Cycle-based Programming of Distributed Systems: The Synchrony - - PowerPoint PPT Presentation

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Cycle-based Programming of Distributed Systems: The Synchrony - - PowerPoint PPT Presentation

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Cycle-based Programming of Distributed Systems: The Synchrony Hypothesis Michael Mendler Faculty of Information Systems and Applied Computer Sciences University of Bamberg, Germany M. Mendler tubs.CITY, Braunschweig, 1.7.2009 1 Overview 1.

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  • M. Mendler

tubs.CITY, Braunschweig, 1.7.2009 1

Cycle-based Programming of Distributed Systems: The Synchrony Hypothesis

Michael Mendler

Faculty of Information Systems and Applied Computer Sciences University of Bamberg, Germany

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  • M. Mendler

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Overview

  • 1. Synchronous Programming
  • 2. The Synchrony Hypothesis
  • 3. Causal Reaction = Fixed Point ?
  • 4. What‘s in a Step ?: Notions of Causality
  • 5. The Synchrony Hypothesis (Hypo-)Thesis
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  • 1. Synchronous Programming
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  • M. Mendler

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Data flow paradigms Control flow paradigms

Synchronous Programming

Statecharts (Harel) Esterel (Berry, Gonthier) Signal (Benveniste, LeGuernic) Lustre (Caspi, Halbwachs)

iCONNECT Statemate Stateflow Modecharts VisualState SyncCharts Argos UMLStatecharts

...

RSML LabView Simulink SCADE Lustre V7 Syndex

...

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  • M. Mendler

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Example: SCADE – Esterel Tech

Data Flow: SCADE Lustre

wA

A/arm

wB

B/arm

WaitAandB

done

/ AB

dA dB

ABSync Reset signal arm

idle cnt 1

arm Detection Inhib

Timer

2 T / disarm

eot

disarm

2

signal disarm

Control Flow: SCADE Safe State Machines

  • embedded systems

domain (avionics, automotive)

  • rigorous semantics
  • verification & testing

(certification)

  • code-generation
  • hw/sw codesign
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Orthogonality in Time and Space

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Data Flow

data flow

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Data Flow

data flow Q: How do we treat the cyclic DF dependencies ? A: Continuitiy Hypothesis, Kahn stream semantics !

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  • M. Mendler

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Orthogonality in Time and Space

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  • M. Mendler

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State Flow

state flow

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  • M. Mendler

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State Flow

state flow Q: How do we treat the cyclic SF dependencies ? A: Synchrony Hypothesis, Fourman response semantics

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  • M. Mendler

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  • 2. The Synchrony Hypothesis
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  • M. Mendler

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Synchrony Hypothesis

Environment view: Reactions are

  • atomic
  • deterministic
  • bounded

System view: Reactions may be

  • non-atomic
  • non-deterministic
  • unbounded

“A reactive system is faster than its environment, hence reactions can be considered atomic”

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  • M. Mendler

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“A reactive system is faster than its environment, hence reactions can be considered atomic”

R2 R1

The Synchrony Paradox

Environment view: Reactions are

  • atomic
  • deterministic
  • bounded

System view: Reactions may be

  • non-atomic
  • non-deterministic
  • unbounded

Paradox ?

faster faster

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  • M. Mendler

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Programming Synchronous Reactions

  • logical transitions
  • conjunctions =

parallelism

  • negations code

choices, priorities and hierarchy logical transitions parallelism choice, priority

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  • M. Mendler

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Programming Synchronous Reactions

  • logical transitions
  • conjunctions =

parallelism

  • negations code

choices, priorities and hierarchy

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  • M. Mendler

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Programming Synchronous Reactions

  • logical transitions
  • conjunctions =

parallelism

  • negations code

choices, priorities and hierarchy

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  • M. Mendler

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In which sense does REACT describe an atomic macro step ?

Synchronous Abstraction

input stimulus instantaneous reaction

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  • M. Mendler

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Synchronous Abstraction

Cyclic dependencies ? => Fixed-Points !

In which sense does REACT describe an atomic macro step ?

input stimulus instantaneous reaction

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  • M. Mendler

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  • 3. Causal Reaction = Fixed-Point ?
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Synchronous Reactive Component

positive, negative triggers, actions , atomic logical signals, logical transitions

action

„response function“

enabled

Reactive component Response of C

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  • M. Mendler

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Reaction = Fixed-Point ?

"A signal s is present in an instant if and only if an `emit s' statement is executed in this instant."

Logical Coherence [Berry]

  • A response S is logically coherent iff

S is a fixed-point of AEC, i.e., S = AEC(S).

  • C is logically reactive iff it in every activation state

and environment, AEC has a fixed-point. Logical Coherence & Reactiveness

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Problem The response function is not monotonic !

Causal Response = Unique Fixed Point ?

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  • M. Mendler

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Problem The response function is not monotonic !

Causal Response = Unique Fixed Point ?

contravariant covariant

  • no unique (least) fixed points !
  • compositionality and full-abstraction problems !
  • different computation methods !

→ different notions of steps, instants, reactions ...

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  • M. Mendler

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Example

For all inputs there is a unique stationary Boolean fixed

  • point. Thus, the system is logically reactive.

≈

We can compile & execute Boolean solution atomically ! But what if we are compiling for a component-based and distributed architecture ?

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Example

Oscillation under up-bounded inertial delay scheduling [Brzozowski & Seger]

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Example

schedule s1, s3 with higher priority than s2 or implement s1, s3 atomically, as a 2in/2out block. Oscillation can be avoided if we Then, whenever s2 is executed, we maintain the invariant

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  • 4. What is in a Step ? Notions of Causality
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What is in a Step ? - A Profusion of Options

1 Avoid Negations

  • nly positive triggers [Modecharts´94, Argos´89]

2 Modify Semantics of Negation

give up global consistency [Huizing&al.´88, Modecharts´96]

3 Give up Synchrony Hypothesis (no abstraction)

all signals delayed[Statemate´90,VHDL,RSML´95,PretC´09] add consistency as implicit trigger

[Maggiolo-Schettini &al.´96, Lüttgen &al.´99]

negative triggers delayed [Saraswat TCCP´94,

Boussinot & deSimone SL´95, Boussinot FunLoft‘07]

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What is in a Step ? - A Profusion of Options

4 Conflict-avoiding Schedules

  • nly accept stratifiable (statically schedulable) programs

[Normal Logic Programming] sequential schedule (endochrony) [Benveniste &al.´00] NRSA „no reaction to signal absence“ (weak endochrony, concurrent input reading) [Butucaru, Caillaud´06]

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5 Self-scheduled Run-time (explicit absence, dual rail)

What is in a Step ? - A Profusion of Options

non-deterministic speculation on absence

[Pnueli & Shalev´91; Boussinot‘s „basic semantics“ ‘98]

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What is in a Step ? - A Profusion of Options

non-deterministic speculation on absence

[Pnueli & Shalev´91; Boussinot‘s „basic semantics“ ‘98]

„Feel free to assume the absence of a signal as long as it is consistent to do so; if necessary, backtrack!“

  • fully-abstract, compositional intuitionistic Kripke semantics

[Lüttgen & Mendler´01]

  • game-theoretic “lazy“ fixed-points [Aguado & Mendler´05]

5 Self-scheduled Run-time (explicit absence, dual rail)

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What is in a Step ? - A Profusion of Options

constructiveness = “computed“ absence [Berry´00]

5 Self-scheduled Run-time (explicit absence, dual rail)

non-deterministic speculation on absence

[Pnueli & Shalev´91; Boussinot‘s „basic semantics“ ‘98]

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  • M. Mendler

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What is in a Step ? - A Profusion of Options

constructiveness = “computed“ absence [Berry´00]

“Accept the absence of a signal only under computable evidence that it may not occur later“

  • game-theoretic “eager“ fixed-points [Aguado & Mendler´05]
  • delay-insensitivity = non-inertial delay

= constructive modal logic [Mendler & Shiple & Berry´07]

& many other hardware approaches

  • speed-independence, semi-modularity, distributivity, ...

5 Self-scheduled Run-time (explicit absence, dual rail)

SugarCubes [Boussinot ´98] (Esterel v3,v4,v5,v6,v7)

non-deterministic speculation on absence

[Pnueli & Shalev´91; Boussinot‘s „basic semantics“ ‘98]

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  • 5. The Synchrony Hypothesis Thesis
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Outlook

Thesis 1

There are as many notions of constructive causality as there are scheduling/run-time models Synchronous reaction requires intensional semantics:

classical Boolean logic ⇒ constructive logic (e.g., Heyting algebra) least and greatest fixed points ⇒ general game-theoretic fixed points

Thesis 2

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  • M. Mendler

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Thank You !