Checking correctness properties of object-oriented programs

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Checking correctness properties of
object-oriented programs

• K. Rustan M. LeinoMicrosoft Research, Redmond, WA

Lecture 1EEF summer school on Specification,
Refinement, and Verification20 Aug 2002, Turku,
Finland
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Exercise

• Implement a union-find class in Java and check it
  with ESC/Java

class UnionFind // creates a union-find data
structure with size elements, // each in a
separate equivalence class public UnionFind(int
size) // returns the representative for
the equivalence class containing c public int
find(int c) // merges the equivalence
classes containing elements c and d public
void union(int c, int d)
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Commands

• A command may
• terminate normally
• go wrong (crash the computer)
• diverge (fail to terminate, infinite recursion)
• block (fail to start, also called miraculous
  termination)

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Exercise

• Define specification statement where
  postcondition mentions x,x instead of x0,x
• Example xtrue, xltx

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Exercise

• Define while inv J B do w S end where
  w is the list of targets in Sin terms of the
  commands seen so far.

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Answer
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References

• Edsger W. Dijkstra. A Discipline of Programming.
  Prentice Hall, 1976.
• Greg Nelson. A Generalization of Dijkstra's
  Calculus. TOPLAS 11(4), pp. 517-561, ACM, 1989.
• Ralph-Johan Back and Joakim von Wright.
  Refinement Calculus A Systematic Introduction.
  Graduate Texts in Computer Science,
  Springer-Verlag, 1998.
• C.A.R. Hoare. An axiomatic basis for computer
  programming. CACM 12(10), pp. 576-580,583, Oct.
  1969.
• Carroll Morgan. The specification statement.
  TOPLAS 10(3), pp. 403-419, ACM, Jul. 1988.
• John McCarthy and James Painter. Correctness of
  a compiler for arithmetic expressions. In J.-T.
  Schwartz, ed., Proceedings of Symposia in Applied
  Mathematics, American Mathematical Society, 1967.

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References

• O.-J. Dahl, E.W. Dijkstra, and C.A.R. Hoare.
  Structured Programming. Academic Press, 1972.
• C.A.R. Hoare and Niklaus Wirth. An axiomatic
  definition of the programming language PASCAL.
  In Acta Informatica 2, Springer, 1973.
• G. Birkhoff. Lattice Theory. Volume 25 of
  Colloquium Publications 25. American
  Mathematical Society, 1967.
• David L. Parnas. A Technique for Software
  Module Specification with Examples. CACM 15(5),
  pp. 330-336, ACM, May 1972.
• K. Rustan M. Leino, James B. Saxe, and Raymie
  Stata. Checking Java programs via guarded
  commands. In Bart Jacobs, et al., eds., Formal
  Techniques for Java Programs, Technical Report
  251, FernUniversität Hagen, May 1999.