Related papers: Simplifying explicit subtyping coercions in a poly…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
The emergence of large language models (LLMs) like GPT-4 has revolutionized natural language processing (NLP), enabling diverse, complex tasks. However, extensive token counts lead to high computational and financial burdens. To address…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
Shape types are a general concept of process types which work for many process calculi. We extend the previously published Poly* system of shape types to support name restriction. We evaluate the expressiveness of the extended system by…
We classify programming languages according to evaluation order: each language fixes one evaluation order as the default, making it transparent to program in that evaluation order, and troublesome to program in the other. This paper…
Current algorithms for context-free parsing inflict a trade-off between ease of understanding, ease of implementation, theoretical complexity, and practical performance. No algorithm achieves all of these properties simultaneously. Might et…
In this paper, we present a generalization of a syntax-directed editor calculus, which can be used to instantiate a specialized syntax-directed editor for any language, given by some abstract syntax. The editor calculus guarantees the…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
The Calculus of Audited Units (CAU) is a typed lambda calculus resulting from a computational interpretation of Artemov's Justification Logic under the Curry-Howard isomorphism; it extends the simply typed lambda calculus by providing…
Complex software can be hard to read, adapt, and maintain. Refactoring it can create cleaner and self-explanatory code. Refactoring tools try to guide developers towards better code, with more quality. However, most of them take too long to…
Algebraic effects & handlers are a modular approach for modeling side-effects in functional programming. Their syntax is defined in terms of a signature of effectful operations, encoded as a functor, that are plugged into the free monad;…
The recursive polynomial expansion for construction of a density matrix approximation with rigorous error control [J. Chem. Phys. 128, 074106 (2008)] is implemented in the quantum chemistry program Ergo [SoftwareX 7, 107 (2018)] using the…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
We revisit various PTAS's (Polynomial Time Approximation Schemes) for minimization versions of dense problems, and show that they can be performed with sublinear query complexity. This means that not only do we obtain a…
We study classes of Dynamic Programming (DP) algorithms which, due to their algebraic definitions, are closely related to coefficient extraction methods. DP algorithms can easily be modified to exploit sparseness in the DP table through…
Manifest contract calculi, which integrate cast-based dynamic contract checking and refinement type systems, have been studied as foundations for hybrid contract checking. In this article, we study techniques to reasoning about a…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…