11. Functional Modeling

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Functional Modeling

Joseph Valacich, Joey George and Jeff Hoffer,

Essentials of System Analysis and Design , 4 th edition,

Prentice Hall, 2009.

Outline

• Definition and construction of functional models

• Documenting functional models---Data flow diagram (DFD)

• Structuring and organizing DFDs

2

Review: Modeling

• Functional: what happens

• Dynamic: when it happens

• Static: what it happens to

3

Functional Models

• Describes computations and transformation of data

– How are outputs derived from inputs

– Specifies results of computations, not how or when they are computed input x program y = f ( x ) output y

4

Functional Models (Cont.)

• Does not describe timing

– Has no regard for order of operations

– No control information

– Not a flow chart

• Uses diagrams

– Use cases

– Data flow diagram (DFD, not a UML diagram)

– Activity diagrams

5

Steps in Constructing

Functional Model

1. Identify input and output values

2. Build data flow diagrams (DFD) showing functional dependencies.

3. Describe the functions.

4. Identify the constraints.

6

1. Identify Input/Output

• At the highest level of abstraction, these are the system inputs and outputs.

• Each lower level has inputs and outputs defined by some higher level.

input x program output y

7

2. Build Diagrams

• Start with each output and determine what function computes it.

• (Or trace forward from inputs.)

• Expand each non-trivial process in a higherlevel diagram by constructing a lower-level diagram.

f

1 f

11 f

13 f

12

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3. Describe Each Function

• Write a description of each function

(using any of the specification techniques discussed earlier).

Function, f : Integer

Integer, such that f(x) = -1 if x < 0 f(x) = 0 if x == 0 f(x) = 1 otherwise

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4. Identify Constraints

• Constraints are functional dependencies between objects that are not related by an input-output dependency.

– Between two objects at the same time

– Between instances of the same object at different times

– Between different objects at different times.

• State the time the condition must hold.

• E.g. “no account balance may ever become negative.”

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Specifying Functions

• Need a signature (syntactic or interface)

• Need transformations (semantics or meaning)

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Specifying Functions (Cont.)

• Need a signature (syntactic or interface)

– Name

– Arguments (number, order, types)

– Values returned (number, order, types)

• Need transformations (semantics or meaning)

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Specifying Functions (Cont.)

• Need a signature (syntactic or interface)

• Need transformations (semantics or meaning)

– Equations and formulae

– Tables of values

– Pre and post conditions

– Decision tables

– Pseudo code

– Natural language

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Functions

• Trivial

– Access: read or write attributes. May not be necessary to show all of these.

• Non-trivial

– Queries: no side effects

– Actions: “instantaneous” (atomic)

– Activities: duration over time

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Outline

 Definition and construction of functional models

• Documenting functional models---Data flow diagram (DFD)

• Structuring and organizing DFDs

15

Documenting Functional Models

• Uses diagrams

– Data Flow Diagram (DFD)

– UML Activity Diagram

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Data Flow Diagram (DFD)

• Semi-formal notation for specifying

– Functions of an information system and

– How data flow from functions to functions

• Describes systems as

– Collections of functions that manipulate data

– Data can

• Be stored in data repository ,

• Flow in data flows , and Customer

Items

• Be transferred to or from the environment .

Price List

Find Cost

Cost

Customer

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DFDs Are Not For Specifying

• Order of operations (functions)

• Control information

• Flow charts

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DFD Notation

• Four components

– Processes

– Data flows

– Data stores

– Sources/sinks

(or )

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Processes

• Transform data values

• Drawn as ellipses with fixed number of in-arrows and out-arrows dividend divisor quotient

Divide

Integer remainder

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Data Flows

• Connect processes

• Represent intermediate data

• Values are not changed by data flow

• Arrow with name or type of data integer a copy address city split zip city street address zip aggregation

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Data Store

• Stores persistent data for later use

• Has exactly two operations:

– Store

– Retrieve

• Drawn as: data store

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Sources/Sinks

• Producers or consumers of data

• Also called terminators and actors

Customer

Producer (source)

Printer

Consumer (sink)

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DFD Example 1

Price Lists

Price List

Item Name

Find Cost

Cost

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DFD Example 2

Teaching

Assistant

Names

Scores

Enter scores

Grade Book

Names

Scores

Scores

Names

Scores

Average

Compute statistics

Average

Median

Names

Scores

Grades

Create report

Grade report

Grades

Calculate grades

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Data Dictionary

• Repositories to store information about all data items defined in the DFD

• DD may include:

– Name of data item

– Aliases (other names for item)

– Description and purpose

– Range of values

– Data flow (generated by, used by)

– Data structure definition and form

Alan Davis, Software Requirements , Prentice Hall, 1993.

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DD Example

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In Class: Candy Machine

Pairs (5 minutes): Model the function of a candy machine described below.

– Customer inserts coins

– Machine validates coins

– Customer selects a candy

– Machine validates candy selection

– Machine validates transaction

– Machine dispenses change

– Machine dispenses product

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Outline

 Definition and construction of functional models

 Documenting functional models---Data flow diagram (DFD)

• Structuring and organizing DFDs

29

Problems with This DFD?

Organizing DFDs

• Apply levels of abstraction (leveling)

• The initial DFD is: input program output

• This can be expanded into lower levels.

• Eventually, the process must stop.

– When atomic processes can be described.

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Context Diagram (Level 0)

• Describes the system at the highest, most abstract level.

• Determines the scope of the system

• Provides a general view of the system environment identifying external interfaces.

• Comprised of:

– One bubble (the name of the system)

– System terminators (sources and sinks)

– External inputs and outputs

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Level 0: Payroll System

Employee info

Timecard info

Pay info

Process

Payroll

Acct info

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Concept of Leveling:

Rules of Decomposition

I1

I2

1. A

O

Level n

O

I1

I2

1.1 J dx dx

1.2 K

1.3 L dy dy dz

Data storage Level n+1

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Concept of Leveling:

Rules of Decomposition (Cont.)

I

1. B

O

Level n

I dx

I1

I2

1.1 J dy

1.2 K

1.3 L

O1

O2 dy

O

Level n+1

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Level 1: Payroll Process

Inputs and outputs to level n+1 match level n

Timecard info

4: Format paycheck

Pay info

(formatted)

Pay info

Employee info 3: Calculate withholding

1: Validate timecard

Gross pay

Valid timecard info

2: Calculate gross pay

Acct. Info

5: Format accounting

Acct. Info

(formatted)

Level 2: Calculate Withholding

Emp. info 3.1: Compute withholding rate

Gross pay

Rate

Pay info

3.2: Compute net pay

Acct. info

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Notes:

• Show all possible computation paths for values.

• Do not show what paths are executed in what order (that’s the job of the dynamic model).

• There may be many Level N+1 diagrams for each Level N diagram. Level N+1 expands a single node of a Level N diagram.

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Guidelines for Designing

DFDs

1. Describe the system at the highest, most abstract level (context diagram)

2. Decompose the system and represent it as a

DFD with multiple bubbles.

2.1 Document the processes

2.2 Fill out the data dictionary

3. Decompose a process (following step 2) until the problem is understood

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Identifying Data

• At the highest level of abstraction, these are the system inputs and outputs.

• Each lower level has inputs and outputs defined by some higher level.

40

Identifying Processes

• Start with each output and determine what function computes it.

• (Or trace forward from inputs.)

• Expand each non-trivial function

(process) by constructing a lower-level diagram.

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Things to Check in DFDs

1. Is each requirements function represented by a transform in the DFDs?

2. Is each system input and output represented in the DFDs?

3. Is each I/O from a higher-level DFD reproduced correctly on the lower-level

DFDs?

4. Is each transform in the lowest-level DFDs primitive?

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Things to Check in DFDs

5. Are all labels of information flows in the data dictionary?

6. Do all data dictionary entries appear in the

DFDs?

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In Class: Groups of 3

• Draw the DFD for the gas pump controller

(see handout).

• Draw a Level 0, Level1, and 2 Level 2 diagrams.

• (15 minutes)

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