1. Software Engineering Lecture 8
Vladimir Safonov,
Professor, head of laboratory
St. Petersburg University
WWW:
Язык программирования Java. Лекция 1

2. Program specification
Specification – the stage of software lifecycle, to follow by the requirements & goals stage
Specification – a formalized, external, precise and complete description of the task to be solved by the program or its part in question
Simply: specification is WHAT, rather than HOW
Typical element of specification is a mathematical formula, e.g., fact(n) = 1 * 2 * … * n
Implementation of an algorithm, data representation, etc. are not elements of specification
Complete specification: taking into account all the alternatives, e.g., n = 0 for fact(n): fact(0) = 1
(C) Vladimir O. Safonov, 2004

3. Specification techniques
Natural language
HIPO diagrams (Hierarchical Input-Process-Output)
Decision tables
Program calculus (operator schemas) by R. Floyd – C.A.R. Hoare:
P {S} Q A{S}B, B{T}C |- A{S;T} C
Denotational semantics (D. Scott, J.Donahue at al.): program is a transformer of predicates: P(x1, … xn) -> Q(x1, …, xn), where xi – free (global) variables
Vienna Definition Method (VDM; IBM Research): program – system of mutually related finite-state automata
Algebraic (G.A. Goguen et al.): program – a collection of ADT, each of them specified as multi-sorted algebra
Petri nets – specifying asynchronous programs and computing systems (see: Kotov V. E. Petri nets.: Nauka, 1986)
(C) Vladimir O. Safonov, 2004

4. Specification languages
VDM – specification using the concept of finite automaton (Ollongren A. Defining programming languages by interpretive automata. – Prentice Hall, 1977)
OBJ, CLEAR, SDL, LARCH – algebraic specification languages (please see OBJ description in J.A. Goguen’s papers)
CIP/L (“Wide Spectrum Multi-Layered Language) – Technical University, Munich, 1979
References to VDM, Z, LARCH – please see: I. Sommerville’s textbook
(C) Vladimir O. Safonov, 2004

5. OBJ3 (Prof. G. A. Goguen). Example (1/2) ftp://www. cs. ucsd
OBJ3 (Prof. G. A. Goguen). Example (1/2) ftp:// University of California, San Diego
obj NAT is sort Nat .
op 0 : -> Nat .
op s_ : Nat -> Nat [prec 1] .
endo
obj NATOPS is pr NAT .
op 1 : -> Nat .
eq 1 = s 0 . 
op _+_ : Nat Nat -> Nat [assoc comm prec 3] .
vars M N : Nat .
eq M + 0 = M .
eq M + s N = s(M + N) .
(C) Vladimir O. Safonov, 2004

6. OBJ3: Example (2/2) op _*_ : Nat Nat -> Nat [assoc comm prec 2] .
eq M * 0 = 0 .
eq M * s N = M * N + M . 
op _**_ : Nat Nat -> Nat [prec 4] .
eq M ** 0 = 1 .
eq M ** s N = (M ** N) * M . 
op _-_ : Nat Nat -> Nat .
eq M - 0 = M .
eq 0 - M = 0 .
eq s M - s N = M - N . [ SKIP … ]
  [lemma1] cq (N * N)**(M %2) = N ** M if even M .
[lemma2] cq N *(N **(M - s 0)) = N ** M if pos M .
endo
(C) Vladimir O. Safonov, 2004

7. A monograph on OBJ and algebraic specifications
(C) Vladimir O. Safonov, 2004

8. Other approaches to specification
B Liskov. CLU (M.I.T.):
GCD = proc (int M, N) signals (overflow)
requires N > 0;
effects GCD(M, N) = greatest common divisor of M, N
- ср. с “Design-by-Contract” (Dr. B. Meyer, Eiffel)
M. Shaw. ALPHARD (Carnegie-Mellon Univ.)
ADT specifications (forms) – by R. Floyd, C.A.R. Hoare.
For each ADT, the pre- & post-conditions for each abstract operation, and also abstract invariant and concrete invariant are indicated – a predicate to hold on the abstract (concrete) data items participating in the ADT definition: e.g., SP > 0
(C) Vladimir O. Safonov, 2004

9. Automated program synthesis by specification (E. Tougu, S.S. Lavrov)
Task formulation: Given a specification of the application domain D (as a collection of equates) and a specification of the pre- and post-conditions: Pre {S} Post
Goal: authoated synthesis of the program S
Tools intended to solve similar tasks (U.S.S.R):
- PRIZ -> NUT (E. Tougu; please see his monograph: Conceptual programming, Moscow, Science Publishers, 1984)
- SPORA (S. Lavrov; automated program synthesis system with the specification language DESCARTES, 1980s)
(C) Vladimir O. Safonov, 2004

10. References
Agafonov V.N. Program specification. Concepts and their organization. – Novosibirsk: Science Publishers, 1988
Mathematical logic in programming. - Moscow: World Publishers, 1991
Requirements and Specifications on Program Development. - Moscow, World Publishers, 1984
(C) Vladimir O. Safonov, 2004