Programming - Syntax, Semantics, and Segfaults

Computer Architecture

Memory Locality in the Age of Virtualization: Optimizing Database Performance in Hidden NUMA Topologies

1. Introduction Modern cloud infrastructure presents a fascinating paradox: as we advance toward more sophisticated hardware architectures, virtualization increasingly obscures these same architectures from the software running within virtual machines. This phenomenon is particularly evident in Non-Uniform Memory Access (NUMA) systems, where memory access times depend on the memory location

Information Retrieval

Rethinking Data Structures for Search Engines in the Era of Modern Hardware

1. Introduction For decades, computer science education and practice have followed certain established patterns when it comes to selecting data structures. We learn that linked lists offer $O(1)$ insertion and deletion, that skip lists provide $O(\log n)$ search with simpler implementation than balanced trees, and that hash tables

Computer Architecture

Bridging Computing Eras: A 64-bit Extension of the 8086 Architecture

1. Introduction The evolution of computer architectures represents one of the most fascinating chapters in computing history. While modern processors have embraced radical design changes to achieve unprecedented performance, there remains significant educational and research value in understanding the architectural foundations upon which they were built. My childhood memories of

Thoughts

Addressing the Conjunction Fallacy in Probabilistic Information Retrieval: From Theory to Practice

1. Introduction In our previous explorations of probabilistic frameworks for information retrieval, we examined how transformations like softmax and sigmoid convert raw similarity scores into probabilities, enabling principled fusion of heterogeneous retrieval systems. While these transformations provide elegant mathematical foundations for ranking, they introduce a critical challenge when handling conjunctive

Programming

The Computational Power of C++ Templates: A Formal Proof of Turing Completeness

Abstract This essay presents a rigorous mathematical proof demonstrating that C++ template metaprogramming is Turing complete. By constructing a formal mapping between the components of a Turing machine and C++ template metaprogramming mechanisms, we establish that templates can simulate any computation performable by a Turing machine. Beyond the theoretical implications,

Thoughts

Syntax, Semantics, and Type Inference: A Practical Implementation in C++23

Introduction In our previous explorations of programming language theory—from the philosophical underpinnings in "A Cross-Disciplinary Analysis," to the rigorous mathematical frameworks in "A Formal Perspective," to the practical implementations in "From Theory to Practice"—we have progressively bridged the gap between abstract theory

Thoughts

Syntax, Semantics, and Computation: Towards Reliable Indirect Turing Completeness

Introduction The advent of Large Language Models (LLMs) has fundamentally altered our understanding of the relationship between natural language and computation. As established in "Syntax, Semantics, and Computation: LLMs and Their Computational Boundaries," these models occupy a unique position in the landscape of computational systems—neither fully Turing-complete

Thoughts

Syntax, Semantics, and Segfaults: From Theory to Practice - Rust's Type System in C++

Introduction In our previous analyses, "Syntax, Semantics, and Segfaults: A Cross-Disciplinary Analysis" and "Syntax, Semantics, and Segfaults: A Formal Perspective," we explored the theoretical foundations that govern programming languages, from the philosophical underpinnings of meaning to the rigorous mathematical frameworks that ensure program correctness. We examined