Towards Overcoming Deficiencies in Constraint Diagrams

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Towards Overcoming Deficiencies in Constraint
Diagrams

• Gem Stapleton and Aidan Delaney
• Supported by the Leverhulme Trust and the EPSRC

www.cmis.brighton.ac.uk/research/vmg
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Background

• Formal specification
• Safety critical
• Invariants
• Operation contracts
• UML -gt OCL
• Constraint diagrams (Kent, 1997)

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Background

• Invariant Members can only borrow Films from the
  collections of Stores that they have joined

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Background

• Gurr and Tourlas, Towards the Principled Design
  of Software Engineering Diagrams, 2000
• Studies have indicated that the most effective
  representations are those which are well-matched
  to what they represent
• Q Are constraint diagrams an effective
  representation?

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Well-Matchedness and Reasoning

• Well-matched
• Mirroring of semantic properties
• Accuracy of interpretation
• Ease with which constraint enforced
• Reasoning
• About the model
• Determining an implementation
• Proof of correctness

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Contributions

• Partly well-matched
• Expose counter-intuitive features
• Reading
• Writing
• Reasoning
• Propose generalized constraint diagrams
• Discuss design philosophy

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Overview of Constraint Diagrams
universal spider
zones minimal regions arrows contours given
vs derived
habitat
domain
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Overview of Constraint Diagrams
reading tree
existential spiders
shading
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Overview of Constraint Diagrams
There is a film, p, of which every store, q, has
two copies, r and s.
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Overview of Constraint Diagrams

• Multiple reading trees

valid
invalid
A tree is valid if it allows us to make
statements relating elements when the diagram
requires it
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Summary of syntax

• Euler diagrams
• Existential spiders
• Universal spiders
• Shading
• Arrows
• Derived contours
• Reading trees (directed)
• Formalized by Fish et al, JVLC 2005

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Well-matched features

• Euler diagrams
• Mirror subset and disjointness relations

Euler diagrams
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Well-matched features

• Spiders
• Mirror set membership by containment
• Mirror distinctness by distinctness

Spider diagram
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Well-matched features

• Shading
• nothing else is present -- fills out region

Spider diagram
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Well-matched features

• Shading
• nothing else is present -- fills out region

Enables exploitation of desirable properties
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Well-matched features

• Arrows
• Mirrors a is related to b by having source a
  and target b

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Well-matched features

• Derived contours
• Similar to Euler diagrams

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Well-matched features

• Reading trees
• Indicate quantifier order using directed edges

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Well-Matchedness and Reasoning

• Well-matched
• Mirroring of semantic properties
• Accuracy of interpretation
• Ease with which constraint enforced
• Reasoning
• About the model

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Reading constraints

• Habitat differs from domain
• Unhelpful symmetry

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Reading constraints

• Shading inside quantification
• Inexplicit reading order

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Reading constraints

• Fish and Masthoff (VLHCC 05)
• Start at left most spider
• Prioritise domain habitat
• Follow arrows

This diagram violates all these preferences
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Reading constraints summary

• Decipher spider domain
• Inexplicit reading order of some syntax
• Reading order has profound impact on semantics
• Illustrates lack of modularity
• Empirical evidence suggests some diagrams are not
  intuitive

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Writing constraints

• Expressiveness limitations
• First order language
• Distinctness of elements
• Disjunction issues involving binary relations

How do we express Every film has a lead actor
or no actors
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Writing constraints
How do we express Every film has a lead actor
or no actors Attempt
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Writing constraints
How do we express There is a film that has a
lead actor and a director Attempt 1
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Writing constraints
How do we express There is a film that has a
lead actor and a director Attempt 2
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Reasoning

• Conjunction vs disjunction

and
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Reasoning

• Conjunction vs disjunction

or
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Observations

• Individual pieces of syntax well-matched
• Reading constraints variety of problems
• Writing constraints expressiveness limits
• Reasoning discrepancy, non-intuitiveness
• Q Can we improve the notation to overcome the
  deficiencies?

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Generalized Constraint Diagrams

• Design principles
• Well-matched syntax mirrors semantics
• Explicit information ease of meaning extraction
• Consistency syntax has fixed meaning
• Expressiveness naturalness of assertion
• Simple construction rules wfd
• Considered impact on reasoning

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Generalized Constraint Diagrams

• Utilize existing syntactic components
• Remove need for reading tree
• View a diagram as a partial order
• Extends building sequence (Fish et al)

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Generalized Constraint Diagrams

• Partial orders

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Generalized Constraint Diagrams

• Fixing habitat not equal to domain

Every member can borrow a set of films
and every one of those films is available to
that member
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Generalized Constraint Diagrams

• Fixing shading in scope and explicit quantifier
  ordering

Every film has a set of lead actors
and there is exactly one actor
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Generalized Constraint Diagrams

• Fixing for all and or issues

has a lead actor
Every film
OR
has no actors
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Generalized Constraint Diagrams

• Not enforcing distinctness

can borrow a film
There is a member that
AND
has borrowed a film
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Conclusion

• Constraint diagrams have good aspects
• Constraint diagrams have deficiencies
• Proposed generalization
• Next steps
• Formalize syntax and semantics
• Conjecture expressiveness increased
• Fully explore well-matchedness
• Investigate second-order extension

www.cmis.brighton.ac.uk/research/vmg
39

• September 19 21, 2008
• Herrsching, Germany
• www.cmis.brighton.ac.uk/diagrams2008

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Reasoning

• Adding zones

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Generalized Constraint Diagrams

• Fixing reasoning with zones

New syntax forces scoping