1. Problem Frames 7 - Model domains and real worlds

2. Adding a “model” domain Technique for information display problems A problem frame variant A way of decomposing a problem into two subproblems Makes the problem simpler Describes the machine more accurately

3. Information Display: problem frame diagram Real world Display Information machine C C Display - Real world RW!C1 IM!E2 C3 Y4

4. Information Display with model Real world Display machine C C Display - Model RW!C1 IM!E2 C3 Y4 Model X X Modeling machine Model - Real world Y6 MM!E5 DM!E7

5. Decomposing Invent the model Split requirements into requirements for building the model, and requirements for displaying the results Make two specifications

6. Composition Two requirements should compose to form the original requirements –Except for extra model phenomena Two specifications should compose to form the original specification –Compositions should be easy, because –One creates model, the other reads it

7. Why use a model? Lets machine remember phenomena from the past –Model determines the questions that can be answered –Model indicates memory that is needed Lets machine carry out some calculations incrementally

8. Why use a model? Can model defined terms as if they correspond to separate phenomena Can model processes of a conceptual domain as if they were physical entities Can capture and embody inference rules Can provide surrogates for private phenomena of the modelled domain

9. Model imperfections Model makes assumptions Continuously varying phenomena are modeled by discrete samples Samples are gathered at different times Time lag: sample is gathered after event happened

10. Model Imperfections Incompleteness: missing samples or values –Value doesn’t exist –Value is unknown Errors

11. Example: Experimental voltages Measure voltages at 32 points in a circuit Display voltages as columns side by side on the screen Display average voltage over all the points

12. More experimental voltages Display the average voltage of each point since the experiment began –Discrete –Finite number of samples –Time lag Model: for each point, a count and a total

13. More experimental voltages Average over last 5 minutes –Must keep set of samples for 5 minutes Maximum voltage –Keep maximum for each point

14. Example: Payroll System Inputs: Time cards, New employee form, benefit choice, raise, W4 form Outputs: Pay checks, W1 form, W2 form, check and forms to insurance company

15. Payroll problem diagram fitted to information display frame Payroll System Payroll forms Output C C d a b c Requirements for payroll a: Pf! {time cards, new employee form, benefit choice, raise, W4} C1 b: PS! {paychecks, W1, W2, checks and forms to insurance} E2 c: Pf! {time cards, new employee form, benefit choice, raise, W4} C3 d: O! {paychecks, W1, W2, checks and forms to insurance} Y4

16. Payroll input Real world Payroll DB C X Y6 RW!C1 PI!E5 C3 DB - Real world Reports machine Payroll DB Reports X C Y4 MD!Y7 RM!E2 Y6 Reports -DB

17. Checkwriting machine Payroll DB Paycheck X C Y4 PD!Y7 CM!E2 Y6 Paychecks - DB W2 machine Payroll DB W2 X C Y4 PD!Y7 WM!E2 Y6 W2 - DB

18. Model Domains are common Compilers (Transformation) –symbol table, abstract syntax tree Robotics (controlled behavior) –map, where we are on the map Commanded behavior, Workpieces –undo, selections

19. Conclusion Models are useful for information display Models are probably useful for other problem frames Models are an example of a problem variant, and an example of decomposing problems and composing specifications