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

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