Quicksort Revisited

Abstract

Abstract. We verify the correctness of a recursive version of Tony Hoare's quicksort algorithm using the Hoare-logic based verification tool Dafny. We then develop a non-standard, iterative version which is based on a stack of pivot-locations rather than the standard stack of ranges. We outline an incomplete Dafny proof for the latter.

Transformational Verification of Quicksort

“…Since then, many hand-made proofs have been worked out, for several variants (both recursive and iterative) of the algorithm (see, for instance, the book by Apt et al [2]). Also semi-automated proofs have been presented, using program verifiers that implement Hoare logic, such as DAFNY [8,27] and STAINLESS [20]. However, the success of program verifiers is very much dependent on the assertions provided by the programmer.…”

Saturating Sorting without Sorts

“…While Quicksort has been proven correct on multiple occasions, first and foremost in the famous 1971 pen-and-paper proof by Foley and Hoare [7], not many have investigated a fully automated proof of the algorithm. A partially automated proof of Quicksort relies on Dafny [18], where loop invariants are manually provided [4]. While [4] claims to prove some of the lemmas/invariants, not all invariants are proved correct (only assumed to be so).…”

“…A partially automated proof of Quicksort relies on Dafny [18], where loop invariants are manually provided [4]. While [4] claims to prove some of the lemmas/invariants, not all invariants are proved correct (only assumed to be so). Similarly, the Why3 framework [6] has been leveraged to prove sortedness and permutation equivalence of Mergesort [19] over parameterized lists and arrays.…”