We present VOQC, the first fully verified optimizer for quantum circuits, written using Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, simple intermediate representation, which is deeply embedded Coq. Optimizations and other transformations functions, proved correct with respect to semantics of SQIR programs. uses matrices complex nu...

Verified artificial intelligence (AI) is the goal of designing AI-based systems that are provably correct with respect to mathematically-specified requirements. This paper considers Verified AI from a formal methods perspective. We describe five challenges for achieving Verified AI, and five corresponding principles for addressing these challenges.

The software toolchain includes static analyzers to check assertions about programs; optimizing compilers to translate programs to machine language; operating systems and libraries to supply context for programs. Our Verified Software Toolchain verifies with machine-checked proofs that the assertions claimed at the top of the toolchain really hold in the machine-language program, running in the...

We describe the mechanisation of an SLR parser produced by a parser generator, covering background properties of context-free languages and grammars, as well as the construction of an SLR automaton. Among the various properties proved about the parser we show, in particular, soundness: if the parser results in a parse tree on a given input, then the parse tree is valid with respect to the gramm...