Related papers: La Valeur d'un Entier Classique en $\lambda\mu$-Ca…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It…
Decimal-to-binary conversion is important to modern binary computers. The classical method to solve this problem is based on division operation. In this paper, we investigate a decimal-to-binary conversion method based on addition…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
We generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize the classical mean value…
We present a method to obtain arbitrarily accurate solutions for conservative classical oscillators. The method that we propose here works both for small and large nonlinearities and provides simple analytical approximations. A comparison…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
We first consider a method of centering and a change of variable formula for a quantum integral. We then present three types of quantum integrals. The first considers the expectation of the number of heads in $n$ flips of a "quantum coin".…
In each variant of the lambda-calculus, factorization and normalization are two key-properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants…
Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term…
We present here a new method for evaluating determinants -- the reduction method. Firstly, in the section 2, we apply it to third-order determinants and after, in the section 3, we generalize it to higher-order determinants. In the section…
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus…