PSD 2005 ‒ 1

Designing Constraint Maintainersfor User Interaction

Lambert Meertens

Kestrel Institute, Palo Alto, CA&

Utrecht University

PSD 2005 ‒ 2

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 ------ 235.53edit

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Examples of Maintained Constraints – 2

• UNIX’ make

Constraints:– %.dvi: %.tex *.bib latex $* bibtex $* latex $* (unidirectional )

edit

@book{AristoCat,author = ”Aristotle”,title = ”Category”,

[5] Aristotle. Category. Athens Academic Press. 350 BCE.

@book{AristoCat,author = ”Aristotle”,title = ”Categories”,

[5] Aristotle. Categories. Athens Academic Press. 350 BCE.

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Examples of Maintained Constraints – 3• Rename file

Constraint:– prez.name = prez.file.name (bidirectional!)

edit

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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

: ST Tsatisfying, 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

PSD 2005 ‒ 10

The Principle of Least Change

Don’t make a larger change than is neededto restore the constraint

2.5

3.5

A

B

5.0

5.0

A

B

edit

2.5

5.0

A

B

edit

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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 requirementx 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 Δ 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 Δ t' , so that t' t Δ d• EST is then s t Δ d

• The smallest solution of EST is d s – t

• This gives us:

s t t' t Δ d t Δ (s – t ) s U t

PSD 2005 ‒ 14

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 , wheren 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