TMT for CHR v in SFC

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Séminaire Interne Contraintes, Paris Rocquencourt 16/9/2009

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TMT for CHRv in SFC

Pierre Deransartwith

Rafael Ferreira Oliveira

CR INRIA-Paris-Rocquencourt

16 septembre 2009

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Development Methodology of a Generic Trace for CHRv based on the Simple Fluent

Calculus

• Development Methodology: Trace Meta-Theory (TMT)

• Constraint Handling Rules with Disjunction (CHRv)

• Simple Fluent Calculus (SFC)

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1. TMT , Generic Trace Development

2. SFC (short introduction)

3. CHRv semantics in SFC (t)

4. OS of CHRv in SFC

5. GT Development, next steps

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Trace Meta Theory

Pierre Deransart, Mireille Ducassé and Gérard Ferrand, Observational Semantics of the Resolution Box Model, Proceedings of the 17th Workshop on Logic-based Methods in Programming Environments (WLPE'07), 2007, eds.Wim Vanhoof and Patricia Hill, Porto, Portugal

Pierre DeransartConception de traces et applications (vers une méta-théorie des traces), Progress reports on http://hal.inria.fr/ (last march 2009)

Followup work of OADymPPaC Project (2001-2004)Outils d'Analyse Dynamique Pour la Programmation Par Contrainteshttp://contraintes.inria.fr/OADymPPaC

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TMT, Generic Trace Development

1. Valid for several processes

2. Usable by several analysers

3. Easy to extend and to standardize

4. Generic trace: generic query language

5. Several levels of analysis (abstr/subtrace)

Objectives

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(Full) Actual Trace Twt = <s0,wt*>

Unbounded sequence of trace events wt (t > 0)

wt : (t, at)

•t : chrono: « time » of the trace

•at: set of attributes

or current full actual state

Interpretative Semantics (IS):

Tvt = I(Tw

t)

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(Full) Virtual Trace Tvt = <(s0,)et*>

Unbounded sequence of trace events(t > 0)

et: (t, rt, st)

•t: chrono: timestamps of the trace event

•rt: type of trace event: an identifier characterizing the type of action which produced the transition st-1 to st

rt belongs to a finite set R.

•st = p1,t..., pn,t : set of parameter values at chrono t. st is the current virtual state

Observational Semantics (OS):

Twt = E(Tv

t)

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The two traces of a process

•Virtual Trace TV = <S0,et*> OS

•Actual Trace TA = <S0,wt*> IS

TV

Tw

IE

E: extraction

I: interpretation (reconstruction)

E ° I = I ° E = i

Illustration

(Informal equations)

Condition to satisfy: (faithfulness)

Twt = E(Tv

t) et Tvt = I(Tw

t)

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Sémantique Observationnelle (“Labelled Transition System”)

SO: < S, R, E, T, S0 > où

• S ensemble des états virtuels,

• R est un ensemble fini de type d’évènements de trace

• T fonction de transition d’état T : R x S -> S

• E fonction d’extraction de l’événement de trace lors d’une transition E : R x S -> A

• S0 ensemble des états initiaux I S

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Sémantique Observationnelle (représentation)

Schéma de règle de transition:

TypeAction : {un identificateur r}

ActionCond : { Conditions d'exécution de l'action, portant sur l'état virtuel courant : une formule logique du premier ordre utilisant des prédicats sur les paramètres }

Extcond : { Conditions d'exécution de l'action faisant intervenir des variables externes à l'état (donc non décrite dans le modèle).

Sera dite condition externe ou influence}

VSEffect : { Effet de l'action r sur l'état courant s, résultant en un nouvel état s’ }

Etrace : { Trace produite par l'action r : l'état actuel extrait a}

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Idealized (biologically unrealistic) rabbit population (Fibonacci)

SO: < S, R, E, T, S0 >

< N*, {mg}, E, T, {[1,1]} >

st = [popu(0,…,popu(t),popu(t+1)], s0 = [1,1]

TypeAct : {Mg (monthly growing)}

ActionCd : {true}

Extcond : {true}

VSEffect : {s’= s [plast(s)+last(s)] } (T)

Etrace : {last(s’)} = w = E(r,s)

Tv5 = <[1,1],[(1,Mg,[1,1,2]), (2, Mg,[1,1,2,3]),…,

(4, Mg,[1,1,2,3,5,8]),(5, Mg,[1,1,2,3,5,8,13])]>

Tw5 = <[1,1],[(1,2),(2,3),(3,5),(4,8),(5,13)]>

I(Twt)= et =(t,Mg,[1,1,a1, a2,…, at-1, at])

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2. SFC (short introduction) and OS in SFC




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Fluent Calculus

M. Thielscher, Introduction to the fluent calculus,Electronic Transactions on Artificial Intelligence, 1998, pp 179--192, v 2, n 3-4, http://www.ep.liu.se/ej/etai/1998/006/

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FC interesting because…

• Easy expression of OS: the idea of trace is “naturally” contained in the notion of situation

• Logical proofs become simpler in the SFC (less deductions, at least for “direct closed” effects)

• A solution to the “frame problem” (persistence of unafected partial state)

• Symetry of “state axioms” allows forward and bakward reasonning (useful for proofs of faithfulness)

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Simple Fluent Calculus(Partial) state: set of fluents

Fluents

Actions

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Simple Fluent Calculus (ctd)

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OS in SFC As many pairs of axioms as there are action types

The actual trace is in the situation

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OS of Fibonacci in SFC

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Frame Problem

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CHRv semantics in SFC (vt)

Marcos Aurélio Almeida da Silva, CHORD: Constraint Handling Object-Oriented Rules with Disjunctions, Mestrado Thesis, Feb 2009

Gregory J.Duck, Peter Stuckey, Maria Garcia de la Banda, Christian Holzbaur, The refined Operational Semantics of CHR, In Proceedings of the 20th International Conference on Logic Programming (ICLP’04), pp 90-104, Saint-Malo, France, 2004, Springer Verlag

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Different semantics of CHR (t r vt v

r)

3 actions for CHR t semantics (th. Oper. Sem.) solve, introduce, apply

6 actions for CHR r semantics (refined. Oper. Sem.) solve, activate, reactivate, drop, simplify, propagate

3 actions for CHR vt semantics (th. Oper. Sem.)

derive, clean, split

8? actions for CHR vr semantics

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CHR semantics in SFC (t)6 parameters (virtual state)

Initial state:S0 = Goal(Q) o Udcs([])o InBics(true) o InPropHistory([]) o NextId(1)

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CHR semantics in SFC (t)

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CHR semantics in SFC (t) (ctd)

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3. CHR semantics in SFC (t)

4. OS of CHR in SFC (t)


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OS of CHR in SFC (t)6 parameters (virtual state)

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OS of CHR in SFC (t) (ctd)

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OS of CHR in SFC (t) (ctd)

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3. CHR semantics in SFC (t)

4. OS of CHR in SFC


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CONCLUSIONGT Development, next steps

1. CHRv refined operational semantics in SFC (vr): 8 basic

actions

2. Interpretative semantics (reconstruction function in SFC?)

3. Proof methods of OS/IS properties using SFC and Flux

4. Equivalente specification in OOSFC (Object Oriented SFC) using the platform CHROME-REF

5. Implementation in Java and tests

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TMT for CHR v in SFC

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