Skill

discover-systems-theory

Discovers 32 skills on eBPF, information retrieval, programming language theory, and formal methods for kernel tracing, compilers, parsers, type systems, Z3, and Lean.

developer-tools

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npx claudepluginhub rand/cc-polymath --plugin cc-polymath

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This skill uses the workspace's default tool permissions.

Preview

- eBPF, kernel tracing, XDP, kprobes, BPF

SKILL.md

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Stats

Stars75

Forks5

Last CommitFeb 28, 2026

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Systems Theory & Language Design Skills Discovery

When This Skill Activates

eBPF, kernel tracing, XDP, kprobes, BPF
Compilers, parsers, interpreters, AST, bytecode
Type systems, type theory, programming language design
LLVM, IR, SSA, code generation, optimization passes
Information retrieval, search, ranking, vector search
Formal verification, theorem proving, model checking
SAT, SMT, Z3, Lean, constraint solving

Available Skills (32 total)

eBPF (4 skills)

ebpf-fundamentals - eBPF programs, verifier, maps
ebpf-networking - XDP, TC, socket filtering
ebpf-security-monitoring - LSM hooks, syscall tracing
ebpf-tracing-observability - kprobes, tracepoints, profiling

Information Retrieval (5 skills)

ir-search-fundamentals - Indexing, tokenization, TF-IDF, BM25
ir-query-understanding - Query parsing, expansion, intent
ir-ranking-reranking - Learning to rank, cross-encoders
ir-vector-search - Embeddings, ANN, HNSW, FAISS
ir-recommendation-systems - Collaborative/content-based filtering

Programming Language Theory (13 skills)

type-systems - Type theory, inference, polymorphism
lambda-calculus - Lambda calculus, reduction, Church encodings
curry-howard - Propositions as types, proofs as programs
dependent-types - Dependent types, refinement types
operational-semantics - Small-step, big-step semantics
program-verification - Hoare logic, invariants, correctness
structure-editors - Structural editing, projectional editors
hazelnut-calculus - Hazelnut typed holes calculus
live-programming-holes - Live programming with typed holes
typed-holes-foundations - Typed holes theory and foundations
typed-holes-interaction - Interactive typed hole filling
typed-holes-llm - LLM-powered typed hole completion
typed-holes-semantics - Typed holes formal semantics

Formal Methods (10 skills)

z3-solver-basics - Z3 SMT solver, constraints, assertions
sat-solving-strategies - SAT solving, DPLL, CDCL
smt-theory-applications - SMT theories, bitvectors, arrays
lean-proof-basics - Lean 4 basics, tactics, terms
lean-tactics - Advanced Lean tactics and automation
lean-theorem-proving - Theorem proving patterns in Lean
lean-mathlib4 - Mathlib4 library usage
csp-modeling - Constraint satisfaction problems
constraint-propagation - Arc consistency, propagation
backtracking-search - Backtracking, branch and bound

Load Full Category Details

Read ../ebpf/INDEX.md Read ../ir/INDEX.md Read ../plt/INDEX.md Read ../formal/INDEX.md

Progressive Loading

Level 1: This gateway loads automatically (~70 lines)
Level 2: Load category INDEX.md for full skill listings
Level 3: Load specific skills as needed