Cyrille Martraire: Monoids, Monoids Everywhere! at I T.A.K.E. Unconference 2015

Monoids,!Monoids everywhere

cyrille martraire!@cyriux

Can you tell the

difference?

Monoid

Glass of beer

This talk is the answer

DDD

FP

(00)

A matter of Taste

http://rosshirt.blogspot.fr/

The Code Gourmet

(dedicated to @ziobrando)

http://rosshirt.blogspot.fr/

Passionate developer

PARIS Since 1999

!@cyriux

Cyrille Martraire

Paris Software Craftsmanship Community

http://www.meetup.com/paris-software-craftsmanship/

http://www.meetup.com/paris-software-craftsmanship/

TDDBDDDDDLegacy

WARNINGThe following show features no spectacular stunt, no live coding, only trivial Java code. You can re-create or re-enact at home with no danger.

a bit personal

Adopted 2005 Still in love

a question

What do DDD & FP have in common?

"My first encounter with FP concepts was from DDD"

FP = ?

http://www.jaider.net/archives/609-intro-to-functional-programming/

PURE

http://www.jaider.net/archives/609-intro-to-functional-programming/

No State No War

So what do DDD & FP

have in common?

Value Objects................................................................................................. 19

Learn one

and get the other

one for FREE!

DDDFP

(OO)

NICE STYLE

of code

DDD+FP = ?

Example PLZ?

MONOIDZ!

@cyriux

Closure Associativity

Neutral Element

only 3 numbers in

programming

0, 1, MANY

Monoid: encapsulate

diversity inside

0, 1, MANY

Neutral Element

Element

Operation

Encapsulate special cases

→ simple again

Battle against complexity

× × × …

× × × …

× × × …

Applied often:

→ scalable process

→ can grow to high complexity

Scalable in complexity

For a given interface I find myself doing often 0, 1, Many

OO FTW!

0, 1, MANY

NullObject

Implementation(s)

Composite

Identity Element = NullObject

VatCalculation.NONE

Example PLZ!

Numbers int+int=int

(3+5)+2=3+(5+2) 0

Lists (.)+(.,.)=(.,.,.)

(a ︎)+(b,︎c)=(a ︎, b)+(c) ()

Strings "hello"+"world" "cy"+"ri"+"lle"

""

look simplistic; the key to very

complex behavior

The key to infinite scalability!

(space)

The key to infinite incremental computing!

(ti

me)

Hadoop x Storm

Composeability

Abstractions in the small that

compose at large

Monoids ☛ reduce

Monoids ☛ domain

Monoids ☛ domain

Monoids: typical FP

FP: Everything is a

value

Therefore: Monoids are

values!

PROOF

VALUE OBJECTS

Immutable Equals by value

Value Object

A DDD pattern to import FP-ish

values in OO languages

Not Anemic

18 m + 16 m = 34 m

returns a new instance

Change -> new instance

SIDE-EFFECT -free

FUNCTIONS

Immutability &

Side-effect-free functions!

“Functional-First” style

90%“Functional-First” style

Value Objects

(Ok, gut feeling, I did’nt measure)

Money

(25, EUR) +

(30, EUR) =

(55, EUR)

(25, EUR) +

(30, USD) =

exception

Money

amount currencyadd(Money): Money

<<ValueObject>>

Cashflows (Payments)

(25, EUR, today) +

(30, EUR, today) =

(55, EUR, today)

(25, EUR, today) +

(30, EUR, next day) =

exception

CashFlow

amount currency date

add(CashFlow):CashFlow

<<ValueObject>>

CLOSURE of

OPERATION

Cashflows Sequences

(10, EUR, 20/03)

(30, EUR, 21/03)

(25, EUR, 21/03)

(12, EUR, 22/03)

(10, EUR, 20/03)

(55, EUR, 21/03)

(12, EUR, 22/03)

+

=

Cashflow Sequence +

Cashflow Sequence =

Cashflow Sequence

Object Arithmetics

This is how domain experts THINK

about itSAY

SKETCH

Ranges

[1, 3] Union* [2, 4]

= [1, 4]

* for a bounding box-kind definition of union

[1, 3] Union [2, 4]

= [1, 4] ][

Predicates

Filter AND Filter

= Filter

Filter AND Filter

= Filter

Always

True

Filter OR

Filter =

Filter

Filter OR

Filter =

FilterAlways

False

Grants

Read, Write, Execute !

"most secure wins" !

r + w = r w + x = w

Configuration Maps

Color BLUE

Enable TrueTimeout 30 +

=

Color RED

Enable FalseTimeout 25

Desk FX

Color RED

Enable TrueTimeout 25

Desk FX

Default Desk-specific

Color BLUE


=

Color RED


Desk FX

Color RED


Desk FX


overw

rite

logic

al OR

min

Color BLUE


=

Color RED


Desk FX

Color RED


Desk FX


overw

rite

logic

al OR

min

Values are monoids too!

Color BLUE


=Color BLUE


Color NONE

Enable FalseTimeout +∞

Desk ALLNeutral Element

Color BLUE


=Color BLUE


Neutral Element

Color BLUE


=Color BLUE


Value Objects may be

*BIG* object trees!

(DOM)

Non-Linear Stuff (average, std dev,

K-clustering, barycenters...)

Average + Average = WRONG

Average + Average Not Composeable!

avg = sum / count !

avg = sum / count !

avg = sum / count !

avg = sum / count !

+

avg = sum / count !

avg = sum / count !

+ +

avg = sum / count !

avg = sum / count !

avg = sum / count

+

=

+

=

(sum, count) !

(sum, count) !

(sum, count)

+

=

Average

(sum, sum2, count) !

(sum, sum2, count) !

(sum, sum2, count)

+

=

Std deviation

Can model as a monoid even non-

linear stuff!

MOAR MATHS

PLZ!

Monoid several times...

toString(): String union(MailingList): MailingList intersection(MailingList): MailingList nobody(): MailingList everybody(): MailingList

MailingList

Space Vectors

average temperature! = t1.add(t2)! .scale(1/2)

returns a new instance

Change -> new instance

Space Vector

toCelsius(): Temperature toFarenheit(): Temperature add(Temperature): Temperature scale(double): Temperature

Temperature

Why is it useful?

(10, EUR, 20/03)

(30, EUR, 21/03)

(25, EUR, 21/03)

(12, EUR, 22/03)

(10, EUR, 20/03)

(55, EUR, 21/03)

(12, EUR, 22/03)

+

=

Cashflow Sequence +

Cashflow Sequence =

Cashflow Sequence

This is how domain experts THINK

about itSAY

SKETCH

DECLARATIVE STYLE

Much less code Much less bugs

// without monoids PaymentsFees(...) PaymentsFeesWithOptions(...) PaymentsFeesWithInsuranceAndOptions(...) PaymentsFeesWithInsurance(...) NoFeesButInsurance(...) ...

// with monoids fees(...) : Payments options(...) : Payments insurance(...) : Payments !Payments.add(Payments) : Payments

side-effect-free

operation

Very easy to test

input output

Much less stuff to learn

Cashflow Sequence +

Cashflow Sequence =

Cashflow Sequence

Monoid/Vector Spaces/Cyclic Group

Literature Documented

ESTABLISHED FORMALISMS

@annotations

@Monoid(neutral="emptyList") intersection(MailingList): MailingList !emptyList(): MailingList

MailingList

LIVING DOCUMENTATION

Write code that tells the business

domain stories

generic naming

@Monoid(neutral="emptyList") intersection(MailingList): MailingList !emptyList(): MailingList

MailingList

Domain-Specific naming

@Monoid(neutral="nobody") overlapping(MailingList): MailingList !nobody(): MailingList

MailingList

SELF-EXPLAINING VALUES

We Want:Traceability of processing

No worry!

Just enrich our types



!

label field

Monad-ish No logging needed Each value stores

its history

http://stuartcook.files.wordpress.com/2010/11/happy-monkey.jpg

http://stuartcook.files.wordpress.com/2010/11/happy-monkey.jpg

In Closing

Composeability Composeability Composeability Composeability Composeability Composeability

Invest time: Learn DDD, and get

free FP exposure

A paradox: FP influence helps craft better Object-

Oriented code!

So simple, most people

have no appreciation

of that!

Monoids are good: Eat Them!

LOOK 4 Ur DOMAIN MONOIDZ!

Also learn other maths structures

Wikipedia is your friend!

DDD+FP=

http://wadler.blogspot.fr/2008/04/functional-programming-is-beautiful.html

http://wadler.blogspot.fr/2008/04/functional-programming-is-beautiful.html

Taste-Driven Development

TDD @cyriux

Questions? Did you try similar things too?

Let’s discuss!

@cyriux

Follow me @cyriux !

Slides: slideshare.net/cyriux Blog: cyrille.martraire.com

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Merci