Advanced union-find data structures are examined, focusing on offset relationships, thinnings, and their implications in category theory and unification problems.
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Philip Zucker is a physicist and computer scientist interested in programming, compilers, and physics.
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The post details the externalization of the Nelson-Oppen method for combining SMT solvers like Z3 and CVC5, focusing on purification and propagation techniques.
The blog post discusses the concept of unification in the context of solving equations using SMT (Satisfiability Modulo Theories) solvers. It explores methods for using SMT solvers to achieve more general unification solutions, in...
The blog post discusses Zermelo-Fraenkel set theory, focusing on the construction and properties of sets, particularly through the lens of a new sort called ZFSet. It follows Halmos' 'Naive Set Theory' and explores various axioms ...
The post outlines the creation of a Python-based binary verification tool for RISC-V assembly, enhancing debugging and usability through improved symbolic execution methods.
Thinnings serve as mathematical witnesses to sublist questions, simplifying problem-solving in programming and offering insights into lambda calculus and Prolog.
This post details the implementation and efficiency of an Associative-Commutative Hash Cons and its matching process, highlighting code examples and theoretical insights.
Exploring the integration of SMT solvers and compiler design, the post discusses using z3py AST for functional representations and the implications of SSA in optimization.
The post delves into the complexities of term structures in programming, exploring equality, subterm relationships, and normalization processes across various term types.
Contextual union finds are explored through various implementations, highlighting the complexities of managing parent-child relationships and the importance of structural canonization.
Asymmetric completion utilizes inequality relationships in union-find algorithms to enhance computational algebra and automated reasoning, with practical code examples provided.
A semi-interactive proof experience for assembly code is developed using Python and Knuckledragger, enhancing usability through various tools and libraries.
The blog post discusses various advanced variations of the union-find data structure, including primitive, leveled, and quantifier union finds. It explores how these structures can be adapted for different contexts, such as handli...
The post discusses Binary Decision Diagrams (BDDs), a data structure for storing boolean functions. It explains how BDDs can be viewed as a compressed representation of if-then-else expressions, emphasizing their efficiency in che...
The blog post discusses the author's experience in proving the infinitude of primes using the Knuckledragger proof assistant, referencing Euclid's theorem and the formalization of mathematical proofs. The author details the proces...
This post explores the weighted union-find data structure and its applications in egraphs and ground Knuth-Bendix completion, highlighting its implementation and efficiency.
An update on Knuckledragger's development, focusing on kernel changes, AI integration, and the author's shift towards personal interests in proof assistant design.
The post delves into the complexities of ground lexicographic path ordering in term rewriting, highlighting its significance and challenges in functional programming.
A workshop on egraphs and compilers inspired the author with new insights, potential collaborations, and reflections on the unique atmosphere of the event and German culture.
Enhancements to the Knuckledragger project improve Python's syntax for logical expressions, integrating lean-like syntax and the Lark parser for better readability and usability.
6.1SAT Etudes 2: Toy DPLL
2025-12-01 • python sat algorithms lpddr smd components
The blog post discusses the implementation of a toy DPLL (Davis-Putnam-Logemann-Loveland) SAT solver in Python, inspired by the Z3py API. It explains the concept of SAT problems, the DPLL algorithm, and the importance of backtrack...
Integration of Lean with Python via the leancall library enhances programming capabilities, enabling tasks like reinforcement learning and ray tracing with improved performance.
4.5Phil Wrapped 2025
2026-01-01 • reflection health software development e-graphs yoga
A personal reflection on the past year, highlighting achievements, challenges, and future aspirations in both health and professional projects.
The author recounts a chaotic experience when a fire broke out in the building where they lived, detailing the response from firefighters and the Red Cross. They express gratitude for the assistance received but also highlight the...