Related papers: Discrete Math with Programming: A Principled Appro…
The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…
The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…
We show how to systematically implement an algorithm in any imperative or functional programming language. The method is based on the premise that it is easy to write down how an algorithm proceeds on a concrete input. This…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…
There is a sharp disconnect between the programming and mathematical portions of the standard undergraduate computer science curriculum, leading to student misunderstanding about how the two are related. We propose connecting the subjects…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
With the future likely to see even more pervasive computation, computational thinking (problem-solving skills incorporating computing knowledge) is now being recognized as a fundamental skill needed by all students. Computational thinking…
How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
This invited paper is a passionate pitch for the significance of logic in scientific education. Logic helps focus on the essential core to identify the foundations of ideas and provides corresponding longevity with the resulting approach to…
This book provides a comprehensive introduction to the foundational concepts of machine learning (ML) and deep learning (DL). It bridges the gap between theoretical mathematics and practical application, focusing on Python as the primary…
Natural language processing for programming aims to use NLP techniques to assist programming. It is increasingly prevalent for its effectiveness in improving productivity. Distinct from natural language, a programming language is highly…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
We present the approach underlying a course on "Domain-Specific Languages of Mathematics", currently being developed at Chalmers in response to difficulties faced by third-year students in learning and applying classical mathematics (mainly…