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Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
The present paper introduces Scala-of-Coq, a new compiler that allows a Coq-based synthesis of Scala programs which are "correct-by-construction". A typical workflow features a user implementing a Coq functional program, proving this…
Theory-guided machine learning has demonstrated that including authentic domain knowledge directly into model design improves performance, sample efficiency and out-of-distribution generalisation. Yet the process by which a formal domain…
Nested relations, built up from atomic types via product and set types, form a rich data model. Over the last decades the nested relational calculus, NRC, has emerged as a standard language for defining transformations on nested…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the…
A key feature in trusted computing is attestation, which allows encapsulated components (enclaves) to prove their identity to (local or remote) distrusting components. Reasoning about software that uses the technique requires tracking how…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
The notion of computability closure has been introduced for proving the termination of higher-order rewriting with first-order matching by Jean-Pierre Jouannaud and Mitsuhiro Okada in a 1997 draft which later served as a basis for the…
We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order…
We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
Limit computable functions can be characterized by Turing jumps on the input side or limits on the output side. As a monad of this pair of adjoint operations we obtain a problem that characterizes the low functions and dually to this…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…