An intruder model for verifying termination in security protocols

We formally describe an intruder that is suitable for checking fairness properties of security protocols. The intruder is proved to be equivalent to the Dolev-Yao intruder that respects the resilient communication channels assumption, in the sense that, if a fairness property holds in one of these models, it also holds in the other

A constructive proof of the Heine-Borel covering theorem for formal reals

The continuum is here presented as a formal space by means of a finitary inductive definition. In this setting a constructive proof of the Heine-Borel covering theorem is given

Sound Atomicity Inference for Data-Centric Synchronization

Data-Centric Concurrency Control (DCCC) shifts the reasoning about concurrency restrictions from control structures to data declaration. It is a high-level declarative approach that abstracts away from the actual concurrency control mechanism(s) in use. Despite its advantages, the practical use of DCCC is hindered by the fact that it may require many annotations and/or multiple implementations of the same method to cope with differently qualified parameters. Moreover, the existing DCCC solutions do not address the use of interfaces, precluding their use in most object-oriented programs. To overcome these limitations, in this paper we present AtomiS, a new DCCC model based on a rigorously defined type-sound programming language. Programming with AtomiS requires only (atomic)-qualifying types of parameters and return values in interface definitions, and of fields in class definitions. From this atomicity specification, a static analysis infers the atomicity constraints that are local to each method, considering valid only the method variants that are consistent with the specification, and performs code generation for all valid variants of each method. The generated code is then the target for automatic injection of concurrency control primitives, by means of the desired automatic technique and associated atomicity and deadlock-freedom guarantees, which can be plugged-into the model's pipeline. We present the foundations for the AtomiS analysis and synthesis, with formal guarantees that the generated program is well-typed and that it corresponds behaviourally to the original one. The proofs are mechanised in Coq. We also provide a Java implementation that showcases the applicability of AtomiS in real-life programs

Pointfree approach to Constructive Analysis in Type Theory

The first paper in this thesis presents a machine checked formalisation, in Martin-Löf's type theory, of pointfree topology with applications to domain theory. In the other papers pointfree topology is used in an approach to constructive analysis. The continuum is defined as a formal space from a base of rational intervals. Then the closed rational interval [a, b] is defined as a formal space, in terms of the continuum, and the Heine-Borel covering theorem is proved constructively. The basic definitions for a pointfree approach to functional analysis are given in such a way that the linear functionals from a seminormed linear space to the reals are points of a particular formal space, and in this setting the Alaoglu and the Hahn-Banach theorems are proved in an entirely constructive way. The proofs have been carried out in intensional Martin-Löf type theory with one universe and finitary inductive definitions, and the proofs have also been mechanically checked in an implementation of that system. ..

A Machine Assisted Proof of the Hahn-Banach Theorem

We describe an implementation of a pointfree proof of the Alaoglu and the HahnBanach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in "The Hahn-Banach Theorem in Type Theory" [4]. The implementation was partially developed simultaneously with [4] and it was a help in the development of the informal proofs. 1 Introduction We present a machine assisted formalisation of pointfree topology in Martin-Lof's type theory. The continuum and the basic definitions needed in a pointfree approach to functional analysis are given and in this setting we describe implementations of localic formulations of the Alaoglu and the Hahn-Banach theorems. The classical Hahn-Banach theorem says that, if M is a subspace of a normed linear space A and f is a bounded linear functional on M , then f can be extended to a linear functional F on A so that kFk = kfk. (In our proof we use the equivalent formulation: if kfk 1 then f can be extended to F so that kFk 1.) A..

Entailment relations and distributive lattices

To any entailment relation [Sco74] we associate a distributive lattice. We use this to give a construction of the product of lattices over an arbitrary index set, of the Vietoris construction, of the embedding of a distributive lattice in a boolean algebra, and to give a logical description of some spaces associated to mathematical structures