1 deransart, ducassé, ferrand wlpe 20071 observational semantics of the prolog resolution box model...

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Observational Semantics of the Prolog Resolution

Box Model

Pierre Deransart, Mireille Ducassé, Gérard FerrandINRIA-Rocquencourt, IRISA-Rennes, LIFO-Orléans13 September 2007WLPE’07

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LoriaPissaro, 1871

Sophia Antipolis

Irisa

Rhône-Alpes

Futurs

Research Centers

Rocquencourt, 2007

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ICLP 2005, St Malo

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JFPLC 97, Orléans

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Prolog Box Model by Lawrence Byrd, 1980

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Prolog Box Model, latter

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CONTEXT, HISTORYFrom DiSCiPl to OADymPPaC

•DiSCiPl (1997-2000): enhance constraint debugging: resulted in prototypes, but still ad-hoc tools for correctness and performance analysis, but also showed usefulness of “visual traces”.

Book: P. Deransart and M. Hermenegildo and J. Maluszynski, Analysis and Visualization Tools for Constraint Programming, LNCS 1870, 2000

•OADymPPaC (2001-2004) URL: http://contraintes.inria.fr/OADymPPaC participants: A. Aggoun, T. Baudel, P. Deransart, M. Ducassé, F.Fages, J.D. Fekete, N. Jussien, C. de Sainte-Marie, …

main solved challenges:• Interoperability of tools: splitting: “trace” and “visualization”

• Scaling: possibility to handle hundreds of variables and constraints ----> use of specialized HMI

Resulted in powerful analyzers (prototypes and products), but worked on one domain and raised some problems

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GENERICITY and INTEROPERABILITY PRINCIPLES

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NEW PROBLEMS

OADymPPaC identified some bottlenecks:

•Trace Semantics (related to its genericity): what is the exact nature of the “Observational Semantics”

•Modeling of the Interactions between Observed Process and Analysis Tools

•How to keep the whole system efficient (need to evaluate efficiency)

•Is the approach generic itself? Can it be applied to new domains: software engineering, data stream analysis, cognition

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Ways to ANSWER to the PROBLEMS

•*Trace Semantics (related to its genericity): what is the exact nature of the “Observational Semantics”: model of trace for a family of processes

•Modeling of the Interactions between Observed Process and Analysis Tools: Introduction of Tracer Driver and Analyzer Manager

•How to keep the whole system efficient (need to evaluate efficiency): Concepts of Virtual full Trace, Actual incremental Trace extraction and rebuilding

•*Is the approach generic itself? Can it be applied to new domains (not just constraints) in particular in software engineering can the approach (full trace with partial OS, interactive tracer driver) be applied in new domains

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ORGANISATION

•History

•The meaning of traces

•Different traces (virtual and actual)

•Observational semantics of the box model

•Actual trace extraction

•Virtual trace rebuilding

•Conclusions

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What does it mean?

1 1 Call goal

2 2 Call p(X)

2 2 Exit p(a)

3 2 Call eq(a,b)

3 2 Fail eq(a,b)

2 2 Redo p(a)

2 2 Exit p(b)

4 2 Call eq(b,b)

4 2 Exit eq(b,b)

1 1 Exit goal

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And this?

1 Call

2 Call

2 Exit

3 Call

3 Fail

2 Redo

2 Exit

4 Call

4 Exit

1 Exit

??

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Easier?

1 Call

2 Call

2 Exit

3 Call

3 Fail

2 Redo

2 Exit

4 Call

4 Exit

1 Exit

??

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A two stages understanding

1. Finding relevant concepts and relations whose evolution is coded in the trace (Trace Interpretation)

2. Relating these concepts with some real or hypothetic process from which the trace is or may be originated.(Observational Semantics)

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FULL VIRTUAL TRACE

unbounded sequence of trace events of the form

et: (t, at, St+1)

•et: unique identifier of the event

•t: chrono. Time of the trace

•at: kind of event, an identifier characterizing the kind of actions from which the process changed from St to St+1.

at belongs to a finite set R.

•St = p1,t..., pn,t : values of parameters at chrono t. St is the current full virtual state

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ACTUAL TRACE

unbounded sequence of trace events wt of the form

e’t : (t, At)

•e’t: unique identifier of the event

•t: chrono. Time of the trace

•At = set of attribute values

Extraction function: At = E(St,St+1). (Trace Schema)

Rebuilding function: Qt = C(wt*,Q0).

Q0 restriction of S0 (Trace interpretation)

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Full Virtual Trace: evolution of a full virtual state

Full Virtual State

Initial State: S0

{ {goalcl-listtrfafa

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Virtual Trace: Observational Semantics

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And actual trace extraction:

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Example

goal:-p(X),eq(X,b).

p(a).

p(b).

eq(X,X).

chrono nu(u) lp(u) port pd(u) Reached virtual state

1 1 1 Call goal S2

2 2 2 Call p(X) S3

3 2 2 Exit p(a) S4

4 3 2 Call eq(a,b) S5

5 3 2 Fail eq(a,b) S6

6 2 2 Redo p(a) S7

7 2 2 Exit p(b) S8

8 4 2 Call eq(b,b) S9

9 4 2 Exit eq(b,b) S10

10 1 1 Exit goal S11

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Actual state reconstruction

Full virtual state: S

Actual state Q

Initial state: S0

Initial rebuilt state: Q0 = S0/Q (restriction of S to Q )

{ {goalcl-listtrfafa

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Interpretation Schema (rebuilding)

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Faithfulness

We develop methods to prove faithfulness

C is a faithful trace interpretation w.r.t. the OS and E, if for all actual trace Tw = <Q0,wt*>, t >=0, Q0 = S0/Q

for all i in [0…t-1] , there exists Si+1 such that

Ai = E(Si,Si+1) and C(wt*,Q0)= Si/Q

(Ai attributes of wi)

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CONCLUSIONS

•We may see

• the trace interpretation as the proper semantics of a trace

• the observational semantics as a semantics of the virtual trace

•Faithfulness guarantees that both combine well, and that traces are completely understood (interpretation and production)

•Ongoing work: definition of a virtual trace for CHR

•About the Prolog trace model:

• Our semantics allows trace reading at several levels of comprehensibility

• It is a model of Prolog tracers (not of Prolog, not unique)

• The Byrd’s box model is simple, beautiful, but incomplete, unsatisfactory, etc…but this all of you know very well

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Thank you!

P. Deransart, M. Ducassé, G. FerrandObservational Semantics of the Prolog Resolution

Box Model May 2007(comprehensive version, in French)INRIA, RR 6229http://hal.inria.fr/inria-00151285