Functional Programming Patterns (BuildStuff '14)

Functional Design Patterns
@ScottWlaschin
fsharpforfunandprofit.com

Functional Design Patterns
@ScottWlaschin
fsharpforfunandprofit.com
X

Functional patterns
•Apomorphisms
•Dynamorphisms
•Chronomorphisms
•Zygohistomorphic prepromorphisms

Functional patterns
•Core Principles of FP design
–Functions, types, composition
•Functions as parameters
–Abstraction, Dependency injection
–Partial application, Continuations, Folds,
•Chaining functions
–Error handling, Async
–Monads
•Dealing with wrapped data
–Lifting, Functors
–Validation with Applicatives
•Aggregating data and operations
–Monoids

This talk
A whirlwind tour of many sights
Don't worry if you don't understand everything

Functional programming is scary

Object oriented programming is scary

•Single Responsibility Principle
•Open/Closed principle
•Dependency Inversion Principle
•Interface Segregation Principle
•Factory pattern
•Strategy pattern
•Decorator pattern
•Visitor pattern
•Functions
•Functions
•Functions, also
•Functions
•Yes, functions
•Oh my, functions again!
•Functions
•Functions 
OO pattern/principle
FP pattern/principle
Seriously, FP patterns are different

A short and mostly wrong history of programming paradigms

•What we envisioned:
–Smalltalk
•What we got:
–C++
–Object oriented Cobol
–PHP
–Java
“Worse is better”
Object-Oriented programming

•What we envisioned:
–Haskell, OCaml, F#, etc
•What we got:
–??
Functional programming
Please don’t let this happen to FP!

CORE PRINCIPLES OF FP DESIGN
Important to understand!

Core principles of FP design
Steal from mathematics
Types are not classes
Functions are things
Composition everywhere
Function

Core principle: Steal from mathematics
“Programming is one of the most difficult branches of applied mathematics” - E. W. Dijkstra

Why mathematics
Dijkstra said:
•Mathematical assertions tend to be unusually precise.
•Mathematical assertions tend to be general. They are applicable to a large (often infinite) class of instances.
•Mathematics embodies a discipline of reasoning allowing assertions to be made with an unusually high confidence level.

“Object-oriented programming is an exceptionally bad idea which could only have originated in California.”
E. W. Dijkstra

Mathematical functions
Function add1(x) input x maps to x+1
…
-1
0
1
2
3
…
Domain (int)
Codomain (int)
…
0
1
2
3
4
…
let add1 x = x + 1
val add1 : int -> int

…
-1
0
1
2
3
…
Domain (int)
Codomain (int)
…
0
1
2
3
4
…
int add1(int input)
{
switch (input)
{
case 0: return 1;
case 1: return 2;
case 2: return 3;
case 3: return 4;
etc ad infinitum
}
}
•Input and output values already exist
•A function is not a calculation, just a mapping
•Input and output values are unchanged (immutable)

•A (mathematical) function always gives the same output value for a given input value
•A (mathematical) function has no side effects
…
-1
0
1
2
3
…
Domain (int)
Codomain (int)
…
0
1
2
3
4
…

Functions don't have to be about arithmetic
Function CustomerName(x) input Customer maps to PersonalName
…
Cust1 Cust2 Cust3 Cust3 …
Customer (domain)
Name (codomain)
…
Alice Bob
Sue John
Pam…
Name CustomerName(Customer input)
{
switch (input)
{ case Cust1: return “Alice”;
case Cust2: return “Bob”;
case Cust3: return “Sue”;
etc
}
}

Functions can work on functions
Function List.map int->int maps to int list->int list
…
add1 times2 subtract3 add42 …
int->int
int list -> int list
…
eachAdd1 eachTimes2
eachSubtract3 eachAdd42
…

The practical benefits of pure functions
customer.SetName(newName);
let newCustomer = setCustomerName(aCustomer, newName)
Pure functions are easy to reason about
var name = customer.GetName();
let name,newCustomer = getCustomerName(aCustomer)
Reasoning about code that might not be pure:
Reasoning about code that is pure:
The customer is being changed.

let x = doSomething()
let y = doSomethingElse(x)
return y + 1
Pure functions are easy to refactor

let x = doSomething()
return y + 1

let helper() = let x = doSomething()
return y
return helper() + 1

More practical benefits of pure functions
•Laziness
–only evaluate when I need the output
•Cacheable results
–same answer every time
–"memoization"
•No order dependencies
–I can evaluate them in any order I like
•Parallelizable
–"embarrassingly parallel"

How to design a pure function
Pure Awesomeness!

How to design a pure function
•Haskell
–very pure
•F#, OCaml, Clojure, Scala
–easy to be pure
•C#, Java, JavaScript
–have to make an effort

Core principle: Types are not classes

Types are not classes
Set of valid inputs
Set of valid outputs
So what is a type?

Types separate data from behavior
Lists
Lists
List.map
List.collect
List.filter
List.etc

Core principle: Functions are things
Function

Functions as things
The Tunnel of Transformation
Function apple -> banana
A function is a standalone thing, not attached to a class

Functions as things
let z = 1
int-> int->int
1
let add x y = x + y

Functions as inputs and outputs
let useFn f = (f 1) + 2
let add x = (fun y -> x + y)
int->(int->int)
int ->int
int
int
int->int
let transformInt f x = (f x) + 1
int->int
int
int
Function as output
Function as input
Function as parameter
(int->int)->int
int->int

Core principle: Composition everywhere

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

>>

New Function apple -> cherry
Can't tell it was built from smaller functions!

Types can be composed too
“algebraic types"

Product types
×
=
Alice, Jan 12th
Bob, Feb 2nd
Carol, Mar 3rd
Set of people
Set of dates
type Birthday = Person * Date

Sum types
Set of Cash values
Set of Cheque values
Set of CreditCard values
+
+
type PaymentMethod =
| Cash
| Cheque of ChequeNumber
| Card of CardType * CardNumber

Domain modelling pattern: Use types to represent constraints

Types represent constraints on input and output
type Suit = Club | Diamond | Spade | Heart
type String50 = // non-null, not more than 50 chars
type EmailAddress = // non-null, must contain ‘@’
type StringTransformer = string -> string
type GetCustomer = CustomerId -> Customer option
Instant mockability

Domain modelling pattern: Types are cheap

Design principle: Strive for totality

twelveDividedBy(x) input x maps to 12/x
…
3
2
1
0
…
Domain (int)
Codomain (int)
…
4
6
12
…
Totality
int TwelveDividedBy(int input)
{
switch (input)
{
case 3: return 4;
case 2: return 6;
case 1: return 12;
case 0: return ??;
}
}
What happens here?

…
3
2
1
-1
…
NonZeroInteger
int
…
4
6
12
…
Totality
{
switch (input)
{
case 3: return 4;
case 2: return 6;
case 1: return 12;
case -1: return -12;
}
}
Constrain the input
0 is doesn’t have to be handled
NonZeroInteger -> int
0 is missing
Types are documentation

…
3
2
1
0
-1
…
int
Option<Int>
…
Some 4
Some 6
Some 12
None …
Totality
{
switch (input)
{
case 3: return Some 4;
case 0: return None;
}
}
Extend the output
0 is valid input
int -> int option
Types are documentation

Design principle: Use types to indicate errors

Output types as error codes
LoadCustomer: CustomerId -> Customer
LoadCustomer: CustomerId -> SuccessOrFailure<Customer>
ParseInt: string -> int
ParseInt: string -> int option
FetchPage: Uri -> String
FetchPage: Uri -> SuccessOrFailure<String>
No nulls
No exceptions
Use the signature, Luke!

Domain modelling principle: “Make illegal states unrepresentable”

Domain modelling principle: Use sum-types instead of inheritance

Using sum vs. inheritance
interface IPaymentMethod {..}
class Cash : IPaymentMethod {..}
class Cheque : IPaymentMethod {..}
class Card : IPaymentMethod {..}
| Cash
class Evil : IPaymentMethod {..}
Definition is scattered around many locations
What goes in here? What is the common behaviour?
OO version:

Domain modelling principle: Use sum-types for state machines

type ShoppingCart =
| EmptyCartState
| ActiveCartState of ActiveCartData
| PaidCartState of PaidCartData
Empty Cart
Active Cart
Paid Cart
Add Item
Remove Item
Pay
Add Item
Remove Item

Domain modelling principle: It’s ok to expose public data

It’s ok to expose public data
type PersonalName = {
FirstName: String50
MiddleInitial: String1 option
LastName: String50 }
Immutable
Can’t create invalid values

Domain modelling principle: Types are executable documentation

Types are executable documentation
type Rank = Two | Three | Four | Five | Six | Seven | Eight
| Nine | Ten | Jack | Queen | King | Ace
type Card = Suit * Rank
type Hand = Card list
type Deck = Card list
type Player = {Name:string; Hand:Hand}
type Game = {Deck:Deck; Players: Player list}
type Deal = Deck –› (Deck * Card)
type PickupCard = (Hand * Card) –› Hand

Types are executable documentation
type CardType = Visa | Mastercard
type CardNumber = CardNumber of string
type ChequeNumber = ChequeNumber of int
| Cash

More on DDD and designing with types at fsharpforfunandprofit.com/ddd
Static types only! Sorry Clojure and JS developers 

Design paradigm: Functions all the way down

“Functions in the small, objects in the large”

Low-level operation
ToUpper
Service
Domain logic
High-level use-case
AddressValidator
VerifyEmailAddress
UpdateProfileData
“Service” is the new “microservice”
string
string
AddressResult
EmailVerification
Saga
Http Response
Address
Email
Http Request

Design paradigm: Transformation-oriented programming

Interacting with the outside world
type ContactDTO = {
FirstName: string
MiddleInitial: string
LastName: string
EmailAddress: string
IsEmailVerified: bool
}
type EmailAddress = ...
type VerifiedEmail =
VerifiedEmail of EmailAddress
type EmailContactInfo =
| Unverified of EmailAddress
| Verified of VerifiedEmail
type PersonalName = {
FirstName: String50
MiddleInitial: String1 option
LastName: String50 }
type Contact = {
Name: PersonalName
Email: EmailContactInfo }

Transformation oriented programming
Input
Function
Output

Transformation oriented programming
Input
Transformation to internal model
Internal Model
Output
Transformation from internal model
validation and wrapping happens here
unwrapping happens here

Outbound tranformation
Flow of control in a FP use case
Inbound tranformation
Customer
Domain
Validator
Update
Request DTO
Domain Type
Send
ToDTO
Response DTO
Works well with domain events, FRP, etc

Flow of control in a OO use case
Application Services
Customer
Domain
App Service
App Service
Validation
Value
Entity
Infrastructure
Entity
Customer Repo.
Value
Email Message
Value
Database Service
SMTP Service

Interacting with the outside world
Nasty, unclean outside world
Beautiful, clean, internal model
Gate with filters
Gate with filters
Gate with filters

Interacting with the other domains
Subdomain/ bounded context
Gate with filters
Subdomain/ bounded context
Gate with filters

Interacting with the other domains
Bounded context
Bounded context
Bounded context

Guideline: Parameterize all the things

Parameterize all the things
let printList() =
for i in [1..10] do
printfn "the number is %i" i

It's second nature to parameterize the data input:
let printList aList =
for i in aList do
printfn "the number is %i" i

let printList anAction aList =
for i in aList do
anAction i
FPers would parameterize the action as well:
We've decoupled the behavior from the data

public static int Product(int n)
{
int product = 1;
for (int i = 1; i <= n; i++)
{
product *= i;
}
return product;
}
public static int Sum(int n)
{
int sum = 0;
for (int i = 1; i <= n; i++)
{
sum += i;
}
return sum;
}

let product n =
let initialValue = 1
let action productSoFar x = productSoFar * x
[1..n] |> List.fold action initialValue
let sum n =
let initialValue = 0
let action sumSoFar x = sumSoFar+x
[1..n] |> List.fold action initialValue
Lots of collection functions like this: "fold", "map", "reduce", "collect", etc.

Guideline: Be as generic as possible

Generic code
let printList anAction aList =
for i in aList do
anAction i
// val printList :
// ('a -> unit) -> seq<'a> -> unit
Any kind of collection, any kind of action!
F# and other functional languages make code generic automatically

Generic code
int -> int
How many ways are there to implement this function?
'a -> 'a
How many ways are there to this function?

Generic code
int list -> int list
'a list -> 'a list
How many ways are there to this function?

Generic code
('a -> 'b) -> 'a list -> 'b list

Tip: Function types are "interfaces"

Function types are interfaces
interface IBunchOfStuff
{
int DoSomething(int x);
string DoSomethingElse(int x);
void DoAThirdThing(string x);
}
Let's take the Single Responsibility Principle and the Interface Segregation Principle to the extreme...
Every interface should have only one method!

Function types are interfaces
interface IBunchOfStuff
{
int DoSomething(int x);
}
An interface with one method is a just a function type
type IBunchOfStuff: int -> int
Any function with that type is compatible with it
let add2 x = x + 2 // int -> int
let times3 x = x * 3 // int -> int

Strategy pattern is trivial in FP
class MyClass
{
public MyClass(IBunchOfStuff strategy) {..}
int DoSomethingWithStuff(int x) {
return _strategy.DoSomething(x)
}
}
Object-oriented strategy pattern:
Functional equivalent:
let DoSomethingWithStuff strategy x =
strategy x

Decorator pattern in FP
Functional equivalent of decorator pattern

let logged f x =
printfn "input is %A" x
let result = f x
printfn "output is %A" result
result

let logged f x =
printfn "input is %A" x
let result = f x
printfn "output is %A" result
result
let add1Decorated = // int -> int
logged add1
[1..5] |> List.map add1
[1..5] |> List.map add1Decorated

Tip Every function is a one parameter function

Writing functions in different ways
let add x y = x + y
let add = (fun x y -> x + y)
let add x = (fun y -> x + y)
int-> int->int
int-> int->int
int-> (int->int)

let three = 1 + 2
let add1 = (+) 1
let three = (+) 1 2
let add1ToEach = List.map add1

let names = ["Alice"; "Bob"; "Scott"]
Names |> List.iter hello
let name = "Scott"
printfn "Hello, my name is %s" name
let name = "Scott"
(printfn "Hello, my name is %s") name
let name = "Scott"
let hello = (printfn "Hello, my name is %s")
hello name

Pattern: Use partial application to do dependency injection

type GetCustomer = CustomerId -> Customer
let getCustomerFromDatabase connection
(customerId:CustomerId) =
// from connection // select customer // where customerId = customerId
type of getCustomerFromDatabase =
DbConnection -> CustomerId -> Customer
let getCustomer1 = getCustomerFromDatabase myConnection
// getCustomer1 : CustomerId -> Customer
Persistence agnostic

type GetCustomer = CustomerId -> Customer
let getCustomerFromMemory map (customerId:CustomerId) =
map |> Map.find customerId
type of getCustomerFromMemory =
Map<Id,Customer> -> CustomerId -> Customer
let getCustomer2 = getCustomerFromMemory inMemoryMap
// getCustomer2 : CustomerId -> Customer

Pattern: The Hollywood principle: continuations

Continuations
int Divide(int top, int bottom) {
if (bottom == 0)
{
throw new InvalidOperationException("div by 0");
}
else
{
return top/bottom;
}
}
Method has decided to throw an exception

Continuations
void Divide(int top, int bottom,
Action ifZero, Action<int> ifSuccess)
{
if (bottom == 0)
{
ifZero();
}
else
{
ifSuccess( top/bottom );
}
}
Let the caller decide what happens
what happens next?

Continuations
let divide ifZero ifSuccess top bottom =
if (bottom=0)
then ifZero()
else ifSuccess (top/bottom)
F# version
Four parameters is a lot though!

Continuations
if (bottom=0)
then ifZero()
let ifZero1 () = printfn "bad"
let ifSuccess1 x = printfn "good %i" x
let divide1 = divide ifZero1 ifSuccess1
//test
let good1 = divide1 6 3
let bad1 = divide1 6 0
setup the functions to print a message
Partially apply the continuations
Use it like a normal function – only two parameters

Continuations
if (bottom=0)
then ifZero()
let ifZero2() = None
let ifSuccess2 x = Some x
//test
setup the functions to return an Option

Continuations
if (bottom=0)
then ifZero()
let ifZero3() = failwith "div by 0"
let ifSuccess3 x = x
//test
setup the functions to throw an exception

Pyramid of doom: null testing example
let example input =
let x = doSomething input
if x <> null then
let y = doSomethingElse x
if y <> null then
let z = doAThirdThing y
if z <> null then
let result = z
result
else
null
else
null
else
null
I know you could do early returns, but bear with me...

Pyramid of doom: async example
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 ->
z // final result

Pyramid of doom: null example
let example input =
if x <> null then
if y <> null then
if z <> null then
let result = z
result
else
null
else
null
else
null
Nulls are a code smell: replace with Option!

Pyramid of doom: option example
let example input =
if x.IsSome then
let y = doSomethingElse (x.Value)
if y.IsSome then
let z = doAThirdThing (y.Value)
if z.IsSome then
let result = z.Value
Some result
else
None
else
None
else
None
Much more elegant, yes?
No! This is fugly!
Let’s do a cut & paste refactoring

let example input =
if x.IsSome then
if y.IsSome then
if z.IsSome then
Some result
else
None
else
None
else
None

let doWithX x =
if y.IsSome then
if z.IsSome then
Some result
else
None
else
None
let example input =
if x.IsSome then
doWithX x
else
None

let doWithY y =
if z.IsSome then
Some result
else
None
let doWithX x =
if y.IsSome then
doWithY y
else
None
let example input =
if x.IsSome then
doWithX x
else
None

Pyramid of doom: option example refactored
let doWithZ z =
let result = z
Some result
let doWithY y =
if z.IsSome then
doWithZ z.Value
else
None
let doWithX x =
if y.IsSome then
doWithY y.Value
else
None
let optionExample input =
if x.IsSome then
doWithX x.Value
else
None
Three small pyramids instead of one big one!
This is still ugly!
But the code has a pattern...

Pyramid of doom: option example refactored
let doWithZ z =
let result = z
Some result
let doWithY y =
if z.IsSome then
doWithZ z.Value
else
None
let doWithX x =
if y.IsSome then
doWithY y.Value
else
None
let optionExample input =
if x.IsSome then
doWithX x.Value
else
None
But the code has a pattern...

let doWithY y =
if z.IsSome then
doWithZ z.Value
else
None

let doWithY y =
z |> ifSomeDo doWithZ
let ifSomeDo f x =
if x.IsSome then
f x.Value
else
None

let doWithY y =
y
|> doAThirdThing
|> ifSomeDo doWithZ
let ifSomeDo f x =
if x.IsSome then
f x.Value
else
None

let example input =
doSomething input
|> ifSomeDo doSomethingElse
|> ifSomeDo doAThirdThing
|> ifSomeDo (fun z -> Some z)
let ifSomeDo f x =
if x.IsSome then
f x.Value
else
None

A switch analogy
Some
None
Input ->

Connecting switches
on Some
Bypass on None

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

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

Composing switches


... but composing switches is not allowed!

Composing switches
Two-track input
Two-track input
One-track input
Two-track input



Building an adapter block
Two-track input
Slot for switch function
Two-track output

Two-track input
Two-track output

let bind nextFunction optionInput =
match optionInput with
| Some s -> nextFunction s
| None -> None
Two-track input
Two-track output

Pattern: Use bind to chain options

Pyramid of doom: using bind
let bind f opt =
match opt with
| Some v -> f v
| None -> None
let example input =
if x.IsSome then
if y.IsSome then
if z.IsSome then
Some result
else
None
else
None
else
None

let example input =
doSomething input
|> bind doSomethingElse
|> bind doAThirdThing
|> bind (fun z -> Some z)
Pyramid of doom: using bind
let bind f opt =
match opt with
| Some v -> f v
| None -> None
No pyramids!
Code is linear and clear.
This pattern is called “monadic bind”

Pattern: Use bind to chain tasks

Connecting tasks
When task completes
Wait
Wait

Pyramid of doom: using bind for tasks
let taskBind f task =
task.WhenFinished (fun taskResult ->
f taskResult)
startTask input
|> taskBind startAnotherTask
|> taskBind startThirdTask
|> taskBind (fun z -> z)
a.k.a “promise” “future”
This pattern is also a “monadic bind”

Computation expressions
let example input =
maybe {
let! x = doSomething input
let! y = doSomethingElse x
let! z = doAThirdThing y
return z
}
task { let! x = startTask input
let! y = startAnotherTask x
let! z = startThirdTask z
return z
}
Computation expression
Computation expression

Pattern: Use bind to chain error handlers

Example use case
Name is blank Email not valid
Receive request
Validate and canonicalize request
Update existing user record
Send verification email
Return result to user
User not found Db error
Authorization error Timeout
"As a user I want to update my name and email address"
type Request = { userId: int; name: string; email: string }
- and see sensible error messages when something goes wrong!

Use case without error handling
string UpdateCustomerWithErrorHandling()
{
var request = receiveRequest();
validateRequest(request);
canonicalizeEmail(request);
db.updateDbFromRequest(request);
smtpServer.sendEmail(request.Email)
return "OK";
}

Use case with error handling
{
var isValidated = validateRequest(request);
if (!isValidated) {
return "Request is not valid"
}
db.updateDbFromRequest(request);
return "OK";
}

{
if (!isValidated) {
}
var result = db.updateDbFromRequest(request);
if (!result) {
return "Customer record not found"
}
return "OK";
}

{
if (!isValidated) {
}
try {
if (!result) {
}
} catch {
return "DB error: Customer record not updated"
}
return "OK";
}

{
if (!isValidated) {
}
try {
if (!result) {
}
} catch {
return "DB error: Customer record not updated"
}
if (!smtpServer.sendEmail(request.Email)) {
log.Error "Customer email not sent"
}
return "OK";
}

A structure for managing errors
Request
Success
Validate
Failure
let validateInput input =
if input.name = "" then
Failure "Name must not be blank"
else if input.email = "" then
Failure "Email must not be blank"
else
Success input // happy path
type TwoTrack<'TEntity> =
| Success of 'TEntity
| Failure of string

name50
Bind example
let nameNotBlank input =
if input.name = "" then
Failure "Name must not be blank"
else Success input
let name50 input =
if input.name.Length > 50 then
Failure "Name must not be longer than 50 chars"
else Success input
let emailNotBlank input =
if input.email = "" then
Failure "Email must not be blank"
else Success input
nameNotBlank
emailNotBlank

Switches again
Success!
Failure
Input ->

Connecting switches
Validate
UpdateDb
on success
bypass

Connecting switches
Validate
UpdateDb

Connecting switches
Validate
UpdateDb
SendEmail

World of normal values
int string bool
World of options
int option string option bool option

World of options
int string bool


World of options
int string bool


How not to code with options
Let’s say you have an int wrapped in an Option, and you want to add 42 to it:
let add42 x = x + 42
let add42ToOption opt =
if opt.IsSome then
let newVal = add42 opt.Value
Some newVal
else
None


World of options
add42

Lifting
World of options
'a -> 'b
'a option -> 'b option
Option.map

The right way to code with options
Let’s say you have an int wrapped in an Option, and you want to add 42 to it:
let add42ToOption = Option.map add42
Some 1 |> add42ToOption
Some 1 |> Option.map add42


Pattern: Use “map” to lift functions

Lifting to lists
World of lists
'a -> 'b
'a list-> 'b list
List.map

Lifting to async
World of async
'a -> 'b
'a async > 'b async
Async.map

The right way to code with wrapped types
Most wrapped types provide a “map”
Some 1 |> Option.map add42
[1;2;3] |> List.map add42

Guideline: If you create a wrapped generic type, create a “map” for it.

Maps
type TwoTrack<'TEntity> =
| Success of 'TEntity
| Failure of string
let mapTT f x =
match x with
| Success entity -> Success (f entity)
| Failure s -> Failure s

Tip: Use applicatives for validation

Series validation
name50
emailNotBlank
Problem: Validation done in series.
So only one error at a time is returned

Parallel validation
name50
emailNotBlank
Split input
Combine output
Now we do get all errors at once!
But how to combine?

Creating a valid data structure
type Request= {
UserId: UserId;
Name: String50;
Email: EmailAddress}
type RequestDTO= {
UserId: int;
Name: string;
Email: string}

How not to do validation
// do the validation of the DTO
let userIdOrError = validateUserId dto.userId
let nameOrError = validateName dto.name
let emailOrError = validateEmail dto.email
if userIdOrError.IsSuccess
&& nameOrError.IsSuccess
&& emailOrError.IsSuccess then
{
userId = userIdOrError.SuccessValue
name = nameOrError.SuccessValue
email = emailOrError.SuccessValue
}
else if userIdOrError.IsFailure
&& nameOrError.IsSuccess
&& emailOrError.IsSuccess then
userIdOrError.Errors
else ...


Lifting to TwoTracks
World of two-tracks
createRequest userId name email
createRequestTT userIdOrError nameOrError emailOrError
lift 3 parameter function

The right way
let createRequest userId name email =
{
userId = userIdOrError.SuccessValue
name = nameOrError.SuccessValue
email = emailOrError.SuccessValue
}
let createRequestTT = lift3 createRequest

The right way
let createRequestTT = lift3 createRequest
let requestOrError =
createRequestTT userIdOrError nameOrError emailOrError


The right way
let requestOrError =
createRequest
<!> userIdOrError
<*> nameOrError
<*> emailOrError


Guideline: If you use a wrapped generic type, look for a set of “lifts” associated with it

Guideline: If you create a wrapped generic type, also create a set of “lifts” for clients to use with it
But I’m not going explain how right now!

Thinking like a mathematician
1 + 2 = 3
1 + (2 + 3) = (1 + 2) + 3
1 + 0 = 1
0 + 1 = 1

1 + 2 = 3
Some things
A way of combining them

2 x 3 = 6
Some things

max(1,2) = 2
Some things

"a" + "b" = "ab"
Some things

concat([a],[b]) = [a; b]
Some things

1 + 2
1 + 2 + 3
1 + 2 + 3 + 4
Is an integer
Is an integer
A pairwise operation has become an operation that works on lists!

1 + (2 + 3) = (1 + 2) + 3
Order of combining doesn’t matter
1 + 2 + 3 + 4 (1 + 2) + (3 + 4)
((1 + 2) + 3) + 4
All the same

1 - (2 - 3) = (1 - 2) - 3
Order of combining does matter

1 + 0 = 1
0 + 1 = 1
A special kind of thing that when you combine it with something, just gives you back the original something

42 * 1 = 42
1 * 42 = 42
A special kind of thing that when you combine it with something, just gives you back the original something

"" + "hello" = "hello" "hello" + "" = "hello"
“Zero” for strings

The generalization
•You start with a bunch of things, and some way of combining them two at a time.
•Rule 1 (Closure): The result of combining two things is always another one of the things.
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter.
•Rule 3 (Identity element): There is a special thing called "zero" such that when you combine any thing with "zero" you get the original thing back.
A monoid!

•Benefit: converts pairwise operations into operations that work on lists.
1 + 2 + 3 + 4
[ 1; 2; 3; 4 ] |> List.reduce (+)

1 * 2 * 3 * 4
[ 1; 2; 3; 4 ] |> List.reduce (*)

"a" + "b" + "c" + "d"
[ "a"; "b"; "c"; "d" ] |> List.reduce (+)

•Benefit: Divide and conquer, parallelization, and incremental accumulation.
1 + 2 + 3 + 4

(1 + 2) (3 + 4)
3 + 7

(1 + 2 + 3)

(1 + 2 + 3) + 4

(6) + 4

Issues with reduce
•How can I use reduce on an empty list?
•In a divide and conquer algorithm, what should I do if one of the "divide" steps has nothing in it?
•When using an incremental algorithm, what value should I start with when I have no data?

•Rule 3 (Identity element): There is a special thing called "zero" such that when you combine any thing with "zero" you get the original thing back.
•Benefit: Initial value for empty or missing data

Pattern: Simplifying aggregation code with monoids

type OrderLine = {Qty:int; Total:float}
let orderLines = [
{Qty=2; Total=19.98}
{Qty=1; Total= 1.99}
{Qty=3; Total= 3.99} ]
let addLine line1 line2 =
let newQty = line1.Qty + line2.Qty
let newTotal = line1.Total + line2.Total
{Qty=newQty; Total=newTotal}
orderLines |> List.reduce addLine
Any combination of monoids is also a monoid

Pattern: Convert non-monoids to monoids

Customer + Customer + Customer
Customer Stats + Customer Stats + Customer Stats
Reduce
Map
Not a monoid
A monoid
Summary Stats

Hadoop make me a sandwich
https://twitter.com/daviottenheimer/status/532661754820829185

Guideline: Convert expensive monoids to cheap monoids

Log file (Mon)
+
Log File (Tue)
+
Log File (Wed)
=
Really big file
Summary (Mon)
+
Summary (Tue)
+
Summary (Wed)
Map
Strings are monoids
A monoid
Much more efficient for incremental updates
“Monoid homomorphism”

Pattern: Seeing monoids everywhere

Monoids in the real world
Metrics guideline: Use counters rather than rates
Alternative metrics guideline: Make sure your metrics are monoids
• incremental updates
• can handle missing data

Is function composition a monoid?
>>
New Function apple -> cherry
Not the same thing.
Not a monoid 

>>
Function 1 apple -> apple
Same thing
A monoid! 

“Functions with same type of input and output”
Functions where the input and output are the same type are monoids! What shall we call these kinds of functions?

“Functions with same type of input and output”
“Endomorphisms”
Functions where the input and output are the same type are monoids! What shall we call these kinds of functions?
All endomorphisms are monoids

Endomorphism example
let plus1 x = x + 1 // int->int
let times2 x = x * 2 // int->int
let subtract42 x = x – 42 // int->int
let functions = [
plus1
times2
subtract42 ]
let newFunction = // int->int
functions |> List.reduce (>>)
newFunction 20 // => 0
Endomorphisms
Put them in a list
Reduce them
Another endomorphism

Event sourcing
Any function containing an endomorphism can be converted into a monoid.
For example: Event sourcing
Is an endomorphism
Event
-> State
-> State

Event sourcing example
let applyFns = [
apply event1 // State -> State
apply event2 // State -> State
apply event3] // State -> State
let applyAll = // State -> State
applyFns |> List.reduce (>>)
let newState = applyAll oldState
• incremental updates
• can handle missing events
Partial application of event
A function that can apply all the events in one step

Bind
Any function containing an endomorphism can be converted into a monoid.
For example: Option.Bind
Is an endomorphism
(fn param)
-> Option
-> Option

Event sourcing example
let bindFns = [
Option.bind (fun x->
if x > 1 then Some (x*2) else None)
Option.bind (fun x->
if x < 10 then Some x else None)
]
let bindAll = // Option->Option
bindFns |> List.reduce (>>)
Some 4 |> bindAll // Some 8
Some 5 |> bindAll // None
Partial application of Bind

Predicates as monoids
type Predicate<'A> = 'A -> bool
let predAnd pred1 pred2 x =
if pred1 x
then pred2 x
else false
let predicates = [
isMoreThan10Chars // string -> bool
isMixedCase // string -> bool
isNotDictionaryWord // string -> bool
]
let combinedPredicate = // string -> bool
predicates |> List.reduce (predAnd)
Not an endomorphism
But can still be combined

Series combination
=
>>
Result is same kind of thing (Closure)
Order not important (Associative)
Monoid!

Parallel combination
=
+
Same thing (Closure)
Order not important (Associative)
Monoid!

Monad laws
•The Monad laws are just the monoid definitions in diguise
–Closure, Associativity, Identity
•What happens if you break the monad laws?
–You lose monoid benefits such as aggregation

A monad is just a monoid in the category of endofunctors!

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