Theory of Programming

Prof. Dr. W. Reisig

Service-Orientation as a Paradigm of Computing

Wolfgang ReisigHumboldt-Universität zu Berlin

ICTERIKiev, June 24, 2016

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2012celebrated as the greatest computer scientist of the 20th century.

Basics of theoretical informatics:Turing Machines (1936)

What is the Basic Paradigmof Informatics ?

alphabet Σ; finitely many symbols a, b, c, … ,zwords Σ*; countably many ab, ca, aca, …functions f: Σ* Σ*; uncountably many

Some of those functions are “computable” (countably many).

Each computable function can effectively be computed • by a computer (with unbounded store)• by an amazingly simple kind of machine, a Turing machine.

Yet, no computer can compute more functions.

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Theoretical Informatics in a nutshell

→---

useful, undisputed:

equivalence, abstraction/refinementcompositioncomplexitylogical characterizations

The computable functions pinpoint deep theoretical results and famous open problems.

So, the theory of computable functionsis frequently considered THE theory of informatics.

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… lots of concepts

This talk:

1. Aspects that exceed classical Theoretical Informatics2. A conceptual view on SOC3. Towards a Theory of Services4. Important aspect: Associative Composition

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This talk:

1. Aspects that exceed classical Theoretical Informatics2. A conceptual view on SOC3. Towards a Theory of Services4. Important aspect: Associative Composition

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How establish reliable communication?By sending acknowledgements, copies, etc. ,i.e. by means of distributed algorithms (“protocols”).

Informatics comprises communication

Complexity is not in computation but in communication.

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Informatics comprisesnon-ending behavior

SOC “always on”

cloud

elevator control

business informatics “24/7”

classical view: terminating behavior is intended, infinite behavior is mistaken.

new view: infinite behavior is intended.terminating behavior is mistaken.

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c

a b

c

a b

c

a b

Informatics comprisescausal independence

a b a b a ac c cb …

d e d e d df f fe …

c

a b

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f

ed

e

d

f e

d

f e

d

f

e

a

ab

c

b

Informatics comprisescausal independence

de

d

a

d

f

cbe

……

……

……

…

+ fairness assumption

b…

motivated by “observation”

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c

a b

c

a b

c

a b

e

d

f e

d

f e

d

fc

a b

f

ed

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Distributed Systems and Distributed Runs

a b a b a ac c cb …

d e d e d df f fe …

c

a b

f

ed

a b a b a ac c cb …

d e d e d df f fe …

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a variant: i-th b before i-th f

Avoid a naïve notion of “time”and of “observation”.

Causality structures the world

a deterministic systemno alternativesone behavior (run, execution)

c

a b

f

ed

This talk:

1. Aspects that exceed classical Theoretical Informatics2. A conceptual view on SOC3. Towards a Theory of Services4. Important aspect: Associative Composition

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Paradigms of programming:1. Conventional (procedural) programs

follows the IPO model: input-process-output theoretical foundation/ expressive power: the computable functions

2. Object orientationattributes and methodstheoretical foundation: abstract data types / algebraic specifications / signatures and structures (as for 1st order logic)

3. Service orientationself contained components (reactive systems)loosely coupledtheoretical foundation: missing

… intuitively …

imperative programing

Object Orientation

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Service Oriented Computing

… intuitively …

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The Cloud

… intuitively …

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What is a Service?

… an algorithmic component, frequently software.

a person’s role:• booking a journey, • buying a ticket, • withdrawing cash

from an ATM.

software to • book a journey, • sell a ticket, • offer cash at

an ATM.

a technical system:• elevator • self driving vehicle• mobile phone

an organization, providing • insurance• medical surgery

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Services interact loosely coupled.In general: message passing; not handshaking.Interacting services (instantiations) jointly pursue a goal.They reach their goal

Services interact goal oriented

A frequent goal of composed services:to reach a final state together.

Often: Two services play the role of a provider and a requester, together with a broker.

, or miss it.

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InstantiationsA service may spawn many instantiations.Input as last timedoes NOT yield output as last time

Two instantiations may• temporally overlap, • interact,• behave differently. • Different instantiation may

start in different states.

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A formal foundation is a base to ...• describe semantics of implementations

• characterize expressivity of formalisms

• relate representations (equivalence, simulation)

• clarify the elementary notions of the area

• derive properties from structural and behavioral descriptions

• teach the area systematically

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Structure of textbooks on SOAFirst part:in plain English:“… SOA is an implementation independent concept …”,using many notions, poorly related.

Second part:examples of implementations,confusing conceptual aspects and language dependent aspects

Missing bridge:implementation independent models.

This talk:

1. Aspects that exceed classical Theoretical Informatics2. A conceptual view on SOC3. Towards a Theory of Services4. Important aspect: Associative Composition

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Semantics of Services We should do it in analogy to programming languages:

The semantics of a service is a mathematical object!

True, this is presently not the case.

BUT WE SHOULD spend effort into this!

towards a generic modeling language

aim of ageneric Mod. language

expressive power (L)

all modeling languages Lfor services

aim of, e.g.BPMN:

expressive power (L)

all modeling languages Lfor services

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... a transition system with channelsfor asynchronous communicationwith its environment.

Semantics of S:During a computation, each channel funnels a stream of data.

technically:a relation on – infinite – streams

S

a

b

c

Models of services

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Requirements:

The – elementary – notion of composition of services is a (simple!) mathematical (or logical!) operation.

For services S and T,the composition S ⊕ Tis a service again.

Frequently, S ⊕ T does not interact any more.

ticketing =def

sell_ticket ⊕ buy_ticket

Interaction is represented as composition

How to compose services?

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Composition S ⊕ T has pending channels.… is a service again.

Tb

e

dS ⊕ T

S

a

b

c

Requirements at composed services

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S and T communicate boundedlyS and T communicate responsively

With target states:S ⊕ T weakly terminates S ⊕ T is deadlock freeS ⊕ T is lifelock free

… as CTL* formulas:S ⊕ T AG n-boundedS ⊕ T AGEF responsive

S ⊕ T AGEF terminalS ⊕ T AG (terminal target)S ⊕ T AGEF target

Tb

e

dS ⊕ T

S

a

b

c

Together, services may accomplish a requirement, ρ.

For a requirement ρ …

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S and T communicate boundedlyS and T communicate responsively

With target states:S ⊕ T weakly terminates S ⊕ T is deadlock freeS ⊕ T is lifelock free

Def.: Let ρ be a requirement on services.

(i) S and T are ρ -partnersiff S ⊕ T ρ

(ii) S is substitutable by Tiff for all U,S ⊕ U ρ implies T ⊕ U ρ

(iii) U is a ρ -adapter for S and Tiff S ⊕ U ⊕ T ρ

Tb

e

dS ⊕ T

S

a

b

c

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properties of services Quests at the partners of a service, S ,w.r.t a requirement ρ :

Does S have ρ -partners at all ? Is T a ρ -partner of S ?How construct a canonical ρ -partner of S ?How characterize all ρ -partners of S ?

ControllabilityComposability“most liberal”

Operating Guideline

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Given:• a set S of services,• a composition operator ⊕ : S × S S,• a set Q of requirements ρ1, ... , ρn ⊆ S.This yields the algebraic structure

(S; ⊕ , Q ).

For S, T ∈ S, ρ∈Q,T is a ρ - partner of S,iff S ⊕ T ρ.

Let semρ(S) =def the set of all ρ - partners of S.

The algebraic structure of servicesthe “classical” requirement

ρ : weak termination

derived notions(w.r.t some ρ ):

S may be substituted by S‘ : semρ(S) ⊆ semρ(S‘ )

S and T are equivalent: semρ(S) = semρ(T)

U adapts S and T: S ⊕ U ⊕ T ρ

S ⊕ T ∈ ρρ ( S ⊕ T )

This talk:

1. Aspects that exceed classical Theoretical Informatics2. A conceptual view on SOC3. Towards a Theory of Services4. Important aspect: Associative Composition

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Composing many services

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Tb

e

dS ⊕ T

S

a

b

c

e.g. a supply chain

a simple idea

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(S ⊕ T)

S

a

b

c

Tb

e

d

b

e

f

⊕ U

Ub

e

d

b

e

f

a simple idea

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S

a

b

c

Tb

e

d

b

e

f

Ub

e

d

b

e

f

associativity: inevitable for composition!… and universally feasible:Identify two sets of channels: left port, right port.

S ⊕ (T ⊕ U)

Tb

e

d

b

e

f

leftport

rightport

(S ⊕ T) ⊕ U =

Example: vending machinedad pays, mom selects,

tea!

juice!

momdad

coin coin

tea!

juice!

beverage

vend. mach

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coin

tea!

juice!

beverage

beverage

kid

tea!

juice!

momdad

coin

Example: vending machinedad pays, mom selects, kid drinks.

vend. mach

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juice!

tea!

mom

coin

juice!

tea!

beverage

dad

coin

kid

A variant of the vending machinedad pays, mom selects, kid drinks.

beverage

vend. mach

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N2requester

R1

exclusive requester

N1provider

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N2requester

R1

exclusive requester

N1provider

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N2requester

R1

sharing requester

N1provider

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N2requester

R1

sharing requester

N1provider

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N2‘ requester

N2requester

second sharing requester

N1provider

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N2‘ requester

N2requester

second sharing requester

N1provider

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N2‘ requester

N2requester

third sharing requesterN2‘‘

requester

skip the primes:N1 N2 N2 N2N1

provider

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generic sharing requesters

P provider

Qrequester

D

D

D

D

M

Qrequester

Qrequester

P Q Q

P Q Q Q

P Q

genericreques-ter Q : Q

requester

D

M

RL

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prefer this variant?

P provider

Qrequester

D

D

D

D

M

Qrequester

Qrequester

P Q Q Q

P Q

A

A

A

A

A

A

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P Q Q

genericrequester Q : Q

requester

D

M

RL

prefer this variant?

P provider

Qrequester

D

D

D

D

M

Qrequester

Qrequester

P Q Q

P Q Q Q

P Q

A

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A

genericrequester Q : Q

requester

D

M

RL just make

a member of L

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Cyclic composition: The philosophers

A

32 B 43 C 54 D 15 E

This is A B C D EThe problem: How glue ?Construct the closure (A B C D E)c

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2 32 B 43 C 54 D 15 E1

Cyclic composition: The philosophers

A

This is A B C D EThe problem: How glue ?Construct the closure (A B C D E)c

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... with a generic philosopher

rl p

algebraic form: (p p p p p)c

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rp rp rp rp

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Given:• a set S of services,• a composition operator ⊕ : S × S S,• a set Q of requirements ρ1, ... , ρn ⊆ S.This yields the algebraic structure

(S; ⊕ , Q , ).

For S, T ∈ S, ρ∈QT is a ρ - partner of S,iff S ⊕ T ρ.

Let semρ(S) =def the set of all ρ - partners of S.

The algebraic structure of services

c

The algebraic structure of clouds

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Theory of Programming

Prof. Dr. W. Reisig

Service Orientation as a paradigm of computing

Wolfgang ReisigHumboldt-Universität zu Berlin

ICTERIKiev, June 24, 2016