Functional Specification Software Specification Lecture 41 - PowerPoint PPT Presentation

Loading...

PPT – Functional Specification Software Specification Lecture 41 PowerPoint presentation | free to view - id: 110cb3-ZDc1Z



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Functional Specification Software Specification Lecture 41

Description:

Any program behavior can be represented entirely by a mathematical function in ... Let M be the minuend, S be the subtrahend, and D be the difference. ... – PowerPoint PPT presentation

Number of Views:81
Avg rating:3.0/5.0
Slides: 27
Provided by: vicki85
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Functional Specification Software Specification Lecture 41


1
Functional Specification Software
Specification Lecture 41
  • Prepared by
  • Stephen M. Thebaut, Ph.D.
  • University of Florida

2
Overview
  • Any program behavior can be represented entirely
    by a mathematical function in its effect on data.
  • The domain of a program function corresponds to
    an initial data state that is transformed into a
    final data state by the program.
  • Functional specification scales well and is used
    in Cleanroom Software Development.

Software Engineering, 6th Edition. Chapter 19
3
Cleanroom Software Development
  • Developed in the 70s and 80s by Harlan Mills,
    et al.
  • The name is derived from the Cleanroom process
    in semiconductor fabrication.
  • The philosophy is defect avoidance rather than
    defect removal.
  • Emphasizes precise, logical expression and a
    systematic process for developing correct
    programs.

Software Engineering, 6th Edition. Chapter 19
4
Cleanroom Software Development (contd)
  • A software development process based on
  • Incremental development (if appropriate)
  • Formal specification
  • Static verification using correctness arguments
  • Statistical testing to certify program
    reliability
  • NO defect testing!

Software Engineering, 6th Edition. Chapter 19
5
The Cleanroom Process
Software Engineering, 6th Edition. Chapter 19
6
Cleanroom Process Teams
  • Specification team responsible for developing
    and maintaining the system specification.
  • Development team responsible for developing and
    verifying the software. The software is NOT
    executed or even compiled during this process.
  • Certification team responsible for developing a
    set of statistical tests to measure reliability
    after development.

Software Engineering, 6th Edition. Chapter 19
7
Cleanroom Process Evaluation
  • Results at IBM and elsewhere have been very
    impressive with very few discovered faults in
    delivered systems.
  • Independent assessment shows that the
    (steady-state) process is no more expensive than
    other approaches.

Software Engineering, 6th Edition. Chapter 19
8
What is a Function? (A Brief Tutorial)
  • Sets and Relations
  • Functions
  • Conditional Rules
  • Recursive Functions
  • Lists
  • Assignment Functions

Software Engineering, 6th Edition. Chapter 19
9
Sets and Relations
  • A set is any well-defined collection of objects,
    called members or elements.
  • The relation of membership between a member, m,
    and a set, S, is written
  • m ? S
  • If m is not a member of S, we write
  • m ? S

Software Engineering, 6th Edition. Chapter 19
10
Sets and Relations (contd)
  • A relation, r, is a set whose members (if any)
    are all ordered pairs.
  • The set composed of the first member of each pair
    is called the domain of r and is denoted D(r).
    Members of D(r) are called arguments of r.
  • The set composed of the second member of each
    pair is called the range of r and is denoted
    R(r). Members of R(r) are called values of r.

Software Engineering, 6th Edition. Chapter 19
11
Functions
  • A function, f, is a relation such that for each x
    ? D(f), there exists a unique element
  • (x, y) ? f.
  • (We often express this as y f(x), where y is
    the unique value corresponding to x in the
    function f.)
  • It is the uniqueness of y that distinguishes a
    function from other relations.

Software Engineering, 6th Edition. Chapter 19
12
Functions (contd)
  • It is often convenient to define a function by
    giving its domain and a rule for calculating the
    corresponding value for each argument in the
    domain. For example
  • f (x, y) x?0,1, y x 3x 2

Software Engineering, 6th Edition. Chapter 19
13
Conditional Rules
  • Conditional rules are a sequence of (predicate ?
    rule) pairs separated by vertical bars and
    enclosed in parentheses
  • ( p1 ? r1 p2 ? r2 ... pk ? rk )
  • Its meaning is evaluate predicates p1, p2, ...,
    pk in order for the first predicate, pi, which
    evaluates to true, if any, use the rule ri if no
    predicate evaluates to true, the rule is
    undefined. (Note that ? ? ?.)

Software Engineering, 6th Edition. Chapter 19
14
Conditional Rules (contd)
  • The conditional rule above is read if p1 then
    use r1 else if p2 then use r2 ... else if pk
    then use rk. For example
  • f ((x, y) (x divisible by 2 ? y x/2
  • x divisible by 3 ? y
    x/3
  • true
    ? y x)
  • Note that true ? r has the effect of if all
    else fails, use r.

Software Engineering, 6th Edition. Chapter 19
15
Recursive Functions
  • A recursive function is a function that is
    defined by using the function itself in the rule
    that defines it. For example
  • oddeven(x) (x?0,1 ? x
  • xgt1 ?
    oddeven(x-2)
  • xlt0 ?
    oddeven(x2))
  • Exercise 1 define the factorial function
    recursively.

Software Engineering, 6th Edition. Chapter 19
16
Lists
  • A list is a sequence of items which are all
    members of a single set, called an alphabet.
  • Any computing process must eventually be
    represented by, and be described in terms of
    operations on, a list.
  • The empty list, denoted by ?, is a sequence of no
    items.
  • The fundamental relationship in lists is between
    members of the alphabet and a list.

Software Engineering, 6th Edition. Chapter 19
17
List Operations and Semantics
  • The first item, say a, of a non-empty list, say
    L, is written
  • a head(L), L ? ?
  • A non-empty list L with its first member removed
    is written
  • tail(L)
  • Note that tail(L) may be the empty list, and that
    a ? (a).

Software Engineering, 6th Edition. Chapter 19
18
List Operations and Semantics (contd)
  • Two fundamental operations in lists are (1)
    adding a new item, a, to the head of a list L,
    written
  • a L
  • and (2) concatenating two lists L and M, written
  • LM

Software Engineering, 6th Edition. Chapter 19
19
Assignment Functions
  • Initial and final state space conditions may be
    explicitly represented using assignment
    functions.
  • For example, in a program with data space x, y,
    z, the assignment statement x ?? y corresponds to
    a set of ordered pairs of the form
  • ((x, y, z), (y, y, z))
  • The assignment function representing a program
    consisting of this statement is
  • x, y, z ?? y, y, z

final variable values
initial variable values
Software Engineering, 6th Edition. Chapter 19
20
Assignment Functions (contd)
  • Likewise, the function
  • f (x?0 y?0 ? x, y ?? xy, 0)
  • specifies a program for which the final value of
    x is the sum of the initial values of x and y and
    the final value of y is 0 if x and y are both
    initially ? 0 otherwise the program does not
    terminate (since f is not defined in this case).
  • Can you design a program, P, such that P f ?

Software Engineering, 6th Edition. Chapter 19
21
Exercise 2
  • For each of the following, give appropriate
    assignment functions for the program behavior
    described.
  • Set variable MAX to the maximum value of two
    integers, A and B.
  • Set variable MIN to the minimum value in the
    unsorted, non-empty array A1N.
  • Set variable SUM to the sum of the elements in
    array A1N.

Software Engineering, 6th Edition. Chapter 19
22
Exercise 2 (contd)
  • Given three arrays A1N, B1N, and C1N,
    set each element of A equal to the sum of the
    corresponding elements of B and C.
  • Set variable NPRIME to true if N is prime and to
    false otherwise.
  • Set variable Y to the greatest common divisor of
    integers A and B.

Software Engineering, 6th Edition. Chapter 19
23
Exercise 2 (contd)
  • Set variable R to the remainder of dividing A by
    D.
  • Set variable I to the index of the first instance
    of Y in the array A1N.
  • Perform integer subtraction using the arithmetic
    primitive "subtract 1" and a while loop. Let M
    be the minuend, S be the subtrahend, and D be the
    difference. Assume that the subtrahend is
    nonnegative.

Software Engineering, 6th Edition. Chapter 19
24
Sample Solutions
  • Set variable MAX to the maximum value of two
    integers, A and B.
  • (AgtB ? A, B, MAX ?? A, B, A
  • true ? A, B, MAX ?? A, B,
    B)

Software Engineering, 6th Edition. Chapter 19
25
Sample Solutions (contd)
  • Set variable MIN to the minimum value in the
    unsorted, non-empty array A1N.
  • (MIN, A ?? FIND_MIN(A), A)
  • where
  • FIND_MIN(A) (tail(A)? ? head(A)
  • true ? LESS(head(A),
    FIND_MIN(tail(A))))
  • where
  • LESS(X,Y) (X?Y ? X true ? Y)

Software Engineering, 6th Edition. Chapter 19
26
Functional Specification Software
Specification Lecture 41
  • Prepared by
  • Stephen M. Thebaut, Ph.D.
  • University of Florida
About PowerShow.com