Monoids are mathematical structures that have an associative binary operation and an identity element. The talk discusses how monoids appear frequently in programming, especially in domains and functional programming concepts like value objects. Monoids allow encapsulating diversity and scaling complexity by composing operations. They also enable a declarative programming style that is less error-prone. The talk advocates learning about monoids and applying monoid patterns in domains to gain benefits for object-oriented design from functional programming concepts.

1. Monoids,!
Monoids everywhere
cyrille martraire!
@cyriux

2. Can you tell
the
difference?

3. Monoid

4. Glass of beer

5. This talk is
the answer

6. DDD

7. FP

8. (00)

9. A matter
of Taste
http://rosshirt.blogspot.fr/
The Code
Gourmet
(dedicated to @ziobrando)

10. Passionate
developer
PARIS
Since 1999
!
@cyriux
Cyrille Martraire

11. Paris Software
Craftsmanship Community
http://www.meetup.com/paris-software-craftsmanship/

12. TDD
BDD
DDD
Legacy

13. WARNING
The 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.

14. a bit personal

15. Adopted 2005
Still in love

16. a question

17. What do DDD & FP
have in common?

18. "My first encounter
with FP concepts
was from DDD"

19. FP = ?

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

23. No State
No War

25. So what do
DDD & FP
have in
common?

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

27. Learn one
and get the other
one for FREE!

28. DDD
FP
(OO)

29. NICE
STYLEof code

30. DDD+FP
= ?

32. Example
PLZ?

33. MONOIDZ!

34. @cyriux

35. Closure
Associativity
Neutral Element

37. only 3
numbers in
programming

38. 0, 1, MANY

39. Monoid:
encapsulate
diversity inside

40. 0, 1, MANY
Neutral Element
Element
Operation

41. Encapsulate
special cases
→ simple again

42. Battle against
complexity

43. × × × …

44. × × × …

45. × × × …

46. Applied often:
→ scalable process
→ can grow to
high complexity

47. Scalable in
complexity

48. For a given interface I
find myself doing
often 0, 1, Many
OO FTW!

49. 0, 1, MANY
NullObject
Implementation(s)
Composite

50. Identity Element
= NullObject
VatCalculation.NONE

51. Example
PLZ!

52. Numbers
int+int=int
(3+5)+2=3+(5+2)
0

53. Lists
(.)+(.,.)=(.,.,.)
(a︎)+(b︎,c)=(a︎, b)+(c)
()

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

55. look simplistic;
the key to very
complex behavior

56. The key to infinite
scalability!
(space)

57. The key to infinite
incremental
computing!
(time)

58. Hadoop x Storm

59. Composeability

60. Abstractions in
the small that
compose at large

61. Monoids ☛ reduce

62. Monoids ☛ domain

63. Monoids ☛ domain

64. Monoids:
typical FP

65. FP:
Everything is a
value

66. Therefore:
Monoids are
values!
PROOF

67. VALUE
OBJECTS

68. Immutable
Equals by value

69. Value Object
A DDD pattern
to import FP-ish
values in OO
languages

70. Not Anemic

71. 18 m
+ 16 m
= 34 m

72. returns a new
instance
Change -> new instance

73. SIDE-EFFECT
-free
FUNCTIONS

74. Immutability
&
Side-effect-free
functions!

75. “Functional-First” style

76. 90%
“Functional-First” style
Value Objects
(Ok, gut feeling, I did’nt measure)

77. Money

78. (25, EUR)
+
(30, EUR)
=
(55, EUR)

79. (25, EUR)
+
(30, USD)
=
exception

80. Money
amount
currency
add(Money): Money
<<ValueObject>>

82. Cashflows
(Payments)

83. (25, EUR, today)
+
(30, EUR, today)
=
(55, EUR, today)

84. (25, EUR, today)
+
(30, EUR, next day)
=
exception

85. CashFlow
amount
currency
date
add(CashFlow):CashFlow
<<ValueObject>>

86. CLOSUREof
OPERATION

87. Cashflows
Sequences

88. (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)
+
=

89. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

90. Object
Arithmetics

91. This is how domain
experts THINK
about it
SAY
SKETCH

93. Ranges

94. [1, 3]
Union*
[2, 4]
=
[1, 4]
* for a bounding box-kind definition of union

95. [1, 3]
Union
[2, 4]
=
[1, 4] ][

96. Predicates

97. Filter
AND
Filter
=
Filter

98. Filter
AND
Filter
=
Filter
Always
True

99. Filter
OR
Filter
=
Filter

100. Filter
OR
Filter
=
Filter
Always
False

101. Grants

102. Read, Write, Execute
!
"most secure wins"
!
r + w = r
w + x = w

103. Configuration
Maps

104. Color BLUE
Enable True
Timeout 30 +
=
Color RED
Enable False
Timeout 25
Desk FX
Color RED
Enable True
Timeout 25
Desk FX
Default Desk-specific

105. Color BLUE
Enable True
Timeout 30 +
=
Color RED
Enable False
Timeout 25
Desk FX
Color RED
Enable True
Timeout 25
Desk FX
Default Desk-specific
overw
rite
logical OR
m
in

106. Color BLUE
Enable True
Timeout 30 +
=
Color RED
Enable False
Timeout 25
Desk FX
Color RED
Enable True
Timeout 25
Desk FX
Default Desk-specific
overw
rite
logical OR
m
in
Values are monoids too!

107. Color BLUE
Enable True
Timeout 30 +
=
Color BLUE
Enable True
Timeout 30
Color NONE
Enable False
Timeout +∞
Desk ALL
Neutral Element

108. Color BLUE
Enable True
Timeout 30 +
=
Color BLUE
Enable True
Timeout 30
Neutral Element

109. Color BLUE
Enable True
Timeout 30 +
=
Color BLUE
Enable True
Timeout 30
Value Objects may be
*BIG* object trees!
(DOM)

111. Non-Linear Stuff
(average, std dev,
K-clustering,
barycenters...)

112. Average + Average =
WRONG

113. Average + Average
Not Composeable!

116. avg = sum / count
!
avg = sum / count
!

117. avg = sum / count
!
avg = sum / count
!
+

118. avg = sum / count
!
avg = sum / count
!
+ +

119. avg = sum / count
!
avg = sum / count
!
avg = sum / count
+
=
+
=

120. (sum, count)
!
(sum, count)
!
(sum, count)
+
=
Average

121. (sum, sum2, count)
!
(sum, sum2, count)
!
(sum, sum2, count)
+
=
Std deviation

122. Can model as a
monoid even non-
linear stuff!

124. MOAR
MATHS
PLZ!

125. Monoid several times...
toString(): String
union(MailingList): MailingList
intersection(MailingList): Mailing
nobody(): MailingList
everybody(): MailingList
MailingList

126. Space
Vectors

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

128. returns a new
instance
Change -> new instance

129. Space Vector
toCelsius(): Temperature
toFarenheit(): Temperature
add(Temperature): Temperature
scale(double): Temperature
Temperature

130. Why
is it useful?

131. (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)
+
=

132. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

133. This is how domain
experts THINK
about it
SAY
SKETCH

134. DECLARATIVE
STYLE

135. Much less code
Much less bugs

137. // without monoids
PaymentsFees(...)
PaymentsFeesWithOptions(...)
PaymentsFeesWithInsuranceAndO
PaymentsFeesWithInsurance(...
NoFeesButInsurance(...)
...

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

139. side-effect-
free
operation
Very easy to test
input output

140. Much less stuff to
learn

141. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

142. Monoid/Vector
Spaces/Cyclic Group

143. Literature
Documented

144. ESTABLISHED
FORMALISMS

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

146. LIVINGDOCUMENTATION

147. Write code that
tells the business
domain stories

148. generic naming
@Monoid(neutral="emptyList")
intersection(MailingList): MailingList
!
emptyList(): MailingList
MailingList

149. Domain-Specific naming
@Monoid(neutral="nobody")
overlapping(MailingList): MailingList
!
nobody(): MailingList
MailingList

150. SELF-
EXPLAINING
VALUES

151. WeWant:
Traceability
of processing

152. No worry!

153. Just enrich our
types

154. Just enrich our
types

155. Just enrich our
types
!
label field

156. Monad-ish
No logging needed
Each value stores
its history

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

159. In Closing

160. Composeability
Composeability
Composeability
Composeability
Composeability
Composeability

161. Invest time:
Learn DDD, and get
free FP exposure

162. A paradox:
FP influence helps
craft better Object-
Oriented code!

163. So simple,
most people
have no
appreciation
of that!

164. Monoids
are good:
Eat Them!

165. LOOK 4 Ur
DOMAIN
MONOIDZ!

166. Also learn other
maths structures

167. Wikipedia is
your friend!

168. DDD+FP
=

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

170. Taste-Driven
Development
TDD
@cyriux

172. Questions? Did you try
similar things too?
Let’s discuss!
@cyriux

173. Follow me @cyriux
!
Slides: slideshare.net/cyriux
Blog: cyrille.martraire.com
!
In Paris? Join !

174. Merci