Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.09085

A Symbolic Computing Perspective on Software Systems

Arthur C. Norman·Stephen M. Watt
View original source ↗Read source document ↗Export metadata ↓

Abstract

Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory management, arbitrary precision arithmetic and dependent types. These systems have the feature of being highly complex while at the same time operating in a domain where results are well-defined and clearly verifiable. These software systems span multiple layers of abstraction with concerns ranging from instruction scheduling and cache pressure up to algorithmic complexity of constructions in algebraic geometry. All of the major symbolic mathematical computing systems include low-level code for arithmetic, memory management and other primitives, a compiler or interpreter for a bespoke programming language, a library of high level mathematical algorithms, and some form of user interface. Each of these parts invokes multiple deep issues. We present some lessons learned from this environment and free flowing opinions on topics including: * Portability of software across architectures and decades; * Infrastructure to embrace and infrastructure to avoid; * Choosing base abstractions upon which to build; * How to get the most out of a small code base; * How developments in compilers both to optimise and to validate code have always been and remain of critical importance, with plenty of remaining challenges; * The way in which individuals including in particular Alan Mycroft who has been able to span from hand-crafting Z80 machine code up to the most abstruse high level code analysis techniques are needed, and * Why it is important to teach full-stack thinking to the next generation.

Explore related subjects

cs.SCcs.MScs.SE

Keep this discovery

BibTeXRIS

Arthur C. Norman, Stephen M. Watt. 2024-06-13. A Symbolic Computing Perspective on Software Systems. https://arxiv.org/abs/2406.09085

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Diversity of EML-type operators

The discovery of the EML operator, sufficient to evaluate the standard explicit purely transcendental elementary functions, has led to considerable interest and discussion across multiple scientific disciplines. However, most authors have focused on the binary EML itself, while numerous similar variants with slightly different properties are now known. This article attempts to close this gap by enumerating and classifying them. We also take this opportunity to clarify common misconceptions related to the EML operator. The principal goal, symbolic regression within an architecture as close as possible to proven neural networks which combine matrix multiplication with a single univariate non-linear activation function, remains beyond reach. Instead, we propose a M\"obius layer, with rational functions replacing matrix operations, and showcase the recently discovered activation function eml(x,1/x), which allows exp(x) and ln(x) to be recovered separately, and hence all elementary functions to be evaluated within a rational generalization of the neural network.

cs.SC↗
arXiv2026

Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery

Every data-driven equation discovery method assumes (implicitly and without verification) that the target system obeys a single governing law ($K{=}1$). Here we show that this assumption is the primary bottleneck limiting scientific discovery in multi-mechanism systems, and introduce Physical Law Ecology, a framework that makes $K^*$ (the number of coexisting independent mechanisms) itself the first quantity to be determined from data. The framework automatically mines a pool of topologically distinct candidate equations, constructs a continuous dominance weight field across parameter space, and discovers analytic evolution laws governing mechanism succession---with optional monotonicity constraints encoding irreversible physics. Across four unrelated systems (elastomer mechanics, pool boiling, galactic dynamics, and droplet evaporation), BIC consistently identifies $K^*{=}3$ independent governing topologies. Applied to 163 SPARC galaxies (3,269 spatially resolved measurements), the framework autonomously recovers three gravitational laws whose coexistence provides evidence against the single-universal-acceleration hypothesis of MOND ($p<10^{-34}$). In engineering applications, multi-law weighted prediction reduces error by 67-72\% over single-equation baselines while retaining full interpretability. By establishing the determination of $K^*$ as the zeroth step of scientific discovery-prior to and independent of equation search---this work opens a direction orthogonal to existing symbolic regression: not finding better equations, but mapping the ecology of mechanisms that govern complex systems.

cs.SC↗