Related papers: Finite Vector Spaces as Model of Simply-Typed Lamb…
The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for…
We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.
The differential $\lambda$-calculus studies how the quantitative aspects of programs correspond to differentiation and to Taylor expansion inside models of linear logic. Recent work has generalized the axioms of Taylor expansion so they…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
We introduce $\mathsf{LEM}$, a type-assignment system for the linear $ \lambda $-calculus that extends second-order $\mathsf{IMLL}_2$, i.e., intuitionistic multiplicative Linear Logic, by means of logical rules that weaken and contract…
A parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is presented. We also show how various finite combinatorial objects can be codded in the formalism of Boolean algebras and counted…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
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…
Lambda-S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic linear…
Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
This paper describes a method for converting formulas in finite propositional linear-time temporal logic (Finite LTL) into finite-state automata whose languages are the models of the given formula. Finite LTL differs from traditional LTL in…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
We prove that the semantics of intuitionistic linear logic in vector spaces which uses cofree coalgebras is also a model of differential linear logic, and that the Cartesian closed category of cofree coalgebras is a model of the…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
I discuss possible definitions of categories of vector spaces enriched with a notion of formal infinite linear combination in the likes of the formal infinite linear combinations one has in the context of generalized power series, I call…