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MIT OpenCourseWarehttp://ocw.mit.edu
6.005 Elements of Software Construction
Fall 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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6.005elements ofsoftwareconstructionhow to design a photo catalog Daniel Jackson
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topics or today a problem
� conceptual design of a photo organizer
a new paradigm
� computation over relational structures
� today, the abstract design level: object modelling
� determines, in particular, model part of MVC (see last lecture)
object modelling
� snapshot semantics
� basic notation: domain/range, multiplicity, classification
� some classic patterns
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the problem
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problem
Screenshot of Adobe Photoshop Lightroom removed due to copyright restrictions.
In the Library view, you can select images to add or remove. The left-hand sidebar includes Collections that you can define.
design a photo cataloguing application
� Lightroom, iView MediaPro, iPhoto, Aperture, Picasa, etc© Daniel Jackson 2008 4
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what kind o problem is this?
mostly about conceptual design� what are the key concepts?
� how are they related to one another?
� what kinds of structures?
good conceptual design leads to
� straightforward path to implementation
� simplicity and flexibility in final product
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why a new model?
why not use datatype productions?� tree-like structures only: no sharing
� immutable types only
why not state machines?
� our catalog is a state machine
� but the problem lies in the structure of the state
� our state machine notation assumed simple states
a new approach: object models� structure is a labelled graph
� put another way: sets of objects + relations
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the relational paradigm
computation is about � actions, states, transitions
� functions, expressions, values
� and now: updates and queries on relations
why is this useful?
� conceptual modeling
� relational databases
� object-oriented programming*
� semantic web, document object models, etc
*for proposals to make relations explicit in object-oriented programming, see this survey: James Noble, Roles and Relationships, ECOOP 2007 Workshop on Roles and Relationships in Object-Oriented Programming, Multiagent Systems, and Ontologies; http://iv.tu-berlin.de/TechnBerichte/2007/2007-09.pdf
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basic OM notation
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snapshots
a snapshot or object diagram� shows a single instance of a structure
example for photo organizer
� in this case, two sets
Photo (shown in beige)Collection (in grey)
� and two relations
photos: Collection -> Photo
subs: Collection -> Collection
9
a collection
a relationship:
C0 is subcollection of C1
a photo
a relationship:
P0 in collection C2
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more snapshots
how can we summarize this infinite set?
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an object model
each box� denotes a (maybe empty) set of objects
each arc
� denotes a relation, ie. set of links between objects
note
� objects have no internal structure!
� all structure is in the relations
exercise
� draw a snapshot that the OM rules out
© Daniel Jackson 2008 11
Collection
Photo
subs
photos
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enriching the notation
what’s wrong with these snapshots?� how would we rule them out?
key idea: multiplicity
� measure the in-degree and out-degree of each relation
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multiplicity
A BRm n
multiplicity markings� on ends of relation arc
� show relative counts
interpretation
� R maps m A’s to each B
� R maps each A to n B’s
marking/meaning
+ one or more* zero or more ! exactly one ? at most one omitted marking equivalent to *
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R
kinds o unction
standard kinds of function� easily expressed with multiplicities
?A B
A
R
BR
R is a function
!R is a total function
? !A B
A
R
BR
R is an injection
+ !R is a surjection
! !A B R is a bijection
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multiplicity example
we’ve added naming� always an important and subtle issue
� is the multiplicity constraint desirable? necessary?
Collection
Photo
subs
photos
CollectionName
name
?!
*
*
?
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classiying objects
suppose we to classify photos� by file location: online, offline, missing
� by selection: selected, focusPhoto
Photo
Offline MissingOnline
Selected
Focus
oval means
singleton set
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classifcation syntax
can build a taxonomy of objects� introduce subsets
� indicate which are disjoint
� and which exhaust the superset
A
B
A
B C
abstract A
B C
B 㱪 B 㱯 C = 㱵 B 㱮 C = A
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relations on subsets
when placing a relation� can place on subset
� loose multiplicity is a hint
Photo Filepathpath!
Offline MissingOnline
Volume Date
vol since
! !
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composite
a classic pattern� hierarchical containment
� file systems, org charts, network domains, etc
you’ve seen this with datatypes
� technical differences though
� OM allows cycles (but often rule out)
� OM can say just one root
Collection
FolderFolio
subs
Photo
photos
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hotel locking
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example: hotel locking
modelling physical, distributed state
state in OM need not represent
� a centralized store
� data stored in a computer
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hotel locking
recodable locks (since 1980)� new guest gets a different key
� lock is ‘recoded’ to new key
� last guest can no longer enter
how does it work?
� locks are standalone, not wired
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a recodable locking scheme
card has two keysif first matches lock,recode with second
if second matches,
just open
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exercise
draw an object model� showing the essential state of hotel locking
� state includes front desk, locks, keys held by guests
review
� did you exploit multiplicities? keys are all about uniqueness
� did you include only the sets and relations that are needed?
� are your sets really sets, or are some of them ‘singleton placeholders’?
� do all your sets and relations have a clear interpretation?
� where are the various parts of the state stored physically?
� which relations are modifiable?
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a solution
Guest
Card
holds
Room
Key
key
occupies
fst, snd
?
!
!
Issued
g->r in occupies: guest g has checked in
for room r but has not yet checked out
k in Issued: key k has already beenissued by front desk on some card: usedto ensure that locks are always recodedwith fresh keys
some subtleties
� guest may occupy more than one room
� family members may have identical cards
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common errors
Desk
Key
issues
Card
Key
has
Hotel
Guest
guests
Key
SndFst
be wary of top-level singleton� Desk and Hotel not needed
relations represent state, not actions�
so issues is suspectneed enough information in state to support application� has is not enough: need to know which key is first, second
scope of classification� classification of keys into first and second, is by card, not global� so need relation, not subsets to indicate the distinction
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colour palettes
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example: colour palettes
modelling the state of an application� how colours are organized
Screenshots of color schemes in the Keynote and PowerPoint
presentation programs removed due to copyright restrictions.
essential idea
� elements are coloured
� can assign colour from palette
� gives consistent appearance
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colour
colour
colour
palette object modelsthree subtly different approaches
� think what happens when palette is modified� hard vs. soft links: as in Unix
palette
Doc
Element
elements
Palette
Swatch
swatches
palette
Doc
Element
elements
Palette
Swatch
swatches
valuekey
co our
palette
Colour
value
Name
key
Colour
value
coco our
Doc
elements
Palette
Swatch
swatches
Element
Name
keyco our
Name Colour
“Every problem in computer science can be solved by introducing another level of indirection”
-- David Wheeler
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completing the organizer
i l
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issues to resolvecan collections hold photos and subcollections?
� decision: yes, so not Composite pattern
how are “all photos” in catalog represented?
� decision: introduce non-visible root collection
unique collection names?� decision: file system style, so siblings have distinct names
do parents hold children’s photos?
� in logic: all c: Collection | c.subs.photos in c.photos ?
� decision: use two relations instead
c.inserted: the photos explicitly inserted into collection c
c.photos: the photos in collection c implicitly and explicitly
invariant relates these: c.photos = c.inserted + c.subs.photos© Daniel Jackson 2008 31
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fnal object model
Collection
Visible
subs
Photo
inserted,
photos
Root Selected
Imageimage
!
CollectionName
name!
!
additional constraints
� all collections reachable from root (implies acyclic)
Collection in Root.*subs
� implicit photos are inserted photos plus photos in subcollections
all c: Collection | c.photos = c.inserted + c.subs.photos
� names unique within parent
all c: Collection | no c1, c2: c.subs | c1 != c2 and c1.name = c2.name© Daniel Jackson 2008 32
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modeling hints
hi
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hintshow to pick sets
� be as abstract as possible (thus Name, not String; SSN, not Number)
� but values to be compared must have same type (so Date, not Birthday)
� beware of singletons -- often a sign of code thinking
how to pick relations
� represent state, not actions (so atFloor: Elevator->Floor, not arrives)
� direction is semantic; doesn’t constrain ‘navigation’
choosing names
� choose names that make interpretation clear � include a glossary explaining what relations and sets mean
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summary
i i l
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principles
data before function
� before thinking about system function, think about data
an object model is an invariant
� meaning is set of structured states
� declared sets + subset relationships + relations between sets + multiplicities
� augment diagram with textual constraints (in Alloy, as above, or just English)
model objects are immutable
� all state kept in subsets and relations
� model objects have no ‘contents’
� important to keep coding options open