Functional Modeling Joseph Valacich, Joey George and Jeff Hoffer, Essentials of System Analysis and Design, 4th edition, Prentice Hall, 2009. Review: Modeling • Functional: what happens • Dynamic: when it happens • Static: what it happens to 2 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 3 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 4 Steps in Constructing Functional Model • Identify input and output values • Build data flow diagrams showing functional dependencies. • Describe the functions. • Identify the constraints. 5 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 6 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. f1 f11 f13 f12 7 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 8 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.” 9 Specifying Functions • Need a signature (syntactic or interface) • Need transformations (semantics or meaning) 10 Specifying Functions (Cont.) • Need a signature (syntactic or interface) – Name – Arguments (number, order, types) – Values returned (number, order, types) • Need transformations (semantics or meaning) 11 Specifying Functions (Cont.) • Need a signature (syntactic or interface) • Need transformations (semantics or meaning) – – – – – – Functions and equations Tables of values Pre and post conditions Decision tables Pseudo code Natural language 12 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 13 Documenting Functional Models • Uses diagrams – Data Flow Diagram (DFD) – UML Activity Diagram 14 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. 15 DFDs Are Not For Specifying • Order of operations (functions) • Control information • Flow charts 16 DFD Notation • Four components – Processes – Data flows – Data stores (or ) – Sources/sinks 17 Example DFD exam scores Compute average Grade book student names exam scores average score names grades Compute grades names grades Output grades 18 Processes • Transform data values • Drawn as ellipses with fixed number of in-arrows and out-arrows dividend quotient Divide Integer divisor remainder 19 Data Flows • • • • Connect processes Represent intermediate data Values are not changed by data flow Arrow with name or type of data integer a copy city street city address zip zip aggregation address split 20 Data Store • Stores persistent data for later use • Has exactly two operations: – Store – Retrieve • Drawn as: data store (or data store ) 21 Sources/Sinks • Producers or consumers of data • Also called terminators and actors Customer Printer Printer Producer (source) Consumer (sink) 22 DFD Example 1 Price Lists Price List Item Name Cost Find Cost 23 DFD Example 2 Grade Book Teaching Assistant Grades IDs Grades 3. Compute statistics Final grades Average IDs Grades 1. Enter grades 2. Adjust grades Average Median Names Grades Names Final grades Printer Printer Grade report 4. Create report 24 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. 25 DD Example 26 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 27 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. 28 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 29 Level 0: Payroll System Pay info Employee info Employee Printer Timecard info Printer Printer Process Payroll Acct info Accountant Printer 30 Concept of Leveling: Rules of Decomposition I1 1. A I2 I1 O Level n dx 1.1 J dx I2 1.2 K O 1.3 L dy dz dy Data storage Level n+1 31 Concept of Leveling: Rules of Decomposition (Cont.) I 1. B O Level n O1 dx 1.1 J I I1 I2 dy 1.3 L O O2 dy 1.2 K Level n+1 32 Level 1: Payroll Process Inputs and outputs to level n+1 match level n Employee info Pay info 4: Format paycheck 3: Calculate withholding Acct. Info Timecard info 1: Validate timecard Valid timecard info Pay info (formatted) Gross pay 2: Calculate gross pay 5: Format accounting Acct. Info (formatted) Level 2: Calculate Withholding Emp. info 3.1: Compute withholding rate Rate Pay info Gross pay 3.2: Compute net pay Acct. info 34 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. 35 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 36 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. 37 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. 38 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? 39 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? 40 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) 41

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