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The Power Of Composition NDC Oslo 2020 @ScottWlaschin fsharpforfunandprofit.com

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The Power Of Composition 1. The philosophy of composition 2. Ideas of functional programming – Functions and how to compose them – Types and how to compose them 3. Composition in practice – Roman Numerals – FizzBuzz gone functional – Uh oh, monads! – A web service

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THE PHILOSOPHY OF COMPOSITION

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Prerequisites for understanding composition • You must have been a child at some point • You must have played with Lego • You must have played with toy trains

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Lego Philosophy

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Lego Philosophy 1. All pieces are designed to be connected 2. The pieces are reusable in many contexts 3. Connect two pieces together and get another "piece" that can still be connected

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All pieces are designed to be connected

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The pieces are reusable in different contexts

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Connect two pieces together and get another "piece" that can still be connected

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Make big things from small things in the same way

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Wooden Railway Track Philosophy 1. All pieces are designed to be connected 2. The pieces are reusable in many contexts 3. Connect two pieces together and get another "piece" that can still be connected

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All pieces are designed to be connected

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The pieces are reusable in different contexts

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Connect two pieces together and get another "piece" that can still be connected You can keep adding and adding.

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Make big things from small things in the same way

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If you understand Lego and wooden railways, then you know everything about composition!

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THE IDEAS OF FUNCTIONAL PROGRAMMING

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Four ideas behind FP Function 3. Types are not classes 1. Functions are things 2. Build bigger functions using composition 4. Build bigger types using composition

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FP idea #1: Functions are things Function

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The Tunnel of Transformation Function apple -> banana A function is a thing which transforms inputs to outputs

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A function is a standalone thing, not attached to a class

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A function is a standalone thing, not attached to a class It can be used for inputs and outputs of other functions

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A function can be an output thing input

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output A function can be an input thing

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input output A function can be a parameter

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input output input output

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FP idea #2: Build bigger functions using composition

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Function 1 apple -> banana Function 2 banana -> cherry

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>> Function 1 apple -> banana Function 2 banana -> cherry

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New Function apple -> cherry Can't tell it was built from smaller functions! Where did the banana go?

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Function composition in F# and C# using the "piping" approach

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int add1(int x) => x + 1; int times2(int x) => x * 2; int square(int x) => x * x; add1(5); // = 6 times2(add1(5)); // = 12 square(times2(add1(5))); // = 144 Nested function calls can be confusing if too deep

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add1 5 6 times2 12 square 144

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5 |> add1 // = 6 5 |> add1 |> times2 // = 12 5 |> add1 |> times2 |> square // = 144 add1 times2 square 5 6 12 144 F# example

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add1 times2 square 5 6 12 144 5.Pipe(add1); 5.Pipe(add1).Pipe(times2); 5.Pipe(add1).Pipe(times2).Pipe(square); C# example

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Building big things from functions It's compositions all the way up

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Low-level operation ToUpper string string

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Low-level operation Service AddressValidator A “Service” is just like a microservice but without the "micro" in front Validation Result Address Low-level operation Low-level operation

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Service Use-case UpdateProfileData ChangeProfile Result ChangeProfile Request Service Service

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Use-case Web application Http Response Http Request Use-case Use-case

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Http Response Http Request Even for complex applications, data flows only in one direction

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FP idea #3: Types are not classes

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So, what is a type then? A type is a just a name for a set of things Set of valid inputs Set of valid outputs Function

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Set of valid inputs Set of valid outputs Function 1 2 3 4 5 6 This is type "integer" A type is a just a name for a set of things

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Set of valid inputs Set of valid outputs Function This is type "string" "abc" "but" "cobol" "double" "end" "float" A type is a just a name for a set of things

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Set of valid inputs Set of valid outputs Function This is type "Person" Donna Roy Javier Mendoza Nathan Logan Shawna Ingram Abel Ortiz Lena Robbins Gordon Wood A type is a just a name for a set of things

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Set of valid inputs Set of valid outputs Function This is type "Fruit" A type is a just a name for a set of things

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Set of valid inputs Set of valid outputs Function This is a type of Fruit->Fruit functions A type is a just a name for a set of things

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FP idea #4: Types can be composed too

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Algebraic type system

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Bigger types are built from smaller types by: Composing with “AND” Composing with “OR”

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FruitSalad = AND AND Compose with “AND”

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Compose with “AND” enum AppleVariety { Red, Green } enum BananaVariety { Yellow, Brown } enum CherryVariety { Tart, Sweet } struct FruitSalad { AppleVariety Apple; BananaVariety Banana; CherryVariety Cherry; } C# example Apple AND Banana AND Cherry

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Compose with “AND” type AppleVariety = Red | Green type BananaVariety = Yellow | Brown type CherryVariety = Tart | Sweet type FruitSalad = { Apple: AppleVariety Banana: BananaVariety Cherry: CherryVariety } F# example

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Snack = OR OR Compose with “OR” type Snack = | Apple of AppleVariety | Banana of BananaVariety | Cherry of CherryVariety

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A real world example of composing types

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Some requirements: We accept three forms of payment: Cash, Paypal, or CreditCard. For Cash we don't need any extra information For Paypal we need an email address For Cards we need a card type and card number

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interface IPaymentMethod {..} class Cash() : IPaymentMethod {..} class Paypal(string emailAddress): IPaymentMethod {..} class Card(string cardType, string cardNo) : IPaymentMethod {..} In OO design you would probably implement it as an interface and a set of subclasses, like this:

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type EmailAddress = string type CardNumber = string In F# you would probably implement by composing types, like this:

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type EmailAddress = ... type CardNumber = … type CardType = Visa | Mastercard type CreditCardInfo = { CardType : CardType CardNumber : CardNumber }

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type EmailAddress = ... type CardNumber = ... type CardType = ... type CreditCardInfo = ... type PaymentMethod = | Cash | PayPal of EmailAddress | Card of CreditCardInfo

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type EmailAddress = ... type CardNumber = ... type CardType = ... type CreditCardInfo = ... type PaymentMethod = | Cash | PayPal of EmailAddress | Card of CreditCardInfo type PaymentAmount = decimal type Currency = EUR | USD | RUB

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type EmailAddress = ... type CardNumber = ... type CardType = ... type CreditCardInfo = ... type PaymentMethod = | Cash | PayPal of EmailAddress | Card of CreditCardInfo type PaymentAmount = decimal type Currency = EUR | USD | RUB type Payment = { Amount : PaymentAmount Currency : Currency Method : PaymentMethod }

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type EmailAddress = ... type CardNumber = ... type CardType = ... type CreditCardInfo = ... type PaymentMethod = | Cash | PayPal of EmailAddress | Card of CreditCardInfo type PaymentAmount = decimal type Currency = EUR | USD | RUB type Payment = { Amount : PaymentAmount Currency : Currency Method : PaymentMethod }

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Composable types can be used as executable documentation

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type Deal = Deck -> (Deck * Card) type PickupCard = (Hand * Card) -> Hand type Suit = Club | Diamond | Spade | Heart type Rank = Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Jack | Queen | King | Ace type Card = { Suit:Suit; Rank:Rank } type Hand = Card list type Deck = Card list type Player = {Name:string; Hand:Hand} type Game = { Deck:Deck; Players:Player list } The domain on one screen!

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type CardType = Visa | Mastercard type CardNumber = string type EmailAddress = string type PaymentMethod = | Cash | PayPal of EmailAddress | Card of CreditCardInfo | Bitcoin of BitcoinAddress

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A big topic and not enough time   More on DDD and designing with types at fsharpforfunandprofit.com/ddd

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Composition in practice: Time for some real examples!

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COMPOSITION WITH PIPING (ROMAN NUMERALS) Technique #1

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To Roman Numerals • Task: How to convert an arabic integer to roman numerals? • 5 => "V" • 12 => "XII" • 107 => "CVII"

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To Roman Numerals

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To Roman Numerals • Use the "tally" approach – Start with N copies of "I" – Replace five "I"s with a "V" – Replace two "V"s with a "X" – Replace five "X"s with a "L" – Replace two "L"s with a "C" – etc

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To Roman Numerals number etc Replicate "I" Replace_IIIII_V Replace_VV_X Replace_XXXXX_L

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string ToRomanNumerals(int number) { // define a helper function for each step string replace_IIIII_V(string s) => s.Replace("IIIII", "V"); string replace_VV_X(string s) => s.Replace("VV", "X"); string replace_XXXXX_L(string s) => s.Replace("XXXXX", "L"); string replace_LL_C(string s) => s.Replace("LL", "C"); // then combine them using piping return new string('I', number) .Pipe(replace_IIIII_V) .Pipe(replace_VV_X) .Pipe(replace_XXXXX_L) .Pipe(replace_LL_C); } C# example

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let toRomanNumerals number = // define a helper function for each step let replace_IIIII_V str = replace "IIIII" "V" str let replace_VV_X str = replace "VV" "X" str let replace_XXXXX_L str = replace "XXXXX" "L" str let replace_LL_C str = replace "LL" "C" str // then combine them using piping String.replicate number "I" |> replace_IIIII_V |> replace_VV_X |> replace_XXXXX_L |> replace_LL_C F# example

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IT'S NOT ALWAYS THIS EASY…

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function A function B Compose

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function A function B

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function A and B  Easy!

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... But here is a challenge

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function A Input Output function B Input 1 Output Input 2

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function A Input Output function B Input 1 Output Input 2 Challenge #1: How can we compose these? 

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COMPOSITION WITH CURRYING (ROMAN NUMERALS) Technique #2

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The Replace function oldValue outputString newValue inputString Replace

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Uh-oh! Composition problem Replace I / V Replace V / X Replace X / L  

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Bad news: Composition patterns only work for functions that have one parameter! 

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Good news! Every function can be turned into a one parameter function 

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Haskell Curry We named this technique after him

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Input A Uncurried Function Input B Output C Curried Function Input A Intermediate Function Output C Input B What is currying? after currying Function as output

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Input A Uncurried Function Input B Output C Curried Function Input A Intermediate Function Output C Input B What is currying? One input One input Currying means that *every* function can be converted to a series of one input functions

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Replace Before currying input.Replace(oldValue, newValue); string output

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Replace Old New Old New After currying Func replace(string oldVal, string newVal) => input => input.Replace(oldVal, newVal);

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Replace Old New Old New After currying Func replace(string oldVal, string newVal) => input => input.Replace(oldVal, newVal);

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Func replace(string oldVal, string newVal) => input => input.Replace(oldVal, newVal); Replace Old New Old New After currying This lambda (function) is returned one-parameter function

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string ToRomanNumerals(int number) { // define a general helper function Func replace( string oldValue, string newValue) => input => input.Replace(oldValue, newValue); // then use piping return new string('I', number) .Pipe(replace("IIIII","V")) .Pipe(replace("VV","X")) .Pipe(replace("XXXXX","L")) .Pipe(replace("LL","C")); } C# example

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string ToRomanNumerals(int number) { // define a general helper function Func replace( string oldValue, string newValue) => input => input.Replace(oldValue, newValue); // then use piping return new string('I', number) .Pipe(replace("IIIII","V")) .Pipe(replace("VV","X")) .Pipe(replace("XXXXX","L")) .Pipe(replace("LL","C")); } C# example

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string ToRomanNumerals(int number) { // define a general helper function Func replace( string oldValue, string newValue) => input => input.Replace(oldValue, newValue); // then use piping return new string('I', number) .Pipe(replace("IIIII","V")) .Pipe(replace("VV","X")) .Pipe(replace("XXXXX","L")) .Pipe(replace("LL","C")); } C# example Only 2 of the 3 parameters are passed in The other parameter comes from the pipeline

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let toRomanNumerals number = // no helper function needed. // currying occurs automatically in F# // combine using piping String.replicate number "I" |> replace "IIIII" "V" |> replace "VV" "X" |> replace "XXXXX" "L" |> replace "LL" "C" F# example

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let toRomanNumerals number = // no helper function needed. // currying occurs automatically in F# // combine using piping String.replicate number "I" |> replace "IIIII" "V" |> replace "VV" "X" |> replace "XXXXX" "L" |> replace "LL" "C" Only 2 of the 3 parameters are passed in F# example The other parameter comes from the pipeline

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Partial Application

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Partial Application let add x y = x + y let multiply x y = x * y 5 |> add 2 |> multiply 3 Piping provides the missing argument partial application

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Partial Application Replace ReplaceOldNew Old New Old New String.replicate number "I" |> replace "IIIII" "V" |> replace "VV" "X" |> replace "XXXXX" "L" |> replace "LL" "C" Only 2 parameters passed in Piping provides the missing argument

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Pipelines are extensible

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let toRomanNumerals number = String.replicate number "I" |> replace "IIIII" "V" |> replace "VV" "X" |> replace "XXXXX" "L" |> replace "LL" "C" Composable => extensible // can easily add new segments to the pipeline |> replace "VIIII" "IX" |> replace "IIII" "IV" |> replace "LXXXX" "XC"

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function Input Output function Input 1 Output Input 2 Challenge #1: How can we compose these? 

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Here is another challenge

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function A Input Output function B Input Output 1 Output 2

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function A Input Output function B Input Output 1 Output 2 Challenge #2: How can we compose these? 

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COMPOSITION WITH BIND (FIZZBUZZ) Technique #3

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FizzBuzz definition Write a program that takes a number as input • For multiples of three print "Fizz" • For multiples of five print "Buzz" • For multiples of both three and five print "FizzBuzz" • Otherwise, print the original number

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let fizzBuzz n = if (isDivisibleBy n 15) then printfn "FizzBuzz" else if (isDivisibleBy n 3) then printfn "Fizz" else if (isDivisibleBy n 5) then printfn "Buzz" else printfn "%i" n let isDivisibleBy n divisor = (n % divisor) = 0 // helper function A simple F# implementation

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let fizzBuzz n = if (isDivisibleBy n 15) then printfn "FizzBuzz" else if (isDivisibleBy n 3) then printfn "Fizz" else if (isDivisibleBy n 5) then printfn "Buzz" else printfn "%i" n let isDivisibleBy n divisor = (n % divisor) = 0 // helper function A simple F# implementation

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Pipeline implementation number Handle 15 case

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Pipeline implementation Handle 3 case number Handle 15 case

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Pipeline implementation Handle 3 case Handle 5 case number Handle 15 case

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Pipeline implementation Handle 3 case Handle 5 case number Answer Handle 15 case Last step

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number Handle case Handled (e.g. "Fizz", "Buzz") Unhandled (e.g. 2, 7, 13)

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Unhandled Handled Input -> or

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Unhandled Handled Input -> type FizzBuzzResult = | Unhandled of int // the original int | Handled of string // "Fizz", Buzz", etc Idea from http://weblog.raganwald.com/2007/01/dont-overthink-fizzbuzz.html or

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type FizzBuzzResult = | Unhandled of int // the original int | Handled of string // "Fizz", Buzz", etc let handle divisor label n = if (isDivisibleBy n divisor) then Handled label else Unhandled n Idea from http://weblog.raganwald.com/2007/01/dont-overthink-fizzbuzz.html

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type FizzBuzzResult = | Unhandled of int // the original int | Handled of string // "Fizz", Buzz", etc let handle divisor label n = if (isDivisibleBy n divisor) then Handled label else Unhandled n

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12 |> handle 3 "Fizz" // Handled "Fizz" 10 |> handle 3 "Fizz" // Unhandled 10 10 |> handle 5 "Buzz" // Handled "Buzz" handle 5 "Buzz"

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let fizzbuzz n = let result15 = n |> handle 15 "FizzBuzz" match result15 with | Handled str -> str | Unhandled n -> let result3 = n |> handle 3 "Fizz" match result3 with | Handled str -> str | Unhandled n -> let result5 = n |> handle 5 "Buzz" match result5 with | Handled str -> str | Unhandled n -> string n // convert to string First implementation attempt

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let fizzbuzz n = let result15 = n |> handle 15 "FizzBuzz" match result15 with | Handled str -> str | Unhandled n -> let result3 = n |> handle 3 "Fizz" match result3 with | Handled str -> str | Unhandled n -> let result5 = n |> handle 5 "Buzz" match result5 with | Handled str -> str | Unhandled n -> // do something with Unhandled value

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let fizzbuzz n = let result15 = n |> handle 15 "FizzBuzz" match result15 with | Handled str -> str | Unhandled n -> let result3 = n |> handle 3 "Fizz" match result3 with | Handled str -> str | Unhandled n -> // do something with Unhandled value // ... // ...

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let fizzbuzz n = let result15 = n |> handle 15 "FizzBuzz" match result15 with | Handled str -> str | Unhandled n -> // do something with Unhandled value // ... // ...

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if Handled then // return the string if Unhandled then // do something with the number

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If Unhandled If Handled Bypass and return the string

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let ifUnhandledDo f result = match result with | Handled str -> Handled str | Unhandled n -> f n

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep let lastStep result = match result with | Handled str -> str | Unhandled n -> string(n) // convert to string

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> lastStep Composable => easy to extend

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> ifUnhandledDo (handle 7 "Baz") |> lastStep Composable => easy to extend

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> ifUnhandledDo (handle 7 "Baz") |> ifUnhandledDo (handle 11 "Pozz") |> lastStep Composable => easy to extend

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let fizzbuzz n = n |> handle 15 "FizzBuzz" |> ifUnhandledDo (handle 3 "Fizz") |> ifUnhandledDo (handle 5 "Buzz") |> ifUnhandledDo (handle 7 "Baz") |> ifUnhandledDo (handle 11 "Pozz") |> ifUnhandledDo (handle 13 "Tazz") |> lastStep Composable => easy to extend

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Another example: Chaining tasks

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When task completes Wait Wait a.k.a "promise", "future"

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let taskExample input = let taskX = startTask input taskX.WhenFinished (fun x -> let taskY = startAnotherTask x taskY.WhenFinished (fun y -> let taskZ = startThirdTask y taskZ.WhenFinished (fun z -> etc

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let taskExample input = let taskX = startTask input taskX.WhenFinished (fun x -> let taskY = startAnotherTask x taskY.WhenFinished (fun y -> let taskZ = startThirdTask y taskZ.WhenFinished (fun z -> do something

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let taskExample input = let taskX = startTask input taskX.WhenFinished (fun x -> let taskY = startAnotherTask x taskY.WhenFinished (fun y -> do something

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let taskExample input = let taskX = startTask input taskX.WhenFinished (fun x -> do something

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let whenFinishedDo f task = task.WhenFinished (fun taskResult -> f taskResult) let taskExample input = startTask input |> whenFinishedDo startAnotherTask |> whenFinishedDo startThirdTask |> whenFinishedDo ... Parameterize the next step

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MONADS!

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Is there a general solution to handling functions like this?

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Yes! “Bind” is the answer! Bind all the things!

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How do we compose these?

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>> >> Composing one-track functions is fine...

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>> >> ... and composing two-track functions is fine...

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  ... but composing points/switches is not allowed!

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Two-track input Two-track output One-track input Two-track output  

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Two-track input Two-track output

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Two-track input Two-track output A function transformer

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let bind nextFunction result = match result with | Unhandled n -> nextFunction n | Handled str -> Handled str Two-track input Two-track output

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let bind nextFunction result = match result with | Unhandled n -> nextFunction n | Handled str -> Handled str Two-track input Two-track output

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let bind nextFunction result = match result with | Unhandled n -> nextFunction n | Handled str -> Handled str Two-track input Two-track output

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let bind nextFunction result = match result with | Unhandled n -> nextFunction n | Handled str -> Handled str Two-track input Two-track output

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let bind nextFunction result = match result with | Unhandled n -> nextFunction n | Handled str -> Handled str Two-track input Two-track output

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FP terminology • A monad is – A data type – With an associated "bind" function – (and some other stuff) • A monadic function is – A switch/points function – "bind" is used to compose them type FizzBuzzResult = | Unhandled of int | Handled of string

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function A Input Output function B Input Output 1 Output 2 Challenge #2: How can we compose these? 

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KLEISLI COMPOSITION (WEB SERVICE) Technique #4

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compose with Kleisli Composition

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Kleisli Composition

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Kleisli Composition

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Kleisli Composition

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= compose with The result is the same kind of thing Kleisli Composition

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The "Lego" approach to building a web server

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Async HttpContext A HttpHandler "WebPart"

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Async HttpContext A HttpHandler "WebPart"

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= >=> The result is another HttpHandler so you can keep adding and adding Composition of HttpHandlers Kleisli composition symbol

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path "/hello" Checks request path (might fail) matches path doesn't match

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OK "Hello" Sets response 200 OK

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path "/hello" >=> OK "Hello" Checks request path (might fail) Sets response >=> A new WebPart

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choose [ ] Picks first HttpHandler that succeeds

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choose [ path "/hello" >=> OK "Hello" path "/goodbye" >=> OK "Goodbye" ] Pick first path that succeeds

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GET Only succeeds if request is a GET

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GET >=> choose [ path "/hello" >=> OK "Hello" path "/goodbye" >=> OK "Goodbye" ]

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let app = choose [ ] startWebServer defaultConfig app A complete web app GET >=> choose [ path "/hello" >=> OK "Hello" path "/goodbye" >=> OK "Goodbye" ] POST >=> choose [ path "/hello" >=> OK "Hello POST" path "/goodbye" >=> OK "Goodbye POST" ]

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Http Response Http Request No classes, no inheritance, one-directional data flow!

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Review • The philosophy of composition – Connectable, reusable parts – Building bigger things from smaller things • FP principles: – Composable functions – Composable types

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Review A taste of various composition techniques: – Piping with "|>" – Currying/partial application – Composition using "bind" (monads!) – Kleisli composition using ">=>" Don't worry about understanding it all, but hopefully it's not so scary now!

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Why bother? Benefits of composition: • Reusable parts – no strings attached • Testable – parts can be tested in isolation • Understandable – data flows in one direction • Maintainable – all dependencies are explicit • Extendable – can add new parts without touching old code • A different way of thinking – it's good for your brain to learn new things!

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Slides and video here fsharpforfunandprofit.com/composition Thank you! @ScottWlaschin Me on twitter My book