Related papers: Higher order differential calculus in mathlib
This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
Scalar actions are ubiquitous in mathematics, and therefore it is valuable to be able to write them succinctly when formalizing. In this paper we explore how Lean 3's typeclasses are used by mathlib for scalar actions with examples,…
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing…
This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formalize is a Taylor theorem for functions of several variables,…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…
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…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
SOL is an open-source library for scalable online learning algorithms, and is particularly suitable for learning with high-dimensional data. The library provides a family of regular and sparse online learning algorithms for large-scale…
We give several applications of the thick distributional calculus. We consider homogeneous distributions, point source fields, and higher order derivatives of order $0.$
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…