Related papers: Destination Calculus: A Linear {\lambda}-Calculus …
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
Disco is a pure, strict, statically typed functional programming language designed to be used in the setting of a discrete mathematics course. The goals of the language are to introduce students to functional programming concepts early, and…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We explore the integration of metaprogramming in a call-by-value linear lambda-calculus and sketch its extension to a session type system. We build on a model of contextual modal type theory with multi-level contexts, where contextual…
We propose a simple calculus for processing data streams (infinite flows of data series), represented by finite sets of equations built on stream operators. Furthermore, functions defining streams are regularly corecursive, that is, cyclic…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
We provide a general and modular criterion for the termination of simply-typed $\lambda$ -calculus extended with function symbols defined by user-defined rewrite rules. Following a work of Hughes, Pareto and Sabry for functions defined with…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
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…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
Primitive recursion is a mature, well-understood topic in the theory and practice of programming. Yet its dual, primitive corecursion, is underappreciated and still seen as exotic. We aim to put them both on equal footing by giving a…
The ability of Large Language Models (LLMs) to perform complex, multi-step reasoning is a central focus of modern AI research. To evaluate and enhance this capability, the pass@k metric, which measures the probability of obtaining at least…
We consider the problem of scheduling arrivals to a congestion system with a finite number of users having identical deterministic demand sizes. The congestion is of the processor sharing type in the sense that all users in the system at…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
Correctness is a necessary condition for systems to be effective in meeting human demands, thus playing a critical role in system development. However, correctness often manifests as a nebulous concept in practice, leading to challenges in…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…