reciprocal(2)
compute(reciprocal)
} catch (e: IllegalArgumentException) {
log("Failed to take reciprocal”)
}
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Either
A
Left Right
B
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sealed class Either {
data class Left(val a: A) : Either()
data class Right(val b: B) : Either()
}
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fun reciprocal(i: Int): Double {
if (i == 0)
throw IllegalArgumentException(“Can’t be 0")
return 1.0 / i
}
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fun reciprocal(i: Int): {
if (i == 0)
throw IllegalArgumentException(“Can’t be 0")
return 1.0 / I
}
Either
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fun reciprocal(i: Int): {
return if (i == 0) {
} else {
1.0 / i
}
}
Either.left(IllegalArgumentException(“Can’t be 0")
Either
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fun reciprocal(i: Int): {
return if (i == 0) {
} else {
}
}
Either.left(IllegalArgumentException(“Can’t be 0")
Either
Either.right(1.0 / i)
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fun reciprocal(i: Int): {
return if (i == 0) {
} else {
}
}
Either.left(IllegalArgumentException(“Can’t be 0")
Either
Either.right(1.0 / i)
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val either: Either = reciprocal(2)
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val either: Either = reciprocal(2)
when(either) {
is Either.Left "-> log("Failed to take reciprocal")
is Either.Right "-> compute(either.b)
}
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Error Handling
Option
Either
Try
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fun reciprocal(i: Int): Double {
if (i == 0)
throw IllegalArgumentException(“Can’t be 0")
return 1.0 / i
}
External Library
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var reciprocal : Double = try {
reciprocal(0)
} catch (e: IllegalArgumentException) {
1.0
}
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val reciprocal = Try {
reciprocal(2)
}.getOrDefault {
1.0
}
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Try {
reciprocal(0)
}.fold(
{ t: Throwable !->
log("Failed to take reciprocal", t)
},
{ num: Double !->
compute(num)
})
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sealed class Try {
data class Failure(val e: Throwable) : Try()
data class Success(val value: A) : Try()
}
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Adhoc Polymorphism & Type Classes
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Type Classes
Functor, Monad, Monoid, Applicative …
Type Constructors
Option, Try, Either, IO, Ior, Reader, State
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Polymorphism
Ad-hoc Universal
Overloading Coercion Inclusion Parametric
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Parametric Polymorphism
fun head(a : List) : A {
return a[0]
}
• Same implementation for all types.
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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
}
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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?
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Define Type Class
interface Monoid {
fun combine(a: F, b: F): F
}
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Define Type Class
interface Monoid {
fun combine(a: F, b: F): F
}
val monoidMap = mutableMapOf, Monoid"<*">>()
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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
}
}
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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)
}
}
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Getting Instances of Type Class
val monoidMap = mutableMapOf, Monoid"<*">>()
inline fun monoidal(): Monoid {
return monoidMap[F"::class.java] as Monoid
}
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Ad-hoc Polymorphism with Type Class
inline fun combineAll(
a: F, b: F,
ev: Monoid = monoidal()
): F {
return ev.combine(a, b)
}
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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")
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Type Classes in Λrrow
@typeclass
interface Functor : TC {
fun map(fa: HK, f: (A) -> B): HK
}
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Type Classes Instance in Λrrow
@instance(Option"::class)
interface OptionFunctorInstance : Functor {
override fun map(
fa: OptionKind, f: kotlin.Function1
): Option =
fa.ev().map(f)
}
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Type Classes Proposal
typeclass Monoid {
fun A.combine(b: A): A
fun empty(): A
}
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Type Classes Proposal
package intext
instance object IntMonoid : Monoid {
fun Int.combine(b: Int): Int = this + b
fun empty(): Int = 0
}
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Type Classes Proposal
import intext.IntMonoid
1.combine(2) "// 3
Int.empty() "// 0
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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`
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Swift Extension Protocols
extension Int : Monoid {
static func e() "-> Int {
return 0
}
}
extension Bool : Monoid {
static func e() "-> Bool {
return false
}
}
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Suggestions to Learn more!
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Thank you!
twitter.com/heyitsmohit
github.com/msya