A Simpl Shortest Path Checker Verification

Verification of complex algorithms with current verification tools in reasonable time is challenging. Certifying algorithms compute not only an output but also a witness certifying that the output is correct. A checker for a certifying algorithm is a simple program that decides whether the witness is correct for a particular input and output. Verification of checkers is feasible and leads to trustworthy computations. In previous work, we verified checkers from the algorithmic library LEDA using the interactive theorem prover Isabelle/HOL as a backend to the automatic code verifier VCC. More recently, we showed that verification can be carried out completely within Isabelle/HOL and compared this to the previous approach. We concluded that the more recent approach is more trustworthy with comparable efforts. Here we implement a shortest path checker algorithm for graphs with nonnegative edge weights in the imperative pseudocode language Simpl. Moreover, we use the more recent framework and formally verify the checker using Isabelle/HOL.