On the Expressiveness of Infinite Behavior and Name Scoping in - PowerPoint PPT Presentation

On the Expressiveness of Infinite Behavior and Name Scoping in Process Calculi Pablo Giambiagi (KTH, Sweden) Gerardo Schneider (IRISA/INRIA) Speaker: Frank D. Valencia (Uppsala Univ., Sweden) FOSSACS’04, Barcelona, March 2004 FOSSACS’04: Inf. Behaviour and Scoping – p.1/34

Motivation: Process Calculi CCS is an important representative of process calculi FOSSACS’04: Inf. Behaviour and Scoping – p.2/34

Motivation: Process Calculi CCS is an important representative of process calculi : Simplicity of its definition and techniques, Applicability to synchr. communication. Foundational ideas grown out from it. FOSSACS’04: Inf. Behaviour and Scoping – p.2/34

Motivation: Process Calculi CCS is an important representative of process calculi : Simplicity of its definition and techniques, Applicability to synchr. communication. Foundational ideas grown out from it. This talk: CCS Variants wrt infinite behavior and name scoping . Variants exhibits interesting connections wrt Relative Expressiveness . Verification . FOSSACS’04: Inf. Behaviour and Scoping – p.2/34

Motivation: Process Calculi CCS is an important representative of process calculi : Simplicity of its definition and techniques, Applicability to synchr. communication. Foundational ideas grown out from it. This talk: CCS Variants wrt infinite behavior and name scoping . Variants exhibits interesting connections wrt Relative Expressiveness . Verification . FOSSACS’04: Inf. Behaviour and Scoping – p.2/34

✞ ☎ ☛ ☎ ✡ ✠ ✟ ✟ ✁ ✝ ✠ ☎ � ✆ ☎ ✡ ☎ ☎ ☛ � � Motivation: Scoping Variants Consider CCS construct with rule: ✁✄✂ ✁✄✂ REC ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.3/34

✡ ✝ ✠ � ☛ ☎ ✡ ✠ ✟ ✞ ✁ ☎ ✟ ☎ � ✆ ☎ ☛ ✞ ☎ ✂ � ☎ Motivation: Scoping Variants Consider CCS construct with rule: ✁✄✂ ✁✄✂ REC ✁✄✂ Does ✆ ✁� involve name -conversion ? FOSSACS’04: Inf. Behaviour and Scoping – p.3/34

☎ ✝ ✠ � ☛ ✡ ✡ ✠ ✟ ✞ ✁ ☎ ✟ ☎ � ✆ ☎ ☛ ✞ ☎ ✂ � ☎ Motivation: Scoping Variants Consider CCS construct with rule: ✁✄✂ ✁✄✂ REC ✁✄✂ Does ✆ ✁� involve name -conversion ? Name Scoping: If yes, Static else Dynamic . FOSSACS’04: Inf. Behaviour and Scoping – p.3/34

� ✁ ☎ ✡ ☎ ☛ ☎ ✡ ✠ ✟ ✞ ✝ ✠ ☎ ☛ � ✆ ☎ ✞ ✂ ☎ ✂ � ✟ Motivation: Scoping Variants Consider CCS construct with rule: ✁✄✂ ✁✄✂ REC ✁✄✂ Does ✆ ✁� involve name -conversion ? Name Scoping: If yes, Static else Dynamic . This affects not only semantics (e.g., -equivalence), also expressiveness and verification. FOSSACS’04: Inf. Behaviour and Scoping – p.3/34

✂ ✂ ✂ ✂ ☞ ✌ ✁ � ☎ ✞ ✆ ☎ ☎ � ✆ ☎ ✡ Motivation: Infinite Behaviour Ways of specifying infinite behaviour in process calculi: Parametric vs. Constant definitions ✁✄✂ 1. Finitely many constants 2. Finitely many definitions ✝✟✞ ✠☛✡ FOSSACS’04: Inf. Behaviour and Scoping – p.4/34

✂ ✂ ✂ ☞ ✂ ✌ ✁ � ☎ ✞ ✆ ☎ ☎ � ✆ ☎ ✡ Motivation: Infinite Behaviour Ways of specifying infinite behaviour in process calculi: Parametric vs. Constant definitions ✁✄✂ 1. Finitely many constants 2. Finitely many definitions ✝✟✞ ✠☛✡ Can we encode (2) into (1) ? (Without Relabelling or Infinite Sums). FOSSACS’04: Inf. Behaviour and Scoping – p.4/34

✂ ✂ ☞ ✂ ✂ ✌ ✁ � ☎ ✞ ✆ ☎ ☎ � ✆ ☎ ✡ Motivation: Infinite Behaviour Ways of specifying infinite behaviour in process calculi: Parametric vs. Constant definitions ✁✄✂ 1. Finitely many constants 2. Finitely many definitions ✝✟✞ ✠☛✡ Can we encode (2) into (1) ? (Without Relabelling or Infinite Sums). What about other constructions: Replication or Recursive Expressions ? FOSSACS’04: Inf. Behaviour and Scoping – p.4/34

✞ � ✡ ✂ ✂ ✂ ✁ ✂ ☎ ☞ ☎ ✆ ☎ ✆ � ☎ � ✌ Motivation: Infinite Behaviour Ways of specifying infinite behaviour in process calculi: Parametric vs. Constant definitions ✁✄✂ 1. Finitely many constants 2. Finitely many definitions ✝✟✞ ✠☛✡ Can we encode (2) into (1) ? (Without Relabelling or Infinite Sums). What about other constructions: Replication or Recursive Expressions ? In -calculus all forms coincide. What about less expressive cal- culi?. FOSSACS’04: Inf. Behaviour and Scoping – p.4/34

Motivation and Contributions We discuss: Static vs Dynamic Scoping. Parametric vs. Constant definitions. Recursion vs Replication. FOSSACS’04: Inf. Behaviour and Scoping – p.5/34

Motivation and Contributions We discuss: Static vs Dynamic Scoping. Parametric vs. Constant definitions. Recursion vs Replication. ...and show that these issues affect Expressiveness Decidability of Divergency. FOSSACS’04: Inf. Behaviour and Scoping – p.5/34

Overview The finite core Static vs Dynamic scoping Infinite behaviour Expressiveness Concluding Remarks FOSSACS’04: Inf. Behaviour and Scoping – p.6/34

Overview The finite core Static vs Dynamic scoping Infinite behaviour Expressiveness Concluding Remarks FOSSACS’04: Inf. Behaviour and Scoping – p.6/34

✆ ✆ ✂ ✂ ✂ ✡ ✞ ✡ ✂ ✆ ✝ ✄ � ☞ � ☎ ☞ ☛ ✂ ✄ ✂ ✂ ✂ ✡ ✂ ✡ ✞ ✡ ✁ ✡ � ✝ ✄ The Finite Core: Syntax Given: A set of names A set of co-names A set of actions ✟✡✠ ☎✍✌ FOSSACS’04: Inf. Behaviour and Scoping – p.7/34

✂ ✝ ✡ ✂ ✆ ✂ ✄ � ☛ ✆ ☞ ☞ ✝ ✡ ☎ ✆ � ✆ ✂ ✄ ☎ ✂ ✂ ✂ ✞ ✂ ✂ ✂ ☎ � ✡ ✁ ✡ ✞ ✡ ✂ ✡ ✂ ✂ ☎ ✄ ✂ ✞ ✆ ☎ � ✆ � ✄ ✝ ☎ The Finite Core: Syntax Given: A set of names A set of co-names A set of actions ✟✡✠ ☎✍✌ Processes specifying finite behaviour: ☎ ✁� FOSSACS’04: Inf. Behaviour and Scoping – p.7/34

☎ ✞ ☛ ✞ ✡ ✠ � ✞ ✟ ✠ ✞ ☛ ✞ ☎ ✡ ✠ � ✞ ✞ ✡ ☛ ☎ ☎ ✞ ✠ ✡ ☎ ☛ ✞ ✡ ✠ ✠ ✞ ☛ ☎ ✠ � ✠ ☎ ✡ ☛ ✞ ✞ ☎ ✡ ✠ ✡ � ✞ ✠ � ☎ ✞ ✆ ✄ ☎ ✞ ☛ ✡ ✁ ✡ � ✂ ☎ ✂ ✂ ✂ ☎ ✄ ✂ ✠ ☎ ☎ ✂ ✠ ☎ ✝ � ✡ � ☎ ✄ ✝ ☛ ☛ � ✝ ☛ ☎ ✡ ✠ � � ✝ ☎ ✞ FOSSACS’04: Inf. Behaviour and Scoping – p.8/34 if The Finite Core: Semantics RES PAR if ☎ ✄✂ COM SUM PAR

Overview of the presentation The finite core Static vs Dynamic scoping Infinite behaviour Expressiveness Concluding Remarks FOSSACS’04: Inf. Behaviour and Scoping – p.9/34

✝ ✁ � � ☎ ✝ ☎ ✆ � ✞ ✌ � ✂ ✁ ✞ Scoping: Example Consider with ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

� ✝ ✡ ☎ ✆ ✠ � ☎ ✁ � ✞ � ✠ ✡ ☎ ☛ ☎ ✝ ☎ � � ✂ ☎ ☛ ☎ ✆ ✞ ✌ ✝ � ✂ ✁ ✞ ✁ � Scoping: Example Consider with ✁✄✂ Consider the following rule: ✁✄✂ REC ✁✄✂ -conversion . without name FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

✆ ✁ ☎ ☎ � � ☎ ✝ ✞ � ✆ � ✞ ✝ � ✂ ✌ ✝ ✞ � � � ☎ ✝ ☎ ✆ ✞ ✌ ✝ � ✂ ✁ ✞ ✁ ✁ Scoping: Example Consider with ✁✄✂ Then, for the unfolding ✁✄✂ ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

✁ ✝ ✂ � ✞ � ✝ ☎ ✌ ✝ � ✆ � ✞ � ✝ ✂ ✁ ✞ � ✌ ✝ � ✞ ✝ � ✂ ✁ � ✞ ✁ ✞ � � ☎ ✝ ☎ ✆ � ✞ ✝ � ✂ ✁ ✁ � ✌ ✝ � ✌ ☎ ✆ � ✌ ☎ ✝ ✁ ✞ ✆ ✞ Scoping: Example Consider with ✁✄✂ Then, for the unfolding ✁✄✂ ✁✄✂ ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

✁ ✝ ✂ � ✞ � ✝ ☎ ✌ ✝ � ✆ � ✞ � ✝ ✂ ✁ ✞ � ✌ ✝ � ✞ ✝ � ✂ ✁ � ✞ ✁ ✞ � � ☎ ✝ ☎ ✆ � ✞ ✝ � ✂ ✁ ✁ � ✌ ✝ � ✌ ☎ ✆ � ✌ ☎ ✝ ✁ ✞ ✆ ✞ Scoping: Example Consider with ✁✄✂ Then, for the unfolding ✁✄✂ ✁✄✂ ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

� ✝ ✂ ✁ ✞ ✌ � ☎ ✌ ✝ � ✆ � ✞ � ✝ ✂ ✁ ✞ � ✝ ✝ � ✞ ✝ � ✂ ✁ ✞ � ✞ ✌ ✞ � ✁ ☎ � ☎ ✆ � ✞ ✝ � ✂ ✁ ✁ � ✌ ✝ � ✝ ☎ ✆ � ✌ ☎ ✝ ✁ ✞ ✆ ✁ Scoping: Example Consider with ✁✄✂ Then, for the unfolding ✁✄✂ ✁✄✂ ✁✄✂ Then may be executed. FOSSACS’04: Inf. Behaviour and Scoping – p.10/34

✝ ✁ � � ☎ ✝ ☎ ✆ � ✞ ✌ � ✂ ✁ ✞ Scoping: Example 2 Consider again with ✁✄✂ FOSSACS’04: Inf. Behaviour and Scoping – p.11/34