You could then state the following loop invariant: To prove Insertion Sort is correct, you will then demonstrate it for the three stages: Initialization- The subarray starts with the first element of the array,
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 ...
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 ...
where R is the invariant and E the variant • Note that the variant is intended to be a non-negative expression that decreases each time around the WHILE loop • The other annotations, which are enclosed in curly brackets, are meant to be conditions that are true whenever control reaches...
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, ...
The th-=-ird drawback is probably the real challenge. Most invariant design methodologies, including those just mentioned, are in fact trial-and-error methods : "promising candidate invariants" are r...Leslie Lamport. An assertional correctness proof of a distributed al- gorithm. Science of ...
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...