Section: New Results

Deductive Verification

Synthetic topology in HoTT for probabilistic programming.

F. Faissole and B. Spitters have developed a mathematical formalism based on synthetic topology and homotopy type theory to interpret probabilistic algorithms. They suggest to use proof assistants to prove such programs [39] [31]. They also have formalized synthetic topology in the Coq proof assistant using the HoTT library. It consists of a theory of lower reals, valuations and lower integrals. All the results are constructive. They apply their results to interpret probabilistic programs using a monadic approach [28].

Defunctionalization for proving higher-order programs.

J.-C. Filliâtre and M. Pereira proposed a new approach to the verification of higher-order programs, using the technique of defunctionalization, that is, the translation of first-class functions into first-order values. This is an early experimental work, conducted on examples only within the Why3 system. This work was published at JFLA 2017 [29].

Extracting Why3 programs to C programs.

R. Rieu-Helft, C. Marché, and G. Melquiond devised a simple memory model for representing C-like pointers in the Why3 system. This makes it possible to translate a small fragment of Why3 verified programs into idiomatic C code [30]. This extraction mechanism was used to turn a verified Why3 library of arbitrary-precision integer arithmetic into a C library that can be substituted to part of the GNU Multi-Precision (GMP) library [23].

Verification of highly imperative OCaml programs with Why3

J.-C. Filliâtre, M. Pereira and S. Melo de Sousa proposed a new methodology for proving highly imperative OCaml programs with Why3. For a given OCaml program, a specific memory model is built and one checks a Why3 program that operates on it. Once the proof is complete, they use Why3's extraction mechanism to translate its programs to OCaml, while replacing the operations on the memory model with the corresponding operations on mutable types of OCaml. This method is evaluated on several examples that manipulate linked lists and mutable graphs [20].