You probably can't imagine that Monoids (not monads) are so simple maths creatures that you can understand them in just a few minutes. You probably can't imagine that Monoids (not monads) are so simple maths creatures that you can understand them in just a few minutes. But you probably don't imagine either that they can help you craft elegant and powerful domain models that scale very well. Through various examples, we will have a closer look at monoids used for domain modeling in a style that mixes the best of DDD and FP. Even in languages like Java or C#, this talk will influence your coding style forever! 'More entertaining and educational explanation of Monoids I've heard' - Martin Thompson, DDD exchange London 2014. See more at http://skillsmatter.com/conferences/1880-ddd-exchange-nyc-2014#program

1. Ur Domain Haz
Monoids?
DDDx NYC 14
cyrille martraire aka @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. ...

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
STYLE of 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. Neutral Element
0, 1, MANY
Element
Operation

41. Encapsulate
special cases
→ simple again

42. Battle against
complexity

43. × × × …

44. × × × …

45. × × × …

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

47. Scalable in
complexity

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

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

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. Monoids ☛ reduce

61. Monoids ☛ domain

62. Monoids ☛ domain

63. Monoids:
typical FP

64. FP:
Everything is a
value

65. PROOF
Therefore:
Monoids are
values!

66. VALUE OBJECTS

67. Immutable
Equals by value

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

69. Not Anemic

70. 18 m
+ 16 m
= 34 m

71. Change -> new instance
returns a new
instance

72. SIDE-EFFECT
-free
FUNCTIONS

73. Immutability
&
Side-effect-free
functions!

74. “Functional-First” style

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

76. Money

77. (25, EUR)
+
(30, EUR)
=
(55, EUR)

78. (25, EUR)
+
(30, USD)
=
exception

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

81. Cashflows
(Payments)

82. (25, EUR, today)
+
(30, EUR, today)
=
(55, EUR, today)

83. (25, EUR, today)
+
(30, EUR, next day)
=
exception

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

85. CLOSURE of
OPERATION

86. Cashflows
Sequences

87. (30, EUR, 21/03)
(10, EUR, 20/03)
(25, EUR, 21/03)
(12, EUR, 22/03)
(10, EUR, 20/03)
(55, EUR, 21/03)
(12, EUR, 22/03)
+
=

88. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

89. Object
Arithmetics

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

92. Ranges

93. [1, 3]
Union*
[2, 4]
=
[1, 4]
* for a bounding box-kind definition of union

94. [1, 3]
Union
[2, 4]
=
[1, 4] ][

95. Predicates

96. Filter
AND
Filter
=
Filter

97. Filter
AND
Filter
=
Filter Always
True

98. Filter
OR
Filter
=
Filter

99. Filter
OR
Filter
=
Filter Always
False

100. Grants

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

102. Configuration
Maps

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

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

105. Default Desk-specific
Color BLUE
Enable True
Timeout 30 +
Values are monoids too!
=
Color RED
Enable False
Timeout 25
Desk FX
Color RED
Enable True
Timeout 25
Desk FX
overwrite
logical OR
min

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

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

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

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

111. Average + Average =
WRONG

112. Average + Average
Not Composeable!

115. avg = sum / count
!
avg = sum / count
!

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

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

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

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

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

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

123. MOAR MATHS PLZ!

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

125. Space
Vectors

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

127. Change -> new instance
returns a new
instance

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

129. Why
is it useful?

130. (30, EUR, 21/03)
(10, EUR, 20/03)
(25, EUR, 21/03)
(12, EUR, 22/03)
(10, EUR, 20/03)
(55, EUR, 21/03)
(12, EUR, 22/03)
+
=

131. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

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

133. DECLARATIVE STYLE

134. Much less code
Much less bugs

136. // without monoids
PaymentsFees(...)
PaymentsFeesWithOptions(...)
PaymentsFeesWithInsuranceAndOptions(...)
PaymentsFeesWithInsurance(...)
NoFeesButInsurance(...)
...
!
// with monoids
fees(...) : Payments
options(...) : Payments
insurance(...) : Payments
!
Payments.add(Payments) : Payments

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

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

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

140. Much less stuff to
learn

141. 1 interface
to rule them all

142. Cashflow Sequence
+
Cashflow Sequence
=
Cashflow Sequence

143. ESTABLISHED FORMALISMS

144. Monoid/Vector
Spaces/Cyclic Group

145. Literature
Documented

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

147. LIVING DOCUMENTATION

148. Write code that
tells the business
domain stories

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

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

151. SELF-EXPLAINING
VALUES

152. We Want:
Traceability
of processing

153. No worry!

154. Just enrich our
types

155. Just enrich our
types

156. Just enrich our
types
!
label field

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

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

160. In Closing

161. Composeability
Composeability
Composeability
Composeability
Composeability
Composeability

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

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

164. So simple
most people
have no
appreciation
of that!

165. Monoids
are good:
Eat Them!

166. LOOK 4 Ur
DOMAIN
MONOIDZ!

167. Also learn other
maths structures

168. Wikipedia is
your friend!

169. DDD+FP
=

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

171. TDD
Taste-Driven
Development
@cyriux

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

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

175. Merci

176. Abstractions in
the small that
compose at large