Recursive programming with proofs

Recursive Programming with Proofs

There has been a lot of work based on the paradigm “proofs as programs”, leading to sophisticated realizations (see e.g. [2,4, 133). An expected benefit is the development of correct programs, but, so far, no programming language in current use came from these works. The difficulty is the apparent distance between proofs and programs: the proofs are often complicated and the extracted programs ...

SKIL: A System for Programming with Proofs

Interactive proofs with efficient quantum prover for recursive Fourier sampling

We consider the recursive Fourier sampling problem (RFS), and show that there exists an interactive proof for RFS with an efficient classical verifier and efficient quantum prover.

Inductive Beluga: Programming Proofs

belugais a proof environment that provides a rich sophisticated infrastructure for implementing formal systems based on the logical framework LF together with a first-order reasoning language for implementing inductive proofs about them following the Curry-Howard

Mechanized proofs for a recursive authentication protocol

A novel protocol has been formally analyzed using the prover Isabelle/HOL, following the inductive approach described in earlier work [10]. There is no limit on the length of a run, the nesting of messages or the number of agents involved. A single run of the protocol delivers session keys for all the agents, allowing neighbours to perform mutual authentication. The basic security theorem state...