This document discusses behavior modeling using behavior algebra and Akka actors. It provides an example of modeling a coffee machine as a behavior using behavior algebra equations and then implementing it in Scala with Akka actors. Key points covered include: - Defining behaviors as labeled transition systems (LTS) with states, actions, and transitions between states via actions - Composing behaviors using operations like sequential composition, choice composition, and recursion to build larger behaviors from smaller ones - Modeling a basic coffee machine as a behavior that can accept coins and button presses and dispense coffee - Expanding the model to add features like accumulating credit from multiple coins and disabling/enabling the machine - Implementing the coffee machine

1. AKKA <~~> LTS
[?)
Ruslan Shevchenko <ruslan@Shevchenko.Kiev.UA>
http://garuda.ai

2. // BASIC QUESTIONS //
BEHAVIOR DESCRIPTION
• What is a behavior ?
• How we can specify behavior ? (math / akka)
• Qustions with answer:
• Can we bring to programming/verification well-known
techniques from mathematics ?
• Questions without answer:
• Limit of applicability. When this can be useful ?

3. // WHAT IS A BEHAVIOR(?)//
.
Delta = End
STATE (S)
ACTION (A) (EVENTS)
B = E × S → S

4. // WHAT IS A BEHAVIOR(?)//
BEHAVIOR DESCRIPTION
Delta = End
STATE
ACTION (EVENTS)
BLTS = A × S → S
LTS = Labelled Transition System
s ∈ S
a ∈ A
→a ⊆ S × A × S

5. // WHAT IS A BEHAVIOR(?: AKKA)//
BEHAVIOR DESCRIPTION
STATE
ACTION (EVENTS)
Delta = End
BS
Akka ≈ A × BS
Akka → BS
Akka
val behavior(state) = Behaviors.onMessage {
case message => behavior(change(state))
}
Global Context

6. // WHAT IS A BEHAVIOR(?: AKKA)//
BEHAVIOR DESCRIPTION
STATE
ACTION (EVENTS)
Delta = End
BS
Akka ≈ A × BS
Akka → BS
Akka
BS
Akka ≈ BLTS × S
BLTS ≈ A × S → S
Classical OOP / FP difference

7. MAKE BIGGER BEHAVIOR BY COMPOSING RECURSIVE
EQUATIONS
BEHAVIOUR OPERATIONS
0
-1
B =
- 2
1
2
3
Left . (_ + 1) × B +
Right . (_ − 1) × B
Left . (_ + 1)
Right . (_ − 1)

8. SEQUENTIAL COMPOSITION
BEHAVIOUR OPERATIONS
0
-1
B =
- 2
1
2
3
Left . (_ + 1) × B +
Right . (_ − 1) × B
Left . (_ + 1)
Right . (_ − 1)
sequential composition (and then)

9. CHOICE COMPOSITION
BEHAVIOUR OPERATIONS
0
-1
B =
- 2
1
2
3
Left . (_ + 1) × B +
Right . (_ − 1) × B
Left . (_ + 1)
Right . (_ − 1)
sequential composition (and then)
choice composition (or )

10. RECURSIVE EQUATION
BEHAVIOUR OPERATIONS
0
-1
B =
- 2
1
2
3
Left . (_ + 1) × B +
Right . (_ − 1) × B
Left . (_ + 1)
Right . (_ − 1)
sequential composition (and then)
choice composition (or )

11. SCALA (?) — SURE !
BEHAVIOUR OPERATIONS
0
-1
- 2
1
2
3
lazy val behavior: LTSBehavior[Direction,Int] =
Once[Direction,Int](Left)( _ + 1) * behavior +
Once[Direction,Int](Right)(_ - 1) * behavior
val actor = ActorSystem(behavior.toPlainBehaviour(0)
,"counter")
actor ! Left

12. SCALA (?) — SURE !
BEHAVIOUR OPERATIONS
0
-1
- 2
1
2
3
lazy val behavior: LTSBehavior[Direction,Int] =
Once[Direction,Int](Left)( _ + 1) * behavior +
Once[Direction,Int](Right)(_ - 1) * behavior
val actor = ActorSystem(behavior.toPlainBehaviour(0)
,"counter")
actor ! Left

13. COFFE MACHINE - MVP ITERATION
EXAMPLE
s0=Init
s2=Coin
no button
s3 = Output coffe
s1=Button,
no coins
τ
Button
Press Button
Coin
Coin

14. COFFE MACHINE - MVP ITERATION
EXAMPLE
s0=Init
s2=Coin
no button
s3 = Output coffe
s1=Button,
no coins
τ
Button
Press Button
Coin
Coin
B = Button × Coin × Output × B +
Coin × Button × Output × B
case class State(coin:Boolean,
button: Boolean,
makeCoffe: ()=>() )
lazy val behavior: LTSBehavior[In,State] =
Once[In,State](Coin)(_.copy(coin=true))*
Once[In,State](Button)(_.copy(button=true))*
StateFun[In,State]{ s => s.makeCoffe(); s.copy(coin = false, button = false)}*
behavior +
Once[In,State](Coin)(_.copy(coin=true))*
Once[In,State](Button)(_.copy(button=true))*
StateFun[In,State]{ s => s.makeCoffe(); s.copy(coin = false, button = false)}*
behavior

15. COFFE MACHINE - ADD ON/OFF
EXAMPLE
s0=Disabled
s2=Coin
no button
s3 = Output coffe
s1=Button,
no coins
τ
Button
Press Button
Coin
Coin
Ben = Button × Coin × Output × Ben +
Coin × Button × Output × Ben +
OnOff
Off × Bdis
Bdis = On × Ben

16. COFFE MACHINE - ADD ON/OFF
EXAMPLE
s0=Disabled
s2=Coin
no button
s3 = Output coffe
s1=Button,
no coins
τ
Button
Press Button
Coin
Coin
Ben = Button × Coin × Output × Ben +
Coin × Button × Output × Ben +
OnOff
Off × Bdis
Bdis = On × Ben
lazy val disabled: LTSBehavior[In,State] = On * enabled
lazy val enabled: LTSBehavior[In,State] = ….
+ Off * disabled

17. COFFE MACHINE - ADD ACCUMULATING
EXAMPLE
s0=Disabled
s2=Coin
no button
s3 = Output coffe
s1=Button,
sum < consτ
Button
Press Button
Coin(x)
COIN(X), SUM+X >= COST
Ben = Button × Acc(Output × Ben) +
Acc(Button × Output × Ben) +
OnOff
Off × Bdis
Bdis = On × Ben
COIN(X), SUM+X < COST
Acc(Next) = Coin(x) . s + x < Cost →
Action(s = s + x) × Acc(Next) ⋄ Next

18. COFFE MACHINE - SCALA
EXAMPLE
s0=Di
s2=
s3 =
s1=Bτ
But
Press
Coi
COIN(X),
OO
COIN(X),
lazy val disabled: LTSBehavior[In,State] = On * enabled
lazy val enabled: LTSBehavior[In,State] =
Acc(
ConstantInput[In,State](Button)(_.copy(button=true))*
StateFun[In,State]{ s => s.makeCoffe();
s.copy(coins = s.coins - Const, button = false)}*
enabled
) +
ConstantInput[In,State](Button)(_.copy(button=true))*
Acc(
StateFun[In,State]{ s => s.makeCoffe();
s.copy(coins = s.coins - Const, button = false)}*
enabled
) +
Off * disabled
def Acc(next:LTSBehavior[In,State]):LTSBehavior[In,State] =
Condition[Coin,State]((c,s) => s.coins + c.value < Cost)*Acc(next).upcast[In] +
Condition[Coin,State]((c,s) => s.coins + c.value >= Cost)*next

19. BEHAVIOUR SPECIFICATIONS
One Actor:
Set of Actors:
A||B
parallel composition of A,B (start to work in ||)
A × B
A + Ba . f
φ → A ⋄ B

20. BEHAVIOUR LOGIC
[μ]P
Henessy-Milner modal logic with recursion =
P will necessary hold after event
first-order logic +
< μ > P P is possible after event
Words to google: μ − calculus
Behavior Algebra Insertion Modelling
http://garuda.ai

21. BEHAVIOUR LOGIC
[μ]P
Henessy-Milner modal logic with recursion =
first-order logic + < μ > P
http://garuda.ai (demo)
+
We can automatically check feasibility of properties
Non-technical problems:
- verification != business value
- it is possible to kill the project with verification

22. BEHAVIOUR LOGIC
Non-technical problems:
verification !=
business value
carelessly verification
can kill the project
ping me, if anybody
still interested ;)

23. BEHAVIOR ALGEBRA: CONCLUSION
Consider using Behavior Algebra interpreter
onTop/instead
- Actors,
- State-Machines
- Streams
when state graph is not trivial
-
It is possible to analyze properties of you system
completeness, liveness, safety ..
in automated way
// this will be mainstream during next 10-100 years

24. Questions (?)
twitter: @rssh1
e-mail: ruslan@shevchenko.kiev.ua
http://garuda.ai

25. DONEC QUIS NUNC

26. COFFE MACHINE
EXAMPLE