Journal Article10.1145/359461.359466
Subgoal induction
James Morris,Ben Wegbreit +1 more
84
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.
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Abstract: A proof method, subgoal induction, is presented as an alternative or supplement to the commonly used inductive assertion method. Its major virtue is that it can often be used to prove a loop's correctness directly from its input-output specification without the use of an invariant. The relation between subgoal induction and other commonly used induction rules is explored and, in particular, it is shown that subgoal induction can be viewed as a specialized form of computation induction. A set of sufficient conditions are presented which guarantee that an input-output specification is strong enough for the induction step of a proof by subgoal induction to be valid.
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Citations
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- 30 Dec 1899
TL;DR: In this paper, the mathematical theory of computation is discussed and several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms are also presented.
509
Dynamically discovering likely program invariants
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- 01 Jan 2000
TL;DR: This dissertation shows how invariants can be dynamically detected from program traces that capture variable values at program points of interest and presents techniques for detecting such invariants from traces, assesses their efficacy, and points the way for future research.
Automatic Array Privatization
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References
A Basis for a Mathematical Theory of Computation
John J. McCarthy
- 01 Jan 1962
TL;DR: The chapter explores what practical results can be expected from a suitable mathematical theory and presents several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms.
A Basis for a Mathematical Theory of Computation
John J. McCarthy
- 30 Dec 1899
TL;DR: In this paper, the mathematical theory of computation is discussed and several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms are also presented.
509
•Book
Correctness of a compiler for arithmetic expressions
John J. McCarthy,James Painter +1 more
- 29 Apr 1966
TL;DR: This paper contains a proof of the correctness of a simple compiling algorithm for compiling arithmetic expressions into machine language.