Journal Article10.1109/TSE.1975.6312822
Proving loop programs
S. K. Basu,Jayadev Misra +1 more
53
TL;DR: The authors investigate the problem of proving (or disproving) if P computes F over D and show that if P satisfies certain natural constraints, then there is a loop assertion independent of the structure of the loop body, that is both necessary and sufficient for proving the hypothesis.
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Abstract: Given a `DO WHILE' program P and a function F on a domain D, the authors investigate the problem of proving (or disproving) if P computes F over D. It is shown that if P satisfies certain natural constraints (well behaved), then there is a loop assertion independent of the structure of the loop body, that is both necessary and sufficient for proving the hypothesis. These results are extended to classes of loop programs which are not well behaved and to FOR loops. The sufficiency of Hoare's DO WHILE axiom for well-behaved loop programs is shown. Applications of these ideas to the problem of mechanical generation of assertions is discussed.
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Citations
A Method for Analyzing Loop Programs
TL;DR: This paper presents a method for automatically analyzing loops, and discusses why it is a useful way to look at loops and the relationship between the structure building methods presented and programming language constructs.
95
Subgoal induction
James Morris,Ben Wegbreit +1 more
TL;DR: It is shown that subgoal induction can be viewed as a specialized form of computation induction, which can often be used to prove a loop's correctness directly from its input-output specification without the use of an invariant.
84
An interactive program verification system
Donald I. Good,Ralph L. London,W. W. Bledsoe +2 more
- 01 Jan 1975
TL;DR: This paper is an initial progress report on the development of an interactive system for verifying that computer programs meet given formal specifications based on the conventional inductive assertion method.
79
Relational heuristics for the design of deterministic programs
TL;DR: This paper formulate some heuristic solutions to relational equations and shows that the design of deterministic programs can be formulated as the resolution of relational equations.
50
Polynomial Invariants by Linear Algebra
Steven de Oliveira,Saddek Bensalem,Virgile Prevosto +2 more
- 17 Oct 2016
TL;DR: In this paper, a technique for generating polynomial invariants, divided in two independent parts, is presented, a procedure that reduces Polynomial assignments composed loops analysis to linear loops under certain hypotheses and a procedure for generating inductive invariants for linear loops.
References
Symbolic execution and program testing
TL;DR: A particular system called EFFIGY which provides symbolic execution for program testing and debugging is described, which interpretively executes programs written in a simple PL/I style programming language.
An interactive program verification system
Donald I. Good,Ralph L. London,W. W. Bledsoe +2 more
- 01 Jan 1975
TL;DR: This paper is an initial progress report on the development of an interactive system for verifying that computer programs meet given formal specifications based on the conventional inductive assertion method.
79