Designing Constraint Maintainers for User Interaction

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Designing Constraint Maintainersfor User
Interaction

• Lambert Meertens
• Kestrel Institute, Palo Alto, CA
• Utrecht University

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Examples of Maintained Constraints 1

• Spreadsheet
• Constraints
• Cost Qty Item Cost
• Total Cost SUM Cost

Qty Item Cost Cost 2 12.99 25.98 3
6.35 19.05 -----
45.03
Qty Item Cost Cost 2 12.99 25.98 33
6.35 209.55 ------
235.53
edit
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Examples of Maintained Constraints 2

• UNIX make
• Constraints
• .dvi .tex .bib
• latex
• bibtex
• latex (unidirectional )

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Examples of Maintained Constraints 3

• Rename file
• Constraint
• prez.name prez.file.name
• 
  (bidirectional!)

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Maintained Constraints General Case

• A constraint is a relation between objects
• Structured documents
• Presentations are also structured documents
• External agents (user editing, mail delivery,
  clock) may change the value of some object
• A value change may violate a constraint
• A violated constraint must be restored by
  changing the value of some other linked object
• If that is not possible, the original change was
  unlawful

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Issue At Most Constraint

• Physical embodiment
• For any given value of A, there are many values B
  such that A ? B
• Which one to choose?

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Designing Constraint Maintainers

• Constraints operate like the Laws of Physics of a
  virtual universe
• For a constraint-driven system to be usable, it
  must behave in a predictable way
• The way in which constraints are restored must
  follow from simple principles
• Potential bonus automatic derivation for
  declaratively specified constraints

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Semi-Maintainers

• We define a (unidirectional) semi-maintainer a
  (bidirectional) maintainer is then just a pair of
  semi-maintainers, one for each direction
• For now, ignore unlawful changes and constraints
  involving more than two objects
• Call the object that was changed by an external
  agent the source, and the linked object is target
• The semi-maintainer knows the new value of the
  source and the old value of the target

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Definition of Semi-Maintainer

• For a relation R S T, a semi-maintainer is a
  function
• ? S?T ? T
• satisfying, for all x S and y T,
• (EST) x R (x ? y)
• (SKIP) x R y ? x ? y ? y
• EST states that after an update x ? x ? y the
  constraint x R y holds
• SKIP states that an update x ? x ? y has no
  effect if the constraint x R y already holds

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The Principle of Least Change

• Dont make a larger change than is needed
• to restore the constraint

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In Symbols

• From the EST requirement x R (x ? y) we have
  that x ? y is an element of the set
• F(x) ?def y' x R y'
• The Principle of Least Change means that among
  all elements y' ? F(x) we pick one as close as
  possible to the old value y of the target
• Note that the SKIP requirement
• x R y ? x ? y ? y
• is a special case of PLC when y ? F(x)

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Distance

• To give meaning to as close as possible we need
  to define a metric on each type of interest
• For numeric types this is obvious
• For structured types in general, the edit
  distance is a reasonable choice
• For sets, we can take the size of the symmetric
  set difference
• s ? t ?def (s t ) U (t s)

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Example Is Subset Of Constraint

• Relation ? Set(a) Set(a)
• We want to determine t' ? s ? t
• Put d ? t ? t' , so that t' ? t ? d
• EST is then s ? t ? d
• The smallest solution of EST is d ? s t
• This gives us
• s ? t ? t' ? t ? d ? t ? (s t ) ? s U
  t

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Tie Breaking

• What if there are several solutions of EST that
  are all as close as possible to the old value
  of the target?
• Suggested approach
• for each type of interest, define a well-ordering
  (i.e., a total linear ordering such that each
  non-empty set has a least element)
• using as ordering principles that small comes
  before large, left before right and positive
  before negative
• and pick the least allowed element

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Example Converse Abs Constraint

• Relation abs? Z N , where
• n ?abs?? i ?? abs ( i ) ? n
• We want to determine i' ? n ? i
• The possible values are n, n
• Normally one is closer to i than the other, but
  if i 0 while n ? 0 there is a tie
• Positive before negative in that case pick
• i' ? n

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Further Reading

• Steven Pemberton. The VIEWS Application
  Environment. CWI Report CS-R9257, 1992.
  http//www.cwi.nl/ftp/CWIreports/AA/CS-R9257.pdf
• Lambert Meertens, Steven Pemberton. The
  Ergonomics of Computer Interfaces ? Designing a
  System for Human Use. CWI Report CS-R9258, 1992.
  http//www.cwi.nl/ftp/CWIreports/AA/CS-R9258.pdf
• Lambert Meertens. Designing Constraint
  Maintainers for User Interaction.
  http//www.kestrel.edu/home/people/meertens/dcm.ps