discover-systems-theory

Included with Lifetime

$97 forever

Automatically discover eBPF, compiler, programming language theory, information retrieval, and formal verification skills when working with kernel tracing, parsers, type systems, Z3, Lean, or theorem proving

General

What this skill does


# 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

Files: 1

Size: 3.2 KB

Complexity: 12/100

Category: General

Source: https://github.com/rand/cc-polymath/tree/main/skills/discover-systems-theory

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