New insights on architectural connectors

1
New insights on architectural connectors
IFIP TCS 2004, Toulouse, 22-27 August 2004
Ivan Lanese Computer Science Department
University of Pisa
joint work with Roberto Bruni University of
Pisa, Italy Ugo Montanari University of
Pisa, Italy José Luiz Fiadeiro University of
Leicester, UK Antónia Lopes University of
Lisbon, Portugal
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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

3
Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

4
General motivation I

• Comparing the categorical and the algebraic
  approach to systems
• Categorical approach
• Algebraic approach

5
General motivation II

• Comparing the categorical and the algebraic
  approach to systems
• Categorical approach
• objects are system components
• morphisms express simulation, refinement,
• complex systems are modeled as diagrams
• composition via universal construction (colimit)
• Algebraic approach

6
General motivation III

• Comparing the categorical and the algebraic
  approach to systems
• Categorical approach
• Algebraic approach
• System represented by an algebra
• constants are basic components
• operations compose smaller systems into larger
  ones
• structural axioms collapse structurally
  equivalent systems
• operational semantics (SOS style)
• abstract semantics (bisimilarity)

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Specific aim

• Reconcile two selected representatives
• CommUnity (categorical)
• architectural description language
• distinction between computation and coordination
• Tile model (algebraic)
• operational model for concurrent systems
• co-existence of horizontal (space) and vertical
  (time) dimensions

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Specific aim advantages

• Advantage transfer of concepts and techniques
• Semantic model for CommUnity
• Observational equivalence of CommUnity
  configurations
• CommUnity-like connectors in the tile model
• Separation between computation and coordination
  for tiles

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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

10
CommUnity

• System configurations are diagrams
• Components compute locally
• Interactions as architectural connectors

Denotational semantics
Program
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CommUnity programs
design foo is in x, z out v, n do a true ?
v xz nvx b ngtMIN ? nn-x c
vltMAX ? vnz
input/output channels
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Morphisms
output channels cannot be merged
P1
channels of P1 to channels of P2
(names are not important)
actions of P2 to actions of P1
actions of P1 correspond to disjoint sets of
actions of P2
P2
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Example
design P1 is in out do a b
design P is in out do fap faq
far gap gaq gar
hbs
f,g ? a ? p,q,r h ? b ? s
design P2 is in out do f g h
design P3 is in out do p q r
s
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Star-shaped diagrams
glue
cables no output channels actions are true? skip
roles
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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

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Tile model

• Operational and abstract semantics of open
  concurrent systems
• Compositional in space and time
• Deals uniformly with closed and open systems
• Congruence results for particular formats
• Category based but compositionality dealt with
  algebraic methods

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Configurations
output interface
input interface
(interfaces can be typed)
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Configurations
output interface
input interface
parallel composition
symmetries
sequential composition
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Observations
initial interface
final interface
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Tiles

• Combine horizontal and vertical structures
  through interfaces

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Tiles

• Compose tiles
• horizontally

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Tiles

• Compose tiles
• horizontally
• (also vertically and in parallel)

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Operational semantics

• Structural equivalence
• Axioms on configurations (e.g. symmetries)
• LTS
• states configurations
• transitions tiles
• labels (trigger,effect) pairs

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Abstract semantics

• Tile bisimilarity
• Standard bisimilarity applied to previous
  transition system
• Systems are bisimilar iff they can mutually
  simulate transitions
• More powerful than trace equivalence

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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

26
Standard decomposition

• The decomposition of a program is a star-shaped
  diagram
• It highlights the algebraic structure of
  CommUnity programs
• It is the first step of the translation into the
  tile model

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Standard decomposition illustrated

• n output channels
• m actions

P

• n channel managers
• m guard managers
• nm cables
• 1 glue

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Elements of the decomposition

• Glue
• Channel managers
• Guard managers
• Cables
• Morphisms

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Elements of the decomposition

• Glue
• all the channels as input channels
• all the actions as true ? skip
• Channel managers
• Guard managers
• Cables
• Morphisms

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Elements of the decomposition

• Glue
• Channel managers
• one for each output channel
• the assignments to that channel as actions
• the input channels needed to evaluate the
  assignments
• Guard managers
• Cables
• Morphisms

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Elements of the decomposition

• Glue
• Channel managers
• Guard managers
• one for each guard
• one action of the form pred ? skip
• the input channels needed to evaluate the guard
• Cables
• Morphisms

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Elements of the decomposition

• Glue
• Channel managers
• Guard managers
• Cables
• all the channels needed by the role, as input
  channels
• all the actions needed by the role, as true ?
  skip
• Morphisms

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Elements of the decomposition

• Glue
• Channel managers
• Guard managers
• Cables
• Morphisms
• maps the actions and channels of the cables to
  the corresponding ones in the glue and in the
  roles

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Properties of the decomposition

• Correctness
• the colimit of the decomposed program is equal to
  the starting program
• Possible generalization
• a diagram can be decomposed by decomposing each
  role
• morphisms entering a program become morphisms
  entering the glue

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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

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What we need

• We have to define a tile logic from a CommUnity
  program
• We need to define
• objects
• configurations
• observations
• tiles
• to specify the behavior

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Objects

• channels
• with a type and a modality (input/output)
• special boolean objects
• for the evaluation of guards
• synchronization objects
• representing actions

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Structure of a configuration
State
Role or glue
Channel fusion
Action synchro nization
Role or glue


Role or glue
Anchored configuration
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Structure of a configuration
State
Role or glue
Channel fusion
Action synchro nization
Role or glue


Role or glue
Unanchored configuration
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How to build a configuration

• We translate roles and glues
• We build the system using the parallel
  composition through one cable operation
• this allows to build the whole system thanks to
  the property of the decomposition
• we fix an order on cables for translating them
• the operation adds the channel fusion and action
  synchronization parts
• Eventually we add the state

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Constructors for roles and state
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Channel connectors
b
i
o
b
o
b
i
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Action synchronization connectors
1
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Translating the glue
i
i
i
1
i
i
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Parallel composition through one cable

• Channel part channels in the image of the same
  channel of the cable are merged using channel
  connectors
• Action part we have to synchronize in all the
  possible ways the actions of the two groups
  mapped to each action of the cable

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Synchronizing actions
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Observations

• For the action part
• tick (action performed) or
• untick (action forbidden)
• For the channel part terms assigning
• to each output variable its data term
• to each special boolean object a predicate
• to each input variable a term, standing for a
  guess on the actual value

a
r
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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• channel connectors
• channel managers
• guard managers
• action synchronization connectors

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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• update the values with the assignments and check
  the validity of predicates
• channel connectors
• channel managers
• guard managers
• action synchronization connectors

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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• channel connectors
• apply consistent substitutions to data terms
• channel managers
• guard managers
• action synchronization connectors

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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• channel connectors
• channel managers
• produce the assignments to the left and a tick on
  the performed action to the right
• guard managers
• action synchronization connectors

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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• channel connectors
• channel managers
• guard managers
• produce the predicate to the left and a tick to
  the right
• action synchronization connectors

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Tiles

• Specify the semantics of each part of the
  configuration
• Tiles for
• state
• channel connectors
• channel managers
• guard managers
• action synchronization connectors
• select the allowed combinations of tick and
  untick in the interfaces

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Tiles for mutual exclusion
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Tile for channel fusion
i
i
b
b
b
o
o
y1x2gt3 and x3lt4 and x1 y2x21
y1x2lt4 and x1
y1x2gt3 and x1 y2x21
2
1
1
2
2
3
1
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Tile for channel manager
i
cm ltx2x2x1, x2x2-x1gt
o
b
x2x2x1 x3true
a
r
i
cm ltx2x2x1, x2x2-x1gt
o
b
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Notation

• dia CommUnity diagram
• DS(dia) standard decomposition of dia
• TS(dia,) tile configuration for dia where
  cables have been translated in the order
  specified by , without state
• TS(dia,,val) as before, but with state with
  values val

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Properties of the encoding I

• TS(dia,,val) initial configuration of a tile ? ?
  val. TS(dia,,val) is the final configuration
• Such a tile (with empty observation) exists iff
  there exists a computation of colim(dia) with
  starting state val and final state val

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Properties of the encoding II

• To deal with tiles without state we need a
  permutation ? to rearrange the interface
• Bisimilarity results
• TS(dia,,val) TS(dia,,val) for each ,
• TS(dia,) ?TS(dia,) for each ,
• TS(dia,,val) TS(colim(dia),,val)
• TS(dia,) ?TS(colim(dia),,val)

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Roadmap

• Goal
• Background CommUnity
• Background tile logic
• Standard decomposition for CommUnity
• From CommUnity to tiles
• Conclusion and future work

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Algebraic vs categorical

• Algebraic Categorical
• Basic constructors Objects
• Aux. constructors Morphisms
• Representative Colimit
• up to equivalence
• Operat. semantics ?
• ? Architectural aspects

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Future work

• Further analyze the correspondence
• axiomatize connectors to have a correspondence
  between normal form and colimit
• Deal with other aspects of CommUnity
• localities
• mobility
• dynamic reconfiguration
• Mutual transfer of concepts and techniques
  between the two approaches
• Apply the approach to other formalisms

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Thanks
Questions?