Models of the System

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Models of the System

• CptS 443
• Human-Computer Interaction

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Models of the System

• What does the program do?
• Arguing semantics
• Models of the functionality of the core
• Models
• Standard - Z
• Interaction - PIE
• Status/event analysis

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Communication

• Why all the formality?
• Between
• design team
• designers and developers
• Reduces ambiguity
• notation is well defined
• different interpretations of notation

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Analysis

• Why all the formality?
• Consistency
• internal - between system functions
• Verification
• the thing right
• external consistency w.r.t. program
• Validation
• the right thing
• requirements match

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Z Sets

• Examples
• Grade A,B,C,D,F
• Keystroke
• Notation
• Uppercase - set
• lowercase - element
• Schema
• tuple, struct, record
• class.member

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Z Sequences

• Ordered array of zero or more elements
• Examples
• History seq Keystroke
• Grades seq Grade
• Catenation
• Sequence A followed by sequence B
• Notation A ? B

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Z Functions

• Notation
• F A-gtB
• F is a mapping from A to B
• Means B F(A)
• Conceptually an array of ordered pairs
• (a,F(a)) for all a in A
• Domain
• Appropriate input to function
• dom F A

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Z Arrays

• Implemented as functions
• F Id -gt X
• Id is the index, e.g. N - the natural numbers
• X is the type of element stored in the array
• Convention _dict
• F A x B -gt C
• indexed by a in A and b in B
• Type of array is C

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Example Sets

• Name
• Id Digit ? ... ? Digit
• Studentname Id -gt Name
• Student_dict N -gt Id
• Students Studentname x Student_dict
• Score Id x Assignment -gt Grade

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The State of Z

• Special schema containing
• system memory
• constraints that must be satisfied
• Example state
• students Students
• scores Score
• cur_student Id
• -----
• cur_student in dom students.studentname

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Z Operators

• Changing Z state
• Another special schema
• Notation
• variable - value from old state
• variable - value defined for new state
• variable? - performance
• variable! - presentation

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Example Operator

• AssignGrade
• Definitions
• State - old state State - new state
• assignment? Assignment
• newgrade? Grade
• Procedure
• scores scores U cur_student x assignment? -gt
  newgrade?

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PIE Model

• How do we quantify WYSIWYG?
• Black box model
• describe only inputs and outputs
• Differentiates Display from Result
• D - Display - what you see
• R - Result - what you get
• E - Effect - the state of the system
• display E -gt D
• result E -gt R

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Why PIE

• C - Command - word in Input language
• P - Program - history of commands
• I - Interpretation - performance
• I P ? E

E
I
P
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doit

• The all purpose function
• doit E x P -gt E
• executes commands at a given state
• I executes commands from init state
• doit(I(p),q) I(p ? q)
• doit(doit(e,p),q) doit(e, p ? q)

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Pie Chart
R
result
I
P
E
display
D
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Transparency

• How to test observability and predictability
• Transparency
• transparentE D ? E
• transparentE(display(e)) e
• Observability of the state from the display
• Result Transparency
• transparentR D ? R
• transparentR(display(e)) result(e)
• Prediction of the result from the display

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Transparency Diagram
resulttransparency
transparency
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The Observable Effect

• We cant always see the entire state
• O - observable effect
• More information than can be displayed
• Interrogation - scroll bars, popups, etc.

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Observability

• Result observable
• predictR O ? R
• predictR(observe(e)) result(e)
• Predict result by observing presentation
• Fully observable
• transparentO O ? E
• transparentO(observe(e)) e
• Knowing state by observing presentation

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Reachability

• We can get to any state from any other state by
  entering the appropriate commands
• For all states e,e...
• There exists a command sequence p such that...
• doit(e,p) e

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Undo

• Can we get to the last state?
• For all commands c...
• doit(e,c ? undo) e
• Not so fast, buster
• Denote doit(e,x) as ex
• doit(ex,undo) doit(e,x ? undo) e
• doit(e,undo) doit(ex,undo ? undo) ex!!!
• Fix no undo ? undo - use redo instead

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PIE Extensions

• Windowed Systems
• interference properties between windows
• Timing
• input buffers - user faster than cpu response
• Attention
• task uses of display/result
• Non-Determinism
• random appearance to confused users
• Dynamic Pointers
• managing displayed references