Functional Modeling

Joseph Valacich, Joey George and Jeff Hoffer, Essentials of System Analysis and Design, 4th edition, Prentice Hall, 2009.

Outline

• Definition and construction of functional models

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

• Structuring and organizing DFDs

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Review: Modeling

• Functional: what happens• Dynamic: when it happens• Static: what it happens to

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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

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programy = f(x)

input x output y

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

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Steps in Constructing Functional Model

1. Identify input and output values2. Build data flow diagrams (DFD)

showing functional dependencies.3. Describe the functions.4. Identify the constraints.

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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.

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programinput x output y

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 higher-

level diagram by constructing a lower-level diagram.

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f1

f11

f12

f13

3. Describe Each Function

• Write a description of each function (using any of the specification techniques discussed earlier).

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

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

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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• Be transferred to or from the environment.

Price List

Find CostItems Cost

CustomerCustomer

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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

DivideInteger

dividend

divisor

quotient

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

addresscity

zipsplit

addresscity

zip

street

aggregation

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Data Store• Stores persistent data for later use• Has exactly two operations:

– Store– Retrieve

• Drawn as:

data store (or )data store

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Sources/Sinks• Producers or consumers of data• Also called terminators and actors

Customer

Producer (source) Consumer (sink)

PrinterPrinter Printer

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DFD Example 1

Price Lists

Find CostItem Name Cost

Price List

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DFD Example 2

Compute statistics

Calculategrades

NamesScores

Grades

Create report

NamesScores

AverageMedian

Grade Book

NamesScores

Grades

Gradereport PrinterPrinter

AverageEnter

scores

ScoresNamesScores

Teaching Assistant

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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

Outline

Definition and construction of functional models

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

• Structuring and organizing DFDs

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Problems with This DFD?

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Organizing DFDs• Apply levels of abstraction (leveling)• The initial DFD is:

• This can be expanded into lower levels.

• Eventually, the process must stop.– When atomic processes can be described.

programinput output

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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

ProcessPayroll

Employeeinfo

Timecardinfo

Pay info

Acct info

PrinterPrinter

PrinterAccountant

PrinterEmployee

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Concept of Leveling: Rules of Decomposition

1. AI2

I1O

1.1 J 1.3 L

1.2 K

I1

I2

O

Data storage

dx

dy

dydz

dx

Level n

Level n+1

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Concept of Leveling: Rules of Decomposition (Cont.)

1. BI O

1.1 J 1.3 L

1.2 KI

Odx

dydyI1

I2

O1

O2

Level n

Level n+1

Level 1: Payroll Process

3: Calculatewithholding

4: Formatpaycheck

1: Validate timecard

2: Calculategross pay

5: Formataccounting

Employeeinfo

Acct. Info(formatted)

Acct. Info

Pay info

Gross pay

Valid timecard

info

Timecardinfo

Pay info (formatted)

Inputs and outputs to level n+1 match

level n

Level 2: Calculate Withholding

3.1: Computewithholding

rate

Emp. info

Acct. info

Pay infoGross pay

3.2: Computenet pay

Rate

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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.

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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.

Things to Check in DFDs1. 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 DFDs5. 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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