Related papers: Lineal: A linear-algebraic Lambda-calculus
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…
We study Milner's lambda-calculus with partial substitutions. Particularly, we show confluence on terms and metaterms, preservation of \b{eta}-strong normalisation and characterisation of strongly normalisable terms via an intersection…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
The Resource $\lambda$-calculus is a variation of the $\lambda$-calculus where arguments can be superposed and must be linearly used. Hence it is a model for linear and non-deterministic programming languages, and the target language of…
Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…