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Functional Design Patterns 
@ScottWlaschin 
fsharpforfunandprofit.com
Functional Design Patterns 
@ScottWlaschin 
fsharpforfunandprofit.com 
X
Functional Design Patterns 
@ScottWlaschin 
fsharpforfunandprofit.com
Functional patterns 
•Apomorphisms 
•Dynamorphisms 
•Chronomorphisms 
•Zygohistomorphic prepromorphisms
Functional patterns 
•Core Principles of FP design 
–Functions, types, composition 
•Functions as parameters 
–Abstraction...
This talk 
A whirlwind tour of many sights 
Don't worry if you don't understand everything
Functional programming is scary
Functional programming is scary
Object oriented programming is scary
•Single Responsibility Principle 
•Open/Closed principle 
•Dependency Inversion Principle 
•Interface Segregation Principl...
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-Orie...
•What we envisioned: 
–Haskell, OCaml, F#, etc 
•What we got: 
–?? 
Functional programming 
Please don’t let this happen t...
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 ...
Core principle: Steal from mathematics 
“Programming is one of the most difficult branches of applied mathematics” - E. W....
Why mathematics 
Dijkstra said: 
•Mathematical assertions tend to be unusually precise. 
•Mathematical assertions tend to ...
“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 ...
Function add1(x) input x maps to x+1 
… 
-1 
0 
1 
2 
3 
… 
Domain (int) 
Codomain (int) 
… 
0 
1 
2 
3 
4 
… 
Mathematica...
Mathematical functions 
•A (mathematical) function always gives the same output value for a given input value 
•A (mathema...
Functions don't have to be about arithmetic 
Function CustomerName(x) input Customer maps to PersonalName 
… 
Cust1 Cust2 ...
Functions can work on functions 
Function List.map int->int maps to int list->int list 
… 
add1 times2 subtract3 add42 … 
...
Guideline: Strive for purity
The practical benefits of pure functions 
customer.SetName(newName); 
let newCustomer = setCustomerName(aCustomer, newName...
The practical benefits of pure functions 
let x = doSomething() 
let y = doSomethingElse(x) 
return y + 1 
Pure functions ...
The practical benefits of pure functions 
Pure functions are easy to refactor 
let x = doSomething() 
let y = doSomethingE...
The practical benefits of pure functions 
Pure functions are easy to refactor 
let helper() = let x = doSomething() 
let y...
More practical benefits of pure functions 
•Laziness 
–only evaluate when I need the output 
•Cacheable results 
–same ans...
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 
...
Core principle: Types are not classes
X
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 attache...
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 
i...
Core principle: Composition everywhere
Function composition 
Function 1 apple -> banana 
Function 2 banana -> cherry
Function composition 
>> 
Function 1 apple -> banana 
Function 2 banana -> cherry
Function composition 
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 * ...
Sum types 
Set of Cash values 
Set of Cheque values 
Set of CreditCard values 
+ 
+ 
type PaymentMethod = 
| Cash 
| Chequ...
DDD & DOMAIN MODELLING
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, ...
Domain modelling pattern: Types are cheap
Types are cheap 
type Suit = Club | Diamond | Spade | Heart 
type Rank = Two | Three | Four | Five | Six | Seven | Eight 
...
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 Twe...
twelveDividedBy(x) input x maps to 12/x 
… 
3 
2 
1 
-1 
… 
NonZeroInteger 
int 
… 
4 
6 
12 
… 
Totality 
int TwelveDivid...
twelveDividedBy(x) input x maps to 12/x 
… 
3 
2 
1 
0 
-1 
… 
int 
Option<Int> 
… 
Some 4 
Some 6 
Some 12 
None … 
Total...
Design principle: Use types to indicate errors
Output types as error codes 
LoadCustomer: CustomerId -> Customer 
LoadCustomer: CustomerId -> SuccessOrFailure<Customer> ...
Domain modelling principle: “Make illegal states unrepresentable”
Types can represent business rules 
type EmailContactInfo = 
| Unverified of EmailAddress 
| Verified of VerifiedEmailAddr...
Domain modelling principle: Use sum-types instead of inheritance
Using sum vs. inheritance 
interface IPaymentMethod {..} 
class Cash : IPaymentMethod {..} 
class Cheque : IPaymentMethod ...
Domain modelling principle: Use sum-types for state machines
type ShoppingCart = 
| EmptyCartState 
| ActiveCartState of ActiveCartData 
| PaidCartState of PaidCartData 
Empty Cart 
A...
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: String...
Domain modelling principle: Types are executable documentation
Types are executable documentation 
type Suit = Club | Diamond | Spade | Heart 
type Rank = Two | Three | Four | Five | Si...
Types are executable documentation 
type CardType = Visa | Mastercard 
type CardNumber = CardNumber of string 
type Cheque...
More on DDD and designing with types at fsharpforfunandprofit.com/ddd 
Static types only! Sorry Clojure and JS developers 
HIGH-LEVEL DESIGN
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 
UpdateProf...
Design paradigm: Transformation-oriented programming
Interacting with the outside world 
type ContactDTO = { 
FirstName: string 
MiddleInitial: string 
LastName: string 
Email...
Transformation oriented programming 
Input 
Function 
Output
Transformation oriented programming 
Input 
Transformation to internal model 
Internal Model 
Output 
Transformation from ...
Outbound tranformation 
Flow of control in a FP use case 
Inbound tranformation 
Customer 
Domain 
Validator 
Update 
Requ...
Flow of control in a OO use case 
Application Services 
Customer 
Domain 
App Service 
App Service 
Validation 
Value 
Ent...
Interacting with the outside world 
Nasty, unclean outside world 
Nasty, unclean outside world 
Nasty, unclean outside wor...
Interacting with the other domains 
Subdomain/ bounded context 
Gate with filters 
Subdomain/ bounded context 
Gate with f...
Interacting with the other domains 
Bounded context 
Bounded context 
Bounded context
FUNCTIONS AS PARAMETERS
Guideline: Parameterize all the things
Parameterize all the things 
let printList() = 
for i in [1..10] do 
printfn "the number is %i" i
Parameterize all the things 
It's second nature to parameterize the data input: 
let printList aList = 
for i in aList do ...
Parameterize all the things 
let printList anAction aList = 
for i in aList do 
anAction i 
FPers would parameterize the a...
Parameterize all the things 
public static int Product(int n) 
{ 
int product = 1; 
for (int i = 1; i <= n; i++) 
{ 
produ...
public static int Product(int n) 
{ 
int product = 1; 
for (int i = 1; i <= n; i++) 
{ 
product *= i; 
} 
return product; ...
Parameterize all the things 
let product n = 
let initialValue = 1 
let action productSoFar x = productSoFar * x 
[1..n] |...
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...
Generic code 
int -> int 
How many ways are there to implement this function? 
'a -> 'a 
How many ways are there to this f...
Generic code 
int list -> int list 
How many ways are there to implement this function? 
'a list -> 'a list 
How many ways...
Generic code 
('a -> 'b) -> 'a list -> 'b list 
How many ways are there to implement this function?
Tip: Function types are "interfaces"
Function types are interfaces 
interface IBunchOfStuff 
{ 
int DoSomething(int x); 
string DoSomethingElse(int x); 
void D...
Function types are interfaces 
interface IBunchOfStuff 
{ 
int DoSomething(int x); 
} 
An interface with one method is a j...
Strategy pattern is trivial in FP 
class MyClass 
{ 
public MyClass(IBunchOfStuff strategy) {..} 
int DoSomethingWithStuff...
Decorator pattern in FP 
Functional equivalent of decorator pattern 
let add1 x = x + 1 // int -> int
Decorator pattern in FP 
Functional equivalent of decorator pattern 
let add1 x = x + 1 // int -> int 
let logged f x = 
p...
Decorator pattern in FP 
Functional equivalent of decorator pattern 
let add1 x = x + 1 // int -> int 
let logged f x = 
p...
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-...
let three = 1 + 2 
let add1 = (+) 1 
let three = (+) 1 2 
let add1ToEach = List.map add1
Pattern: Partial application
let names = ["Alice"; "Bob"; "Scott"] 
Names |> List.iter hello 
let name = "Scott" 
printfn "Hello, my name is %s" name 
...
Pattern: Use partial application to do dependency injection
type GetCustomer = CustomerId -> Customer 
let getCustomerFromDatabase connection 
(customerId:CustomerId) = 
// from conn...
type GetCustomer = CustomerId -> Customer 
let getCustomerFromMemory map (customerId:CustomerId) = 
map |> Map.find custom...
Pattern: The Hollywood principle: continuations
Continuations 
int Divide(int top, int bottom) { 
if (bottom == 0) 
{ 
throw new InvalidOperationException("div by 0"); 
}...
Continuations 
void Divide(int top, int bottom, 
Action ifZero, Action<int> ifSuccess) 
{ 
if (bottom == 0) 
{ 
ifZero(); ...
Continuations 
let divide ifZero ifSuccess top bottom = 
if (bottom=0) 
then ifZero() 
else ifSuccess (top/bottom) 
F# ver...
Continuations 
let divide ifZero ifSuccess top bottom = 
if (bottom=0) 
then ifZero() 
else ifSuccess (top/bottom) 
let if...
Continuations 
let divide ifZero ifSuccess top bottom = 
if (bottom=0) 
then ifZero() 
else ifSuccess (top/bottom) 
let if...
Continuations 
let divide ifZero ifSuccess top bottom = 
if (bottom=0) 
then ifZero() 
else ifSuccess (top/bottom) 
let if...
MONADS
Pyramid of doom: null testing example 
let example input = 
let x = doSomething input 
if x <> null then 
let y = doSometh...
Pyramid of doom: async example 
let taskExample input = 
let taskX = startTask input 
taskX.WhenFinished (fun x -> 
let ta...
Pyramid of doom: null example 
let example input = 
let x = doSomething input 
if x <> null then 
let y = doSomethingElse ...
Pyramid of doom: option example 
let example input = 
let x = doSomething input 
if x.IsSome then 
let y = doSomethingElse...
Pyramid of doom: option example 
let example input = 
let x = doSomething input 
if x.IsSome then 
let y = doSomethingElse...
Pyramid of doom: option example 
let doWithX x = 
let y = doSomethingElse x 
if y.IsSome then 
let z = doAThirdThing (y.Va...
Pyramid of doom: option example 
let doWithX x = 
let y = doSomethingElse x 
if y.IsSome then 
let z = doAThirdThing (y.Va...
Pyramid of doom: option example 
let doWithY y = 
let z = doAThirdThing y 
if z.IsSome then 
let result = z.Value 
Some re...
Pyramid of doom: option example refactored 
let doWithZ z = 
let result = z 
Some result 
let doWithY y = 
let z = doAThir...
Pyramid of doom: option example refactored 
let doWithZ z = 
let result = z 
Some result 
let doWithY y = 
let z = doAThir...
let doWithY y = 
let z = doAThirdThing y 
if z.IsSome then 
doWithZ z.Value 
else 
None
let doWithY y = 
let z = doAThirdThing y 
z |> ifSomeDo doWithZ 
let ifSomeDo f x = 
if x.IsSome then 
f x.Value 
else 
No...
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...
A switch analogy 
Some 
None 
Input ->
Connecting switches 
on Some 
Bypass on None
Connecting switches
Connecting switches
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
Building an adapter block 
Two-track input 
Two-track output
let bind nextFunction optionInput = 
match optionInput with 
| Some s -> nextFunction s 
| None -> None 
Building an adapt...
let bind nextFunction optionInput = 
match optionInput with 
| Some s -> nextFunction s 
| None -> None 
Building an adapt...
let bind nextFunction optionInput = 
match optionInput with 
| Some s -> nextFunction s 
| None -> None 
Building an adapt...
let bind nextFunction optionInput = 
match optionInput with 
| Some s -> nextFunction s 
| None -> None 
Building an adapt...
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 = 
let x...
let example input = 
doSomething input 
|> bind doSomethingElse 
|> bind doAThirdThing 
|> bind (fun z -> Some z) 
Pyramid...
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) 
let tas...
Computation expressions 
let example input = 
maybe { 
let! x = doSomething input 
let! y = doSomethingElse x 
let! z = do...
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 ...
Use case without error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
validateReq...
Use case with error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
var isValidate...
Use case with error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
var isValidate...
Use case with error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
var isValidate...
Use case with error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
var isValidate...
Use case with error handling 
string UpdateCustomerWithErrorHandling() 
{ 
var request = receiveRequest(); 
var isValidate...
A structure for managing errors 
Request 
Success 
Validate 
Failure 
let validateInput input = 
if input.name = "" then 
...
name50 
Bind example 
let nameNotBlank input = 
if input.name = "" then 
Failure "Name must not be blank" 
else Success in...
Switches again 
Success! 
Failure 
Input ->
Connecting switches 
Validate 
UpdateDb 
on success 
bypass
Connecting switches 
Validate 
UpdateDb
Connecting switches 
Validate 
UpdateDb 
SendEmail
Connecting switches 
Validate 
UpdateDb 
SendEmail
Functional flow without error handling 
let updateCustomer = 
receiveRequest 
|> validateRequest 
|> canonicalizeEmail 
|>...
Functional flow with error handling 
let updateCustomerWithErrorHandling = 
receiveRequest 
|> validateRequest 
|> canonic...
MAPS AND APPLICATIVES
World of normal values 
int string bool 
World of options 
int option string option bool option
World of options 
World of normal values 
int string bool 
int option string option bool option 

World of options 
World of normal values 
int string bool 
int option string option bool option 

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 =...
World of options 
World of normal values 
add42
World of options 
World of normal values 
add42
Lifting 
World of options 
World of normal values 
'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 add...
Pattern: Use “map” to lift functions
Lifting to lists 
World of lists 
World of normal values 
'a -> 'b 
'a list-> 'b list 
List.map
Lifting to async 
World of async 
World of normal values 
'a -> 'b 
'a async > 'b async 
Async.map
The right way to code with wrapped types 
Most wrapped types provide a “map” 
let add42 x = x + 42 
Some 1 |> Option.map a...
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 enti...
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 com...
Creating a valid data structure 
type Request= { 
UserId: UserId; 
Name: String50; 
Email: EmailAddress} 
type RequestDTO=...
How not to do validation 
// do the validation of the DTO 
let userIdOrError = validateUserId dto.userId 
let nameOrError ...
Lifting to TwoTracks 
World of two-tracks 
World of normal values 
createRequest userId name email 
createRequestTT userId...
The right way 
let createRequest userId name email = 
{ 
userId = userIdOrError.SuccessValue 
name = nameOrError.SuccessVa...
The right way 
let createRequestTT = lift3 createRequest 
let userIdOrError = validateUserId dto.userId 
let nameOrError =...
The right way 
let userIdOrError = validateUserId dto.userId 
let nameOrError = validateName dto.name 
let 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 goin...
MONOIDS
Mathematics Ahead
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 
A way of combining them
max(1,2) = 2 
Some things 
A way of combining them
"a" + "b" = "ab" 
Some things 
A way of combining them
concat([a],[b]) = [a; b] 
Some things 
A way of combining them
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 ...
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 ...
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 so...
42 * 1 = 42 
1 * 42 = 42 
A special kind of thing that when you combine it with something, just gives you back the origina...
"" + "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): T...
•Rule 1 (Closure): The result of combining two things is always another one of the things. 
•Benefit: converts pairwise op...
1 * 2 * 3 * 4 
[ 1; 2; 3; 4 ] |> List.reduce (*) 
•Rule 1 (Closure): The result of combining two things is always another ...
"a" + "b" + "c" + "d" 
[ "a"; "b"; "c"; "d" ] |> List.reduce (+) 
•Rule 1 (Closure): The result of combining two things is...
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. 
•Be...
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. 
•Be...
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. 
•Be...
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. 
•Be...
•Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. 
•Be...
Issues with reduce 
•How can I use reduce on an empty list? 
•In a divide and conquer algorithm, what should I do if one o...
•Rule 3 (Identity element): There is a special thing called "zero" such that when you combine any thing with "zero" you ge...
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....
Pattern: Convert non-monoids to monoids
Customer + Customer + Customer 
Customer Stats + Customer Stats + Customer Stats 
Reduce 
Map 
Not a monoid 
A monoid 
Sum...
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...
Pattern: Seeing monoids everywhere
Monoids in the real world 
Metrics guideline: Use counters rather than rates 
Alternative metrics guideline: Make sure you...
Is function composition a monoid? 
>> 
Function 1 apple -> banana 
Function 2 banana -> cherry 
New Function apple -> cher...
Is function composition a monoid? 
>> 
Function 1 apple -> apple 
Same thing 
Function 2 apple -> apple 
Function 3 apple ...
Is function composition a monoid? 
“Functions with same type of input and output” 
Functions where the input and output ar...
Is function composition a monoid? 
“Functions with same type of input and output” 
“Endomorphisms” 
Functions where the in...
Endomorphism example 
let plus1 x = x + 1 // int->int 
let times2 x = x * 2 // int->int 
let subtract42 x = x – 42 // int-...
Event sourcing 
Any function containing an endomorphism can be converted into a monoid. 
For example: Event sourcing 
Is a...
Event sourcing example 
let applyFns = [ 
apply event1 // State -> State 
apply event2 // State -> State 
apply event3] //...
Bind 
Any function containing an endomorphism can be converted into a monoid. 
For example: Option.Bind 
Is an endomorphis...
Event sourcing example 
let bindFns = [ 
Option.bind (fun x-> 
if x > 1 then Some (x*2) else None) 
Option.bind (fun x-> 
...
Predicates as monoids 
type Predicate<'A> = 'A -> bool 
let predAnd pred1 pred2 x = 
if pred1 x 
then pred2 x 
else false ...
Pattern: Monads are monoids
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 i...
A monad is just a monoid in the category of endofunctors!
THANKS!
Functional Programming Patterns (BuildStuff '14)
Functional Programming Patterns (BuildStuff '14)
Functional Programming Patterns (BuildStuff '14)
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Functional Programming Patterns (BuildStuff '14)

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(video of these slides available here http://fsharpforfunandprofit.com/fppatterns/)

In object-oriented development, we are all familiar with design patterns such as the Strategy pattern and Decorator pattern, and design principles such as SOLID.

The functional programming community has design patterns and principles as well.

This talk will provide an overview of some of these, and present some demonstrations of FP design in practice.

Published in: Software

Functional Programming Patterns (BuildStuff '14)

  1. 1. Functional Design Patterns @ScottWlaschin fsharpforfunandprofit.com
  2. 2. Functional Design Patterns @ScottWlaschin fsharpforfunandprofit.com X
  3. 3. Functional Design Patterns @ScottWlaschin fsharpforfunandprofit.com
  4. 4. Functional patterns •Apomorphisms •Dynamorphisms •Chronomorphisms •Zygohistomorphic prepromorphisms
  5. 5. 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
  6. 6. This talk A whirlwind tour of many sights Don't worry if you don't understand everything
  7. 7. Functional programming is scary
  8. 8. Functional programming is scary
  9. 9. Object oriented programming is scary
  10. 10. •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
  11. 11. A short and mostly wrong history of programming paradigms
  12. 12. •What we envisioned: –Smalltalk •What we got: –C++ –Object oriented Cobol –PHP –Java “Worse is better” Object-Oriented programming
  13. 13. •What we envisioned: –Haskell, OCaml, F#, etc •What we got: –?? Functional programming Please don’t let this happen to FP!
  14. 14. CORE PRINCIPLES OF FP DESIGN Important to understand!
  15. 15. Core principles of FP design Steal from mathematics Types are not classes Functions are things Composition everywhere Function
  16. 16. Core principle: Steal from mathematics “Programming is one of the most difficult branches of applied mathematics” - E. W. Dijkstra
  17. 17. 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.
  18. 18. “Object-oriented programming is an exceptionally bad idea which could only have originated in California.” E. W. Dijkstra
  19. 19. 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
  20. 20. Function add1(x) input x maps to x+1 … -1 0 1 2 3 … Domain (int) Codomain (int) … 0 1 2 3 4 … Mathematical functions 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)
  21. 21. Mathematical functions •A (mathematical) function always gives the same output value for a given input value •A (mathematical) function has no side effects Function add1(x) input x maps to x+1 … -1 0 1 2 3 … Domain (int) Codomain (int) … 0 1 2 3 4 …
  22. 22. 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 } }
  23. 23. 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 …
  24. 24. Guideline: Strive for purity
  25. 25. 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.
  26. 26. The practical benefits of pure functions let x = doSomething() let y = doSomethingElse(x) return y + 1 Pure functions are easy to refactor
  27. 27. The practical benefits of pure functions Pure functions are easy to refactor let x = doSomething() let y = doSomethingElse(x) return y + 1
  28. 28. The practical benefits of pure functions Pure functions are easy to refactor let helper() = let x = doSomething() let y = doSomethingElse(x) return y return helper() + 1
  29. 29. 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"
  30. 30. How to design a pure function Pure Awesomeness!
  31. 31. 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
  32. 32. Core principle: Types are not classes
  33. 33. X
  34. 34. Types are not classes Set of valid inputs Set of valid outputs So what is a type?
  35. 35. Types separate data from behavior Lists Lists List.map List.collect List.filter List.etc
  36. 36. Core principle: Functions are things Function
  37. 37. Functions as things The Tunnel of Transformation Function apple -> banana A function is a standalone thing, not attached to a class
  38. 38. Functions as things let z = 1 int-> int->int 1 let add x y = x + y
  39. 39. 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
  40. 40. Core principle: Composition everywhere
  41. 41. Function composition Function 1 apple -> banana Function 2 banana -> cherry
  42. 42. Function composition >> Function 1 apple -> banana Function 2 banana -> cherry
  43. 43. Function composition New Function apple -> cherry Can't tell it was built from smaller functions!
  44. 44. Types can be composed too “algebraic types"
  45. 45. Product types × = Alice, Jan 12th Bob, Feb 2nd Carol, Mar 3rd Set of people Set of dates type Birthday = Person * Date
  46. 46. Sum types Set of Cash values Set of Cheque values Set of CreditCard values + + type PaymentMethod = | Cash | Cheque of ChequeNumber | Card of CardType * CardNumber
  47. 47. DDD & DOMAIN MODELLING
  48. 48. Domain modelling pattern: Use types to represent constraints
  49. 49. 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
  50. 50. Domain modelling pattern: Types are cheap
  51. 51. Types are cheap type Suit = Club | Diamond | Spade | Heart type Rank = Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Jack | Queen | King | Ace type Card = Suit * Rank type Hand = Card list Only one line of code to create a type!
  52. 52. Design principle: Strive for totality
  53. 53. 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?
  54. 54. twelveDividedBy(x) input x maps to 12/x … 3 2 1 -1 … NonZeroInteger int … 4 6 12 … Totality int TwelveDividedBy(int input) { 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
  55. 55. twelveDividedBy(x) input x maps to 12/x … 3 2 1 0 -1 … int Option<Int> … Some 4 Some 6 Some 12 None … Totality int TwelveDividedBy(int input) { switch (input) { case 3: return Some 4; case 2: return Some 6; case 1: return Some 12; case 0: return None; } } Extend the output 0 is valid input int -> int option Types are documentation
  56. 56. Design principle: Use types to indicate errors
  57. 57. 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!
  58. 58. Domain modelling principle: “Make illegal states unrepresentable”
  59. 59. Types can represent business rules type EmailContactInfo = | Unverified of EmailAddress | Verified of VerifiedEmailAddress type ContactInfo = | EmailOnly of EmailContactInfo | AddrOnly of PostalContactInfo | EmailAndAddr of EmailContactInfo * PostalContactInfo
  60. 60. Domain modelling principle: Use sum-types instead of inheritance
  61. 61. Using sum vs. inheritance interface IPaymentMethod {..} class Cash : IPaymentMethod {..} class Cheque : IPaymentMethod {..} class Card : IPaymentMethod {..} type PaymentMethod = | Cash | Cheque of ChequeNumber | Card of CardType * CardNumber class Evil : IPaymentMethod {..} Definition is scattered around many locations What goes in here? What is the common behaviour? OO version:
  62. 62. Domain modelling principle: Use sum-types for state machines
  63. 63. type ShoppingCart = | EmptyCartState | ActiveCartState of ActiveCartData | PaidCartState of PaidCartData Empty Cart Active Cart Paid Cart Add Item Remove Item Pay Add Item Remove Item
  64. 64. Domain modelling principle: It’s ok to expose public data
  65. 65. It’s ok to expose public data type PersonalName = { FirstName: String50 MiddleInitial: String1 option LastName: String50 } Immutable Can’t create invalid values
  66. 66. Domain modelling principle: Types are executable documentation
  67. 67. Types are executable documentation type Suit = Club | Diamond | Spade | Heart 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
  68. 68. Types are executable documentation type CardType = Visa | Mastercard type CardNumber = CardNumber of string type ChequeNumber = ChequeNumber of int type PaymentMethod = | Cash | Cheque of ChequeNumber | Card of CardType * CardNumber
  69. 69. More on DDD and designing with types at fsharpforfunandprofit.com/ddd Static types only! Sorry Clojure and JS developers 
  70. 70. HIGH-LEVEL DESIGN
  71. 71. Design paradigm: Functions all the way down
  72. 72. “Functions in the small, objects in the large”
  73. 73. 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
  74. 74. Design paradigm: Transformation-oriented programming
  75. 75. 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 }
  76. 76. Transformation oriented programming Input Function Output
  77. 77. Transformation oriented programming Input Transformation to internal model Internal Model Output Transformation from internal model validation and wrapping happens here unwrapping happens here
  78. 78. 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
  79. 79. 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
  80. 80. Interacting with the outside world Nasty, unclean outside world Nasty, unclean outside world Nasty, unclean outside world Beautiful, clean, internal model Gate with filters Gate with filters Gate with filters
  81. 81. Interacting with the other domains Subdomain/ bounded context Gate with filters Subdomain/ bounded context Gate with filters
  82. 82. Interacting with the other domains Bounded context Bounded context Bounded context
  83. 83. FUNCTIONS AS PARAMETERS
  84. 84. Guideline: Parameterize all the things
  85. 85. Parameterize all the things let printList() = for i in [1..10] do printfn "the number is %i" i
  86. 86. Parameterize all the things It's second nature to parameterize the data input: let printList aList = for i in aList do printfn "the number is %i" i
  87. 87. Parameterize all the things 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
  88. 88. Parameterize all the things 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; }
  89. 89. 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; } Parameterize all the things
  90. 90. Parameterize all the things 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.
  91. 91. Guideline: Be as generic as possible
  92. 92. 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
  93. 93. Generic code int -> int How many ways are there to implement this function? 'a -> 'a How many ways are there to this function?
  94. 94. Generic code int list -> int list How many ways are there to implement this function? 'a list -> 'a list How many ways are there to this function?
  95. 95. Generic code ('a -> 'b) -> 'a list -> 'b list How many ways are there to implement this function?
  96. 96. Tip: Function types are "interfaces"
  97. 97. 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!
  98. 98. 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
  99. 99. 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
  100. 100. Decorator pattern in FP Functional equivalent of decorator pattern let add1 x = x + 1 // int -> int
  101. 101. Decorator pattern in FP Functional equivalent of decorator pattern let add1 x = x + 1 // int -> int let logged f x = printfn "input is %A" x let result = f x printfn "output is %A" result result
  102. 102. Decorator pattern in FP Functional equivalent of decorator pattern let add1 x = x + 1 // int -> int 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
  103. 103. Tip Every function is a one parameter function
  104. 104. 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)
  105. 105. let three = 1 + 2 let add1 = (+) 1 let three = (+) 1 2 let add1ToEach = List.map add1
  106. 106. Pattern: Partial application
  107. 107. 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
  108. 108. Pattern: Use partial application to do dependency injection
  109. 109. 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
  110. 110. 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
  111. 111. Pattern: The Hollywood principle: continuations
  112. 112. 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
  113. 113. 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?
  114. 114. Continuations let divide ifZero ifSuccess top bottom = if (bottom=0) then ifZero() else ifSuccess (top/bottom) F# version Four parameters is a lot though!
  115. 115. Continuations let divide ifZero ifSuccess top bottom = if (bottom=0) then ifZero() else ifSuccess (top/bottom) 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
  116. 116. Continuations let divide ifZero ifSuccess top bottom = if (bottom=0) then ifZero() else ifSuccess (top/bottom) let ifZero2() = None let ifSuccess2 x = Some x let divide2 = divide ifZero2 ifSuccess2 //test let good2 = divide2 6 3 let bad2 = divide2 6 0 setup the functions to return an Option Use it like a normal function – only two parameters Partially apply the continuations
  117. 117. Continuations let divide ifZero ifSuccess top bottom = if (bottom=0) then ifZero() else ifSuccess (top/bottom) let ifZero3() = failwith "div by 0" let ifSuccess3 x = x let divide3 = divide ifZero3 ifSuccess3 //test let good3 = divide3 6 3 let bad3 = divide3 6 0 setup the functions to throw an exception Use it like a normal function – only two parameters Partially apply the continuations
  118. 118. MONADS
  119. 119. 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...
  120. 120. 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
  121. 121. Pyramid of doom: null 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 Nulls are a code smell: replace with Option!
  122. 122. Pyramid of doom: option example let example input = let x = doSomething 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
  123. 123. Pyramid of doom: option example let example input = let x = doSomething 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
  124. 124. Pyramid of doom: option example let doWithX x = let y = doSomethingElse x if y.IsSome then let z = doAThirdThing (y.Value) if z.IsSome then let result = z.Value Some result else None else None let example input = let x = doSomething input if x.IsSome then doWithX x else None
  125. 125. Pyramid of doom: option example let doWithX x = let y = doSomethingElse x if y.IsSome then let z = doAThirdThing (y.Value) if z.IsSome then let result = z.Value Some result else None else None let example input = let x = doSomething input if x.IsSome then doWithX x else None
  126. 126. Pyramid of doom: option example let doWithY y = let z = doAThirdThing y if z.IsSome then let result = z.Value Some result else None let doWithX x = let y = doSomethingElse x if y.IsSome then doWithY y else None let example input = let x = doSomething input if x.IsSome then doWithX x else None
  127. 127. Pyramid of doom: option example refactored let doWithZ z = let result = z Some result let doWithY y = let z = doAThirdThing y if z.IsSome then doWithZ z.Value else None let doWithX x = let y = doSomethingElse x if y.IsSome then doWithY y.Value else None let optionExample input = let x = doSomething 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...
  128. 128. Pyramid of doom: option example refactored let doWithZ z = let result = z Some result let doWithY y = let z = doAThirdThing y if z.IsSome then doWithZ z.Value else None let doWithX x = let y = doSomethingElse x if y.IsSome then doWithY y.Value else None let optionExample input = let x = doSomething input if x.IsSome then doWithX x.Value else None But the code has a pattern...
  129. 129. let doWithY y = let z = doAThirdThing y if z.IsSome then doWithZ z.Value else None
  130. 130. let doWithY y = let z = doAThirdThing y z |> ifSomeDo doWithZ let ifSomeDo f x = if x.IsSome then f x.Value else None
  131. 131. let doWithY y = y |> doAThirdThing |> ifSomeDo doWithZ let ifSomeDo f x = if x.IsSome then f x.Value else None
  132. 132. 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
  133. 133. A switch analogy Some None Input ->
  134. 134. Connecting switches on Some Bypass on None
  135. 135. Connecting switches
  136. 136. Connecting switches
  137. 137. Composing switches >> >> Composing one-track functions is fine...
  138. 138. Composing switches >> >> ... and composing two-track functions is fine...
  139. 139. Composing switches   ... but composing switches is not allowed!
  140. 140. Composing switches Two-track input Two-track input One-track input Two-track input  
  141. 141. Building an adapter block Two-track input Slot for switch function Two-track output
  142. 142. Building an adapter block Two-track input Two-track output
  143. 143. let bind nextFunction optionInput = match optionInput with | Some s -> nextFunction s | None -> None Building an adapter block Two-track input Two-track output
  144. 144. let bind nextFunction optionInput = match optionInput with | Some s -> nextFunction s | None -> None Building an adapter block Two-track input Two-track output
  145. 145. let bind nextFunction optionInput = match optionInput with | Some s -> nextFunction s | None -> None Building an adapter block Two-track input Two-track output
  146. 146. let bind nextFunction optionInput = match optionInput with | Some s -> nextFunction s | None -> None Building an adapter block Two-track input Two-track output
  147. 147. Pattern: Use bind to chain options
  148. 148. Pyramid of doom: using bind let bind f opt = match opt with | Some v -> f v | None -> None let example input = let x = doSomething 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
  149. 149. 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”
  150. 150. Pattern: Use bind to chain tasks
  151. 151. Connecting tasks When task completes Wait Wait
  152. 152. Pyramid of doom: using bind for tasks let taskBind f task = task.WhenFinished (fun taskResult -> f taskResult) let taskExample input = startTask input |> taskBind startAnotherTask |> taskBind startThirdTask |> taskBind (fun z -> z) a.k.a “promise” “future” This pattern is also a “monadic bind”
  153. 153. Computation expressions let example input = maybe { let! x = doSomething input let! y = doSomethingElse x let! z = doAThirdThing y return z } let taskExample input = task { let! x = startTask input let! y = startAnotherTask x let! z = startThirdTask z return z } Computation expression Computation expression
  154. 154. Pattern: Use bind to chain error handlers
  155. 155. 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!
  156. 156. Use case without error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); validateRequest(request); canonicalizeEmail(request); db.updateDbFromRequest(request); smtpServer.sendEmail(request.Email) return "OK"; }
  157. 157. Use case with error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); var isValidated = validateRequest(request); if (!isValidated) { return "Request is not valid" } canonicalizeEmail(request); db.updateDbFromRequest(request); smtpServer.sendEmail(request.Email) return "OK"; }
  158. 158. Use case with error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); var isValidated = validateRequest(request); if (!isValidated) { return "Request is not valid" } canonicalizeEmail(request); var result = db.updateDbFromRequest(request); if (!result) { return "Customer record not found" } smtpServer.sendEmail(request.Email) return "OK"; }
  159. 159. Use case with error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); var isValidated = validateRequest(request); if (!isValidated) { return "Request is not valid" } canonicalizeEmail(request); try { var result = db.updateDbFromRequest(request); if (!result) { return "Customer record not found" } } catch { return "DB error: Customer record not updated" } smtpServer.sendEmail(request.Email) return "OK"; }
  160. 160. Use case with error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); var isValidated = validateRequest(request); if (!isValidated) { return "Request is not valid" } canonicalizeEmail(request); try { var result = db.updateDbFromRequest(request); if (!result) { return "Customer record not found" } } catch { return "DB error: Customer record not updated" } if (!smtpServer.sendEmail(request.Email)) { log.Error "Customer email not sent" } return "OK"; }
  161. 161. Use case with error handling string UpdateCustomerWithErrorHandling() { var request = receiveRequest(); var isValidated = validateRequest(request); if (!isValidated) { return "Request is not valid" } canonicalizeEmail(request); try { var result = db.updateDbFromRequest(request); if (!result) { return "Customer record not found" } } catch { return "DB error: Customer record not updated" } if (!smtpServer.sendEmail(request.Email)) { log.Error "Customer email not sent" } return "OK"; }
  162. 162. 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
  163. 163. 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
  164. 164. Switches again Success! Failure Input ->
  165. 165. Connecting switches Validate UpdateDb on success bypass
  166. 166. Connecting switches Validate UpdateDb
  167. 167. Connecting switches Validate UpdateDb SendEmail
  168. 168. Connecting switches Validate UpdateDb SendEmail
  169. 169. Functional flow without error handling let updateCustomer = receiveRequest |> validateRequest |> canonicalizeEmail |> updateDbFromRequest |> sendEmail |> returnMessage Before One track
  170. 170. Functional flow with error handling let updateCustomerWithErrorHandling = receiveRequest |> validateRequest |> canonicalizeEmail |> updateDbFromRequest |> sendEmail |> returnMessage After See fsharpforfunandprofit.com/rop Two track
  171. 171. MAPS AND APPLICATIVES
  172. 172. World of normal values int string bool World of options int option string option bool option
  173. 173. World of options World of normal values int string bool int option string option bool option 
  174. 174. World of options World of normal values int string bool int option string option bool option 
  175. 175. 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 
  176. 176. World of options World of normal values add42
  177. 177. World of options World of normal values add42
  178. 178. Lifting World of options World of normal values 'a -> 'b 'a option -> 'b option Option.map
  179. 179. 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 add42 x = x + 42 let add42ToOption = Option.map add42 Some 1 |> add42ToOption Some 1 |> Option.map add42 
  180. 180. Pattern: Use “map” to lift functions
  181. 181. Lifting to lists World of lists World of normal values 'a -> 'b 'a list-> 'b list List.map
  182. 182. Lifting to async World of async World of normal values 'a -> 'b 'a async > 'b async Async.map
  183. 183. The right way to code with wrapped types Most wrapped types provide a “map” let add42 x = x + 42 Some 1 |> Option.map add42 [1;2;3] |> List.map add42
  184. 184. Guideline: If you create a wrapped generic type, create a “map” for it.
  185. 185. 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
  186. 186. Tip: Use applicatives for validation
  187. 187. Series validation name50 emailNotBlank Problem: Validation done in series. So only one error at a time is returned
  188. 188. Parallel validation name50 emailNotBlank Split input Combine output Now we do get all errors at once! But how to combine?
  189. 189. Creating a valid data structure type Request= { UserId: UserId; Name: String50; Email: EmailAddress} type RequestDTO= { UserId: int; Name: string; Email: string}
  190. 190. 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 ... 
  191. 191. Lifting to TwoTracks World of two-tracks World of normal values createRequest userId name email createRequestTT userIdOrError nameOrError emailOrError lift 3 parameter function
  192. 192. The right way let createRequest userId name email = { userId = userIdOrError.SuccessValue name = nameOrError.SuccessValue email = emailOrError.SuccessValue } let createRequestTT = lift3 createRequest
  193. 193. The right way let createRequestTT = lift3 createRequest let userIdOrError = validateUserId dto.userId let nameOrError = validateName dto.name let emailOrError = validateEmail dto.email let requestOrError = createRequestTT userIdOrError nameOrError emailOrError 
  194. 194. The right way let userIdOrError = validateUserId dto.userId let nameOrError = validateName dto.name let emailOrError = validateEmail dto.email let requestOrError = createRequest <!> userIdOrError <*> nameOrError <*> emailOrError 
  195. 195. Guideline: If you use a wrapped generic type, look for a set of “lifts” associated with it
  196. 196. 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!
  197. 197. MONOIDS
  198. 198. Mathematics Ahead
  199. 199. Thinking like a mathematician 1 + 2 = 3 1 + (2 + 3) = (1 + 2) + 3 1 + 0 = 1 0 + 1 = 1
  200. 200. 1 + 2 = 3 Some things A way of combining them
  201. 201. 2 x 3 = 6 Some things A way of combining them
  202. 202. max(1,2) = 2 Some things A way of combining them
  203. 203. "a" + "b" = "ab" Some things A way of combining them
  204. 204. concat([a],[b]) = [a; b] Some things A way of combining them
  205. 205. 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!
  206. 206. 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
  207. 207. 1 - (2 - 3) = (1 - 2) - 3 Order of combining does matter
  208. 208. 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
  209. 209. 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
  210. 210. "" + "hello" = "hello" "hello" + "" = "hello" “Zero” for strings
  211. 211. 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!
  212. 212. •Rule 1 (Closure): The result of combining two things is always another one of the things. •Benefit: converts pairwise operations into operations that work on lists. 1 + 2 + 3 + 4 [ 1; 2; 3; 4 ] |> List.reduce (+)
  213. 213. 1 * 2 * 3 * 4 [ 1; 2; 3; 4 ] |> List.reduce (*) •Rule 1 (Closure): The result of combining two things is always another one of the things. •Benefit: converts pairwise operations into operations that work on lists.
  214. 214. "a" + "b" + "c" + "d" [ "a"; "b"; "c"; "d" ] |> List.reduce (+) •Rule 1 (Closure): The result of combining two things is always another one of the things. •Benefit: converts pairwise operations into operations that work on lists.
  215. 215. •Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. •Benefit: Divide and conquer, parallelization, and incremental accumulation. 1 + 2 + 3 + 4
  216. 216. •Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. •Benefit: Divide and conquer, parallelization, and incremental accumulation. (1 + 2) (3 + 4) 3 + 7
  217. 217. •Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. •Benefit: Divide and conquer, parallelization, and incremental accumulation. (1 + 2 + 3)
  218. 218. •Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. •Benefit: Divide and conquer, parallelization, and incremental accumulation. (1 + 2 + 3) + 4
  219. 219. •Rule 2 (Associativity): When combining more than two things, which pairwise combination you do first doesn't matter. •Benefit: Divide and conquer, parallelization, and incremental accumulation. (6) + 4
  220. 220. 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?
  221. 221. •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
  222. 222. Pattern: Simplifying aggregation code with monoids
  223. 223. 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
  224. 224. Pattern: Convert non-monoids to monoids
  225. 225. Customer + Customer + Customer Customer Stats + Customer Stats + Customer Stats Reduce Map Not a monoid A monoid Summary Stats
  226. 226. Hadoop make me a sandwich https://twitter.com/daviottenheimer/status/532661754820829185
  227. 227. Guideline: Convert expensive monoids to cheap monoids
  228. 228. 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”
  229. 229. Pattern: Seeing monoids everywhere
  230. 230. 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
  231. 231. Is function composition a monoid? >> Function 1 apple -> banana Function 2 banana -> cherry New Function apple -> cherry Not the same thing. Not a monoid 
  232. 232. Is function composition a monoid? >> Function 1 apple -> apple Same thing Function 2 apple -> apple Function 3 apple -> apple A monoid! 
  233. 233. Is function composition 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?
  234. 234. Is function composition a monoid? “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
  235. 235. 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
  236. 236. Event sourcing Any function containing an endomorphism can be converted into a monoid. For example: Event sourcing Is an endomorphism Event -> State -> State
  237. 237. 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
  238. 238. Bind Any function containing an endomorphism can be converted into a monoid. For example: Option.Bind Is an endomorphism (fn param) -> Option -> Option
  239. 239. 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
  240. 240. 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
  241. 241. Pattern: Monads are monoids
  242. 242. Series combination = >> Result is same kind of thing (Closure) Order not important (Associative) Monoid!
  243. 243. Parallel combination = + Same thing (Closure) Order not important (Associative) Monoid!
  244. 244. 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
  245. 245. A monad is just a monoid in the category of endofunctors!
  246. 246. THANKS!

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