Related papers: Tuplix Calculus
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize Gudhi library. It is under constant development, so please do not consider this…
This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
The computation of triangular decompositions are based on two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations relying on modular…
Destination passing -- aka. out parameters -- is taking a parameter to fill rather than returning a result from a function. Due to its apparently imperative nature, destination passing has struggled to find its way to pure functional…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products…
The polymorphic RPC calculus allows programmers to write succinct multitier programs using polymorphic location constructs. However, until now it lacked an implementation. We develop an experimental programming language based on the…
Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications in domains such as machine learning and differential privacy. To establish invariants of interest, many such languages…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
A vector-circulant matrix is a natural generalization of the classical circulant matrix and has applications in constructing additive codes. This article formulates the concept of a vector-circulant matrix over finite fields and gives an…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…