Related papers: Type classes for efficient exact real arithmetic i…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
This notes explains how a standard algorithm that constructs the discrete Fourier transform has been formalised and proved correct in the Coq proof assistant using the SSReflect extension.
We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A…
In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), which is the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
Simulating quantum states on a classical computer is hard, typically requiring prohibitive resources in terms of memory and computational power. Efficient simulation, however, can be achieved for certain classes of quantum states, in…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Gradually-typed languages feature a dynamic type that supports implicit coercions, greatly weakening the type system but making types easier to adopt. Understanding how developers use this dynamic type is a critical question for the design…
Statically analyzing dynamically-typed code is a challenging endeavor, as even seemingly trivial tasks such as determining the targets of procedure calls are non-trivial without knowing the types of objects at compile time. Addressing this…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…
As the Internet grows in size, so does the amount of text based information that exists. For many application spaces it is paramount to isolate and identify texts that relate to a particular topic. While one-class classification would be…
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…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Type analyses of logic programs which aim at inferring the types of the program being analyzed are presented in a unified abstract interpretation-based framework. This covers most classical abstract interpretation-based type analyzers for…
Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence…
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in $E$-theory. The other type is by module multiplications in $K$-theory, which also yields an…