Designing Constraint Maintainers for User Interaction Lambert Meertens

Designing Constraint Maintainers for User Interaction Lambert Meertens Kestrel Institute, Palo Alto, CA & Utrecht University PSD 2005 ‒

Examples of Maintained Constraints – 1 • Spreadsheet Qty Item Cost 2 12. 99 25. 98 3 6. 35 19. 05 ----45. 03 edit Qty Item Cost 2 12. 99 25. 98 33 6. 35 209. 55 -----235. 53 Constraints: – Cost = Qty * Item Cost – Total Cost = SUM Cost PSD 2005 ‒

Examples of Maintained Constraints – 2 • UNIX’ make @book{Aristo. Cat, author = ”Aristotle”, title = ”Category”, @book{Aristo. Cat, author = ”Aristotle”, title = ”Categories”, edit [5] Aristotle. Category. Athens Academic Press. 350 BCE. [5] Aristotle. Categories. Athens Academic Press. 350 BCE. Constraints: – %. dvi: %. tex *. bib latex $* bibtex $* latex $* PSD 2005 ‒ (unidirectional )

Examples of Maintained Constraints – 3 • Rename file edit Constraint: – prez. name = prez. file. name (bidirectional!) PSD 2005 ‒

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 PSD 2005 ‒

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? PSD 2005 ‒

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 PSD 2005 ‒

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 PSD 2005 ‒

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 PSD 2005 ‒

The Principle of Least Change Don’t make a larger change than is needed to restore the constraint A A 2. 5 5. 0 edit PSD 2005 ‒ 3. 5 2. 5 edit B A B 5. 0

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. Ry x y y is a special case of PLC when y F(x) PSD 2005 ‒

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) PSD 2005 ‒

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 ‒

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 nonempty 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 PSD 2005 ‒

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 PSD 2005 ‒

Further Reading • Steven Pemberton. The VIEWS Application Environment. CWI Report CS-R 9257, 1992. http: //www. cwi. nl/ftp/CWIreports/AA/CS-R 9257. pdf • Lambert Meertens, Steven Pemberton. The Ergonomics of Computer Interfaces ‒ Designing a System for Human Use. CWI Report CS-R 9258, 1992. http: //www. cwi. nl/ftp/CWIreports/AA/CS-R 9258. pdf • Lambert Meertens. Designing Constraint Maintainers for User Interaction. http: //www. kestrel. edu/home/people/meertens/dcm. ps PSD 2005 ‒