docs(10_Wiki): 위키 전체 재구성 — Topic_* 폴더를 4개 카테고리로 통합 + 대규모 중복 제거
Topic_Agent/Topic_Blog/Topics/Topics_Biz/Topics_Meeting/Topics_Rag의 마크다운 지식 문서를 Topic_General/Topic_Programming/Topic_Graphic/Topic_Business 4개 카테고리로 재분류. - 중복 제거: frontmatter의 status:duplicate/merged + duplicate_of/redirect_to 필드로 자기 자신을 중복으로 선언한 리다이렉트 stub 1032개 제거, 완전 동일 내용 파일 472개 제거, 동일 파일명·다른 내용 충돌 시 더 큰(완전한) 버전만 유지(162개 제거) — 총 1639개 중복 제거. - 분류: 폴더 단위로 명확한 항목(AI_and_ML/Coding/Architecture 등 → Programming, Comfyui/Visual_Effects → Graphic, Topics_Biz/Topics_Meeting/사업 등 → Business, Poetic_Blog_Writing/창의성/Game_Design 등 → General)은 폴더 우선순위로, 나머지 혼재 폴더(Topic_Agent/Topic_Blog/Topics 루트/Thinking & Reasoning/Other/UI_UX_Assets)는 title/tags 키워드 스코어링으로 파일 단위 분류(불명확한 경우 General로 폴백). 원본 폴더명은 "From_*" 서브폴더로 보존해 추적 가능성 유지. - 최종 배치: Programming 2784 / General 1608 / Graphic 285 / Business 249 = 4926개 문서. - 에이전트 운영 상태(.astra/.agent/.obsidian/sessions/memory/_company/docs/lessons/_shared/src)는 지식 콘텐츠가 아니므로 재분류 대상에서 제외하고 원위치 유지. - Topics/Topic_email(상위 보호 폴더 Topic_email과 파일명 100% 중복) 삭제 — 보호 폴더 자체는 미변경. - 완전히 비게 된 Topic_Agent/Topic_Blog/Topics_Biz/Topics_Rag 폴더 제거.
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Antigravity Agent
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---
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id: wiki-2026-0508-formal-verification-of-software
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title: Formal Verification of Software
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Formal Methods, Program Verification]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [formal-methods, verification, correctness]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Coq/Lean/TLA+
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framework: Dafny/F*
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---
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# Formal Verification of Software
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## 매 한 줄
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> **"매 prove correctness, 매 test correctness 의 X"**. Formal verification 의 mathematical proof 의 program 의 specification 에 대한 conformance — 매 testing 의 fundamental superset. 2026 의 industrial use 의 expanding (AWS s2n-tls, sel4, CompCert, Cardano, Dafny in MS, Lean 4 의 mathlib).
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## 매 핵심
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### 매 Spectrum of rigor
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1. **Type systems**: lightweight, daily (TypeScript, Rust borrow checker).
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2. **Property-based testing**: empirical, partial (QuickCheck).
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3. **Model checking**: finite-state exhaustive (TLA+, SPIN).
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4. **Deductive verification**: machine-checked proofs (Coq, Lean, Dafny, F*).
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5. **Refinement**: high-level spec → low-level impl preserves properties (Event-B).
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### 매 Tools (2026 leaders)
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- **TLA+**: distributed system specs (used by AWS, Azure for protocols).
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- **Coq / Lean 4**: dependent types, proof assistant.
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- **Dafny**: verification-aware imperative language (MS).
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- **F***: ML-style with refinement types (HACL* crypto, EverParse).
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- **Kani / Creusot**: Rust verification.
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- **CBMC**: bounded model checker for C.
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### 매 What gets verified
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- Algorithmic correctness (sorting, hashing).
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- Protocol safety (no deadlock, agreement).
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- Memory safety (no UAF, overflow).
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- Cryptographic implementations (HACL* used in Linux, Firefox).
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- Compiler correctness (CompCert).
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- OS kernel (seL4 — full functional correctness).
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### 매 응용
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1. Safety-critical (avionics DO-178C Level A, automotive ISO 26262).
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2. Crypto libraries (HACL*, Project Everest).
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3. Distributed protocols (Paxos, Raft TLA+).
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4. Smart contracts (Cardano Plutus, MoveProver).
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5. Compilers / kernels (CompCert, seL4).
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## 💻 패턴
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### TLA+ — distributed mutex spec
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```tla
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---- MODULE Mutex ----
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EXTENDS Naturals
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VARIABLES queue, holder
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Init == queue = <<>> /\ holder = NULL
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Request(p) == queue' = Append(queue, p) /\ UNCHANGED holder
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Acquire == /\ queue # <<>>
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/\ holder = NULL
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/\ holder' = Head(queue)
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/\ queue' = Tail(queue)
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MutualExclusion == \A p, q \in Procs : holder = p /\ holder = q => p = q
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THEOREM Spec => []MutualExclusion
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====
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```
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### Dafny — verified binary search
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```dafny
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method BinarySearch(a: array<int>, key: int) returns (idx: int)
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requires forall i, j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
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ensures 0 <= idx ==> idx < a.Length && a[idx] == key
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ensures idx < 0 ==> forall i :: 0 <= i < a.Length ==> a[i] != key
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{
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var lo, hi := 0, a.Length;
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while lo < hi
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invariant 0 <= lo <= hi <= a.Length
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invariant forall i :: 0 <= i < lo ==> a[i] < key
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invariant forall i :: hi <= i < a.Length ==> a[i] > key
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{
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var mid := (lo + hi) / 2;
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if a[mid] < key { lo := mid + 1; }
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else if a[mid] > key { hi := mid; }
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else { return mid; }
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}
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return -1;
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}
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```
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### Lean 4 — proof of a simple lemma
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```lean
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theorem add_zero (n : Nat) : n + 0 = n := by
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induction n with
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| zero => rfl
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| succ k ih => simp [Nat.succ_add, ih]
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```
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### F* refinement types
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```fsharp
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val divide : x:int -> y:int{y <> 0} -> int
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let divide x y = x / y
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// Compiler proves y <> 0 at every call site — divide-by-zero impossible
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```
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### Kani — Rust harness
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```rust
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#[kani::proof]
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fn check_sum_no_overflow() {
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let a: u32 = kani::any();
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let b: u32 = kani::any();
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kani::assume(a < 1000 && b < 1000);
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let sum = a + b;
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assert!(sum == a + b); // proven for ALL inputs in range
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}
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```
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### CBMC — bounded check on C
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```c
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#include <assert.h>
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int main() {
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int x = nondet_int();
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__CPROVER_assume(x >= 0 && x < 100);
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int y = x * x;
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assert(y >= 0);
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return 0;
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}
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// cbmc file.c → reports counterexample if assertion fails
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```
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### Property + spec hybrid (Hypothesis)
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```python
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from hypothesis import given, strategies as st
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@given(st.lists(st.integers()))
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def test_sort_preserves_length(xs):
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assert len(sorted(xs)) == len(xs)
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@given(st.lists(st.integers()))
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def test_sort_is_ordered(xs):
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s = sorted(xs)
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assert all(s[i] <= s[i+1] for i in range(len(s)-1))
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Web app daily | Strong types + property tests |
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| Distributed protocol | TLA+ model |
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| Crypto primitive | F* / HACL* |
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| Smart contract | MoveProver / Plutus |
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| OS / hypervisor | Coq / seL4-style |
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| Rust kernel code | Kani / Creusot |
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**기본값**: types everywhere + property-based for parsers + TLA+ for distributed designs + reach for proof assistants only when life/billions on the line.
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## 🔗 Graph
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- 부모: [[Computer_Science_and_Theory]]
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- 변형: [[Type-safe Error Handling Exhaustiveness Checking]] · [[TypeScript 타입 시스템 (TypeScript Type System)|Type Systems]]
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- 응용: [[Practical-Cryptography]] · [[SAST]]
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- Adjacent: [[Quality-Control]] · [[Test_Automation]]
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## 🤖 LLM 활용
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**언제**: draft TLA+ specs from prose descriptions, suggest invariants, explain failing proofs.
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**언제 X**: never trust LLM-generated proof without checker (Lean/Coq) verifying.
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## ❌ 안티패턴
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- **Spec ≠ implementation**: verify spec, ship different code.
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- **Unverified assumptions**: proofs depend on `axiom` blocks that hide bugs.
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- **Verify everything**: cost > benefit for typical CRUD.
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- **No model**: claim "formally verified" with handwaved diagram.
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## 🧪 검증 / 중복
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- Verified (Lamport TLA+ book, Pierce SF, AWS Builders Library 2024 formal methods).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — spectrum + tool examples |
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