---
name: Systems Theory Discovery
slug: systems-theory-discovery
category: AI Engineering
description: Systems Theory Discovery routes requests about eBPF, compilers, type systems, IR, and formal methods to the relevant skills. Use it when working on tracing, parsers, SMT, Lean, or theorem proving.
github: "https://github.com/rand/cc-polymath/tree/main/skills/discover-systems-theory"
language: Python
stars: 175
forks: 12
install: "npx degit https://github.com/rand/cc-polymath/tree/main/skills/discover-systems-theory ~/.claude/skills/discover-systems-theory"
installs_to: ~/.claude/skills/discover-systems-theory
source_path: skills/discover-systems-theory/SKILL.md
collection_size: 25
category_size: 3475
collection_url: "https://dirskills.com/collections/rand/cc-polymath"
added: 2026-09-07T05:21:42.241Z
last_synced: 2026-09-07T05:21:42.241Z
canonical_url: "https://dirskills.com/skills/systems-theory-discovery"
---

# Systems Theory Discovery

Systems Theory Discovery routes requests about eBPF, compilers, type systems, IR, and formal methods to the relevant skills. Use it when working on tracing, parsers, SMT, Lean, or theorem proving.

**Install:**

```bash
npx degit https://github.com/rand/cc-polymath/tree/main/skills/discover-systems-theory ~/.claude/skills/discover-systems-theory
```

## README

# 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)
1. **ebpf-fundamentals** - eBPF programs, verifier, maps
2. **ebpf-networking** - XDP, TC, socket filtering
3. **ebpf-security-monitoring** - LSM hooks, syscall tracing
4. **ebpf-tracing-observability** - kprobes, tracepoints, profiling

### Information Retrieval (5 skills)
1. **ir-search-fundamentals** - Indexing, tokenization, TF-IDF, BM25
2. **ir-query-understanding** - Query parsing, expansion, intent
3. **ir-ranking-reranking** - Learning to rank, cross-encoders
4. **ir-vector-search** - Embeddings, ANN, HNSW, FAISS
5. **ir-recommendation-systems** - Collaborative/content-based filtering

### Programming Language Theory (13 skills)
1. **type-systems** - Type theory, inference, polymorphism
2. **lambda-calculus** - Lambda calculus, reduction, Church encodings
3. **curry-howard** - Propositions as types, proofs as programs
4. **dependent-types** - Dependent types, refinement types
5. **operational-semantics** - Small-step, big-step semantics
6. **program-verification** - Hoare logic, invariants, correctness
7. **structure-editors** - Structural editing, projectional editors
8. **hazelnut-calculus** - Hazelnut typed holes calculus
9. **live-programming-holes** - Live programming with typed holes
10. **typed-holes-foundations** - Typed holes theory and foundations
11. **typed-holes-interaction** - Interactive typed hole filling
12. **typed-holes-llm** - LLM-powered typed hole completion
13. **typed-holes-semantics** - Typed holes formal semantics

### Formal Methods (10 skills)
1. **z3-solver-basics** - Z3 SMT solver, constraints, assertions
2. **sat-solving-strategies** - SAT solving, DPLL, CDCL
3. **smt-theory-applications** - SMT theories, bitvectors, arrays
4. **lean-proof-basics** - Lean 4 basics, tactics, terms
5. **lean-tactics** - Advanced Lean tactics and automation
6. **lean-theorem-proving** - Theorem proving patterns in Lean
7. **lean-mathlib4** - Mathlib4 library usage
8. **csp-modeling** - Constraint satisfaction problems
9. **constraint-propagation** - Arc consistency, propagation
10. **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