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ALEXANDRIA is an ERC-funded project that started in 2017, with the aim of bringing formal verification to mathematics. The past six years have seen great strides in the formalisation of mathematics and also in some relevant technologies, above all ...

In 1964, Paul Erdős published a paper [5] settling a question about function spaces that he had seen in a problem book. Erdős proved that the answer was yes if and only if the continuum hypothesis was false: an innocent-looking question turned out ...

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today’s powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing ...

Many problems in computer algebra and numerical analysis can be reduced to counting or approximating the real roots of a polynomial within an interval. Existing verified root-counting procedures in major proof assistants are mainly based on the ...

The HOL Light proof assistant is famous for its huge multivariate analysis library: nearly 300,000 lines of code and 13,000 theorems. A substantial fraction of this library has been manually ported to Isabelle/HOL. The Isabelle analysis library ...

Classical security protocols aim to achieve authentication and confidentiality under the assumption that the peers behave honestly. Some recent protocols are required to achieve their goals even if the peer misbehaves. Accountability is a protocol ...

SET (Secure Electronic Transaction) is a suite of protocols proposed by a consortium of credit card companies and software corporations to secure e-commerce transactions. The Purchase part of the suite is intended to guarantee the integrity and ...

The paper reports on experiences of mechanizing various proposals for compositional reasoning in concurrent systems. The work uses the UNITY formalism and the Isabelle proof tool. The proposals investigated include existential/universal ...

Mathematical reasoning may involve several arithmetic types, including those of the natural, integer, rational, real, and complex numbers. These types satisfy many of the same algebraic laws. These laws need to be made available to users, uniformly and ...

Compositional reasoning must be better understood if non-trivial concurrent programs are to be verified. Chandy and Sanders [2000] have proposed a new approach to reasoning about composition, which Charpentier and Chandy [1999] have illustrated by ...

UNITY is an abstract formalism for proving properties of concurrent systems, which typically are expressed using guarded assignments [Chandy and Misra 1988]. UNITY has been mechanized in higher-order logic using Isabelle, a proof assistant. Safety and ...

The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a nontrivial combinatorial identity. The mathematical proof is explained in some detail, leading on to the mechanization of ...

Internet browsers use security protocols to protect sensitive messages. An inductive analysis of TLS (a descendant of SSL 3.0) has been performed using the theorem prover Isabelle. Proofs are based on higher-order logic and make no assumptions concerning ...