In software engineering, the loop invariant assertion of Floyd is still widely used for proving correctness of programming. But the construction of such assertion is very difficult. This difficulty can be much reduced through the modification of Jensen's idea: extension of Jensen's invariant for co...
We formulate a loop-invariant rule for refining a general-correctness specification by a while loop, and we use our general-correctness calculus to verify the new rule.Steve E. DunneIan J. HayesAndy J. GallowayUnifying Theories of Programming: Second International Symposium, UTP 2008, Dublin, ...
k=n numbers, proved Loop invariants and induction Proving loop invariants is similar to mathematical induction: showing that the invariant holds before the first iteration corresponds to the base case, and showing that the invariant holds from iteration to iteration corresponds to the inductive step....
Now we process the buckets from last to first (in the figures, top to bottom), implementing the right-to-left computation of Equation (13.2). Processing a bucket amounts to summing its functions and eliminating the bucket's variable by maximization. BucketG is processed first. The function ...
A form of the binary search algorithm that returns either the position of the item searched for or the position at which it should be inserted is given and proven correct. Since this version of binary search has a non‐obvious loop invariant, it can be used to provide a meaningful ...
arithmetic-invariant detection, loop-induction-variable strength reduction, and redundant array load elimination. I implemented Rhodium's soundness-checking strategy using the Simplify theorem prover, and I have used this implementation to automatically prove that the Rhodium optimizations I wrote were sound...