Sccp forces-2009 v3

IntroductionConcurrent Constraint System

A Simple Example

A Spatial Concurrent-Constraint Calculus(First Report)

John Alexander Vargas

Forces, 2009

John Alexander Vargas A Spatial Concurrent-Constraint Calculus (First Report)


A Simple Example

Preliminars

The Concurrent Constraint Programing is a formalism forreasoning about agents which interact with each other bytelling and asking information represented as logic formulas

The agent can viewed as both process and formulas in theunderlying logic.

The Ambient Calculus model de behavior and structure ofmobile systems.

The Spatial Logic can be use to specify properties of thesesystems.

The utcc calculus allow for the speci�cation of mobilebehaviors in the sense of π-calculus



A Simple Example

Research Proposal

The BioAmbients Calculus is an abstraction for biomolecularsystems using the π-calculus for modeling molecular andbiochemical aspects and ambients calculus for speci�cation ofprocess location and movement.

Mi research proposal is explore the use utcc with spatial logicas underlyng logic of constraint system for modeling mobileproperties.

Model and study a complex multi-cellular system: Thehypothalamic weight regulation system



A Simple Example

Metodology

The metodology is:

1 To de�ne formaly a constraint system with spatial logic asunderlyng logic.

2 To model a simple example with utcc and spatial constraintsystem.

3 Verify spatial properties that satisfy with this calculus.

4 To model the hypothalamic weight regulation system with thiscalculus.

5 Verify that mobile properties can be modeled with thiscalculus.



A Simple Example

Outline

1 Introduction

2 Concurrent Constraint SystemSpatial LogicLogical Inference RulesDeciding Validity by Deduction

3 A Simple ExampleModeling Ambients in utccFirewall and AgentRules of Satisfaction of utcc process



A Simple Example

Spatial LogicLogical Inference RulesDeciding Validity by Deduction

Outline

1 Introduction





A Simple Example


Logical Formulas and Satisfaction



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Example

P , a[m[out a. inb. < c >]] |b[openm.(n).n[]]

P |= a[T] |b[T] |T P includes locations a and b

P |= a[m[T]] |T there is a location m in a

P |=�♦(b[m[T] |T]) a location m will be found in b

P |=�♦ c[] an empty location c will be produced

(a[m[T]]|T)∧�♦(b[m[T] |T])



A Simple Example


Quanti�ers

Fresh-Name Quanti�erP |= x .A , ∃m ∈ Λ, m /∈ fn(P,A)∧P |= A{x ←m}P |= x .A , ∀m ∈ Λ, m /∈ fn(P,A)∧P |= A{x ←m}because any fresh name is as good as any other.

Hidden-Name Quanti�erP |=Hx .Ai� ∃m ∈ Λ, P ′ /∈ Πm /∈ fn(A)∧P ≡ (v m)P ′∧P ′ |=A{x ←m}

Hx .A , x .x R©A



A Simple Example


Describing spatial properties of concurrent systems

This Spatial Logics are used to specify the behavior and spatialstructure of concurrent systems, properties as a fresh or secretresources such as keys, nonces, channels, and locations.



A Simple Example


Outline

1 Introduction





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Propositional



A Simple Example


Composition



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Locations



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Modalities



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Revelation



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Example of Deduction



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Outline

1 Introduction





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Spatial Logic for �nite trees

Due to the growing popularity of semistructured data, andparticularly XML, there is a renewed interest in typedprogramming languages that can manipulate tree-like datastructures.

Spatial Logics was proposed as a rich description language fortree-like data.

View the spatial logics as a type system to semi-structureddata.



A Simple Example


Sequent Calculus

In [CalCarGor02] presented a sequent calculus for spatial logicsof ambients. And show that this calculus is sound andcomplete with respect to an interpretation in terms of thesatisfaction relation, and present a complete proof procedure.

A context, Γ or ∆, is a �nite multiset of entries of the formP : A where P is a tree and A is a formula. A sequent is ajudgment Γ `∆ ` where Γ and ∆ are contexts.



A Simple Example


Rules of the sequents calculus



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Rules of Sequent Calculus



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Decidability

Theorem

(Complete Proof Procedure)

For any Γ `∆ there is a procedure such that: if ¬[[Γ `∆]], thenthe procedure terminates with failure; if [[Γ `∆]], then the

procedure terminates with a derivation for Γ `∆ .



A Simple Example

Modeling Ambients in utccFirewall and AgentRules of Satisfaction of utcc process

Outline

1 Introduction





A Simple Example


Modeling Ambients in utcc with Spatial Logics

P , a[inb.P], Q , b[0], then the reduction of P |Qa[inb.R] |b[0]→ b[a[R]]P , tell (a[R]) || (abs T1,T2; a[T1] |b[T2]) tell (b[a[T1] |T2])Q , tell (b[0])

P , a[out b.R], then the reduction of b[P]b[a[out b.R]]→ b[0] |a[R]P , tell (a[R]) || (abs T1,T2; b[a[T1] |T2]) tell ( b[T2] |a[T1] )Q , tell (b[a[R]])

P , openb.R, Q , b[S ], then the reduction of P |Qopenb.R |b[S ]→ R |SP , tell ( R ) (abs T1, T2; b[T1] |T2) tell (T1 |T2)Q , tell (b[R])



A Simple Example








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A Simple Example


Spatial Formulas in utcc

P ,tell (n[R]Bm[S ])Q ,(abs T1; m[T1]) tell R@n

P||Q|| tell n[R]



A Simple Example


Outline

1 Introduction





A Simple Example


Example in Ambient Calculus

Firewall, (vw)w [k[out w . in k ′. inw ] |openk ′.openk ′′.P]Agent, k ′[openk .k ′′[Q]](v k k ′ k ′′)(Agent |Firewall) ∼= (v w)w [Q |P]



A Simple Example


Example in tcc

Firewall , Agent ,(local w) tell ( k ′[k ′′[Q]] ) ||

tell (w [P] |k[0]) || (abs T1,T2 ; k ′[k[T1]|T2])

(abs T1,T2 ; k ′[T1]|k[T2] ) (tell ( k ′[T1|T2] ) )

( tell ( k ′[k[T2]|T1] ) ||

(abs A,B ; w [A]|k ′[B] )

(tell ( w [A|k ′[B]] ))

) ||

(abs T1,T2 ; w [k ′[T1]|T2])

( tell (w [T1|T2]) ||

(abs A,B ; w [k ′′[A]|B] )

( tell (w [A|B]) )

)



A Simple Example


Outline

1 Introduction





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Satisfaction

tell (c) |= c

P|=A

(local x ,c)P|=Hx .A

P|=A

(abs x ,c)P|=Nx .c∧Hx .A

P|=A∧Q|=B

P |Q|=A |B

P|=A

next P|=◦A



A Simple Example


Future Work

Study the model of hypothalamic weight regulation system inbioambients.

Model this biological system with sccp

Study mobile properties in sccp.



A Simple Example


References

Cristiano Calcagno Luca Cardelli Andrew D. Gordon Deciding

Validity in a Spatial Logic for Trees, 2002

Luca Cardelli, Adrew Gordon. Logical Properties of Name

Restriction.

Luca Cardelli y Andrew Gordón. Mobile Ambients. 1997.

Luca Cardelli y Andrew Gordon. Ambient Logic. 2003

Luis Caires y Luca Cardelli. A Spatial Logic for Concurrency

(Part I). 2007

Carlos Olarte, Catuscia Palamidesi y Frank Valencia. UniversalTimed Concurrent Constraint Programming. 2007

Aviv Regev, E. Panina, W Silverman, L Cardelli y E. Shapiro.BioAmbients: An abstraction for biological compartments. 2003

Vijay A Saraswat, Martin Rinard y Prakash Pamangaden.Semantic foundations of concurrent constraint programming.

1990


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Sccp forces-2009 v3

Technology