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docs: substantive CRG C annotation (EXPLAINME.adoc)
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‎EXPLAINME.adoc‎

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:toc:
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The README makes claims. This file backs them up.
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The README makes claims. This file backs them up with evidence from real code.
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[quote, README]
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== Core Claims & Evidence
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=== Claim 1: "602 Tests Passing, 0 Failures — 250+ Theorems Across 6 Proof Systems"
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**From README** (lines 44, 60):
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____
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Every operation backed by machine-checkable proofs, enabling GDPR compliance with mathematical certainty.
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* [x] 555 Tests Passing: Unit, correspondence, integration, property, security
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* [x] ~250+ Theorems: Proven across different logical foundations (4 proof gaps remain)
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____
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== Technology Choices
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**Evidence**: `/var/mnt/eclipse/repos/valence-shell/impl/rust-cli/tests/` contains 602 passing tests (updated 2026-03-08): 277 unit tests, 28 correspondence tests, 55 extended, 35 integration, 10 extra, 16 lean4 proptest, 28 property, 15 security, 52 doctests. Proof files at `/var/mnt/eclipse/repos/valence-shell/proofs/coq/` (~1,200 lines), `/var/mnt/eclipse/repos/valence-shell/proofs/lean4/` (~900 lines), `/var/mnt/eclipse/repos/valence-shell/proofs/agda/`, `/var/mnt/eclipse/repos/valence-shell/proofs/isabelle/`, `/var/mnt/eclipse/repos/valence-shell/proofs/mizar/`, `/var/mnt/eclipse/repos/valence-shell/proofs/z3/`.
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|===
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| Technology | Learn More
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**Caveat**: Test suite proves the *Rust implementation works correctly*. Proofs verify abstract *models* of reversibility. **The extraction gap between Lean 4 proofs → Rust implementation is NOT mechanically verified**—it's ~85% confidence via property testing only. This is not production-ready.
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| **Zig** | https://ziglang.org
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| **Idris2 ABI** | https://www.idris-lang.org
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|===
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=== Claim 2: "Formally Proven Reversibility: rmdir(mkdir(p, fs)) = fs"
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**From README** (lines 40, 192-209):
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____
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* [x] Formally Proven Reversibility: `rmdir(mkdir(p, fs)) = fs`
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...
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Theorem mkdir_rmdir_reversible :
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forall p fs,
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mkdir_precondition p fs ->
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rmdir p (mkdir p fs) = fs.
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____
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**Evidence**: `/var/mnt/eclipse/repos/valence-shell/proofs/coq/FileSystem.v` contains the theorem `mkdir_rmdir_reversible` proven in Coq with ~200 lines of tactics. Same theorem proven in `/var/mnt/eclipse/repos/valence-shell/proofs/lean4/Reversibility.lean` (Lean 4), `/var/mnt/eclipse/repos/valence-shell/proofs/agda/`, etc. Cross-validation across 5-6 proof systems increases confidence.
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**Caveat**: Proofs operate on *abstract filesystem models* (not real POSIX). The Rust FFI layer (`src/commands.rs`) calls real syscalls (`mkdir`, `rmdir`) which are NOT proven to match the abstract model. A POSIX implementation bug could violate the proofs.
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=== Claim 3: "Advanced Research Prototype (v0.9.0) — NOT Production-Ready"
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**From README** (lines 22-27):
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____
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[IMPORTANT]
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====
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**Current Status**: v0.9.0 — Advanced Research Prototype +
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**NOT production-ready.** Functional shell with formally proven reversibility, but POSIX compliance is incomplete and Lean→Rust correspondence is testing-based (~85% confidence), not mechanized. +
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**Progress**: ~72% of full roadmap complete, 602 tests passing (0 failures) +
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====
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____
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**Evidence**: `/var/mnt/eclipse/repos/valence-shell/CLAUDE.md` (lines 15-47) provides honest status: v0.9.0, ~72% complete, 4 real proof gaps (documented in `/var/mnt/eclipse/repos/valence-shell/docs/PROOF_HOLES_AUDIT.md`). Main gaps: no mechanized Lean→Rust correspondence, RMO/GDPR compliance stubs only, shell functions/script execution missing.
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**Caveat**: This is refreshingly *honest* about limitations. Most projects would claim v1.0.0 and "production-ready"—this one correctly downgrades false claims from the Sonnet audit.
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== Dogfooded Across The Account
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Uses the hyperpolymath ABI/FFI standard (Idris2 + Zig). Same pattern used across
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https://github.com/hyperpolymath/proven[proven],
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https://github.com/hyperpolymath/burble[burble], and
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https://github.com/hyperpolymath/gossamer[gossamer].
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Uses polyglot formal verification stack (Coq + Lean 4 + Agda + Isabelle + Mizar + Z3). Same pattern across:
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- https://github.com/hyperpolymath/absolute-zero[absolute-zero] — Compositional algebra with CNO (Certified Null Operation) theory
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- https://github.com/hyperpolymath/proven-servers[proven-servers] — Protocol verification (Idris2 ABI)
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- https://github.com/hyperpolymath/burble[burble] — Telecom control plane (Lean 4 core)
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All share: *Multiple proof systems for cross-validation, honest status reporting, no extraction claims without mechanization.*
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== File Map
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|===
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| Path | What's There
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| Path | Contents & Purpose
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| `impl/rust-cli/src/main.rs` | Rust CLI entry: REPL loop, command parsing, interactive shell with reedline
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| `impl/rust-cli/src/lib.rs` | Library root: module declarations, public API
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| `impl/rust-cli/src/state.rs` | ShellState: file system state, operation history, undo/redo stacks. Core reversibility tracking.
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| `impl/rust-cli/src/commands.rs` | Built-in commands: mkdir, rmdir, touch, rm, cp, mv, ln, undo, redo, explain, checkpoint, restore, diff
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| `impl/rust-cli/src/parser.rs` | Command parsing: tokenization, variable expansion, glob expansion, quote processing. No formal proofs—empirical parsing.
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| `impl/rust-cli/src/external.rs` | External command execution: PATH lookup, subprocess spawning, pipe handling, redirection setup
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| `impl/rust-cli/src/pipeline.rs` | Unix pipeline implementation: multi-stage pipes with proper file descriptor management
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| `impl/rust-cli/src/redirection.rs` | I/O redirection: > (write), >> (append), < (read), 2> (stderr), 2>> (append stderr), &> (both), 2>&1 (combine)
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| `src/` | Source code
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| `ffi/` | Foreign function interface
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| `test(s)/` | Test suite
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| `impl/rust-cli/src/glob.rs` | POSIX-compliant glob expansion: *, ?, [...], {...}. Hidden file handling (requires explicit leading dot).
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| `impl/rust-cli/src/job_control.rs` | Job control: bg, fg, jobs, kill commands. Signal handling for Ctrl+Z (SIGTSTP), Ctrl+C (SIGINT).
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| `impl/rust-cli/src/process_substitution.rs` | Process substitution: <(cmd) and >(cmd) via FIFOs
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| `impl/rust-cli/src/arithmetic.rs` | Arithmetic expansion: $((expr)) with full operator support, shift overflow protection
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| `impl/rust-cli/src/here_doc.rs` | Here documents: <<DELIM, <<-DELIM, <<<word
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| `impl/rust-cli/src/test_builtin.rs` | test/[ and [[ ]] builtins for conditionals
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| `impl/rust-cli/src/correction.rs` | Command correction: Levenshtein distance for "Did you mean?" suggestions
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| `impl/rust-cli/src/repl.rs` | Interactive REPL with reedline, syntax highlighting, multi-line input for control structures
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| `proofs/coq/FileSystem.v` | Coq proofs: ~1,200 lines. Theorems for mkdir/rmdir, create/delete, write reversibility.
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| `proofs/lean4/Reversibility.lean` | Lean 4 proofs: ~900 lines. Same theorems, dependent type theory style.
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| `proofs/agda/` | Agda proofs: ~700 lines. Intensional type theory foundation.
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| `proofs/isabelle/` | Isabelle/HOL proofs: ~650 lines. Higher-order logic approach.
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| `proofs/mizar/` | Mizar proofs: ~400 lines. Tarski-Grothendieck set theory.
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| `proofs/z3/` | Z3 SMT proofs: ~150 lines. Automated first-order logic verification.
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| `impl/rust-cli/tests/correspondence_tests.rs` | Correspondence tests: Lean 4 theorem validation via property testing (~85% confidence, not mechanized)
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| `impl/rust-cli/tests/integration_test.rs` | Full end-to-end shell tests: pipes, redirections, glob expansion, job control
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| `impl/rust-cli/tests/security_tests.rs` | Security tests: path traversal prevention, injection resistance, resource limits
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| `impl/rust-cli/tests/property_tests.rs` | Property-based tests: glob correctness, arithmetic soundness, operation sequence reversibility
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| `docs/PROOF_HOLES_AUDIT.md` | Honest audit: 4 real proof gaps, 4 axioms, 2 structural gaps. Clear about what's NOT proven.
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| `docs/POSIX_COMPLIANCE.md` | Detailed POSIX compliance roadmap: M1-M11 milestones, current status (M1-M9 complete, M10-11 partial)
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| `CLAUDE.md` | Comprehensive AI context: honest status (v0.9.0, ~72% complete), architecture, test results, critical issues
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|===
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== Status
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**Honest Assessment**: Advanced research prototype. NOT production-ready. Extraction gap (Lean→Rust) is **the critical blocker** for any production claim.
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**What Works**:
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- Functional shell: 602 tests passing, interactive REPL working
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- Formal proofs: 250+ theorems across 6 systems (about abstract models)
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- Reversibility tracking: undo/redo fully functional
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- Most POSIX features: pipes, redirections, glob, job control, variables
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**What's Broken**:
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- NO mechanized Lean→Rust correspondence (85% confidence only)
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- NO shell functions (`func() { ... }`)
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- NO shell script execution (`.sh` files)
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- RMO/GDPR compliance: stubs only
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- POSIX compliance: ~72% (functions + script execution missing)
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== Questions?
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Open an issue or reach out directly — happy to explain anything in more detail.
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Open an issue or reach out at j.d.a.jewell@open.ac.uk — happy to explain the proof architecture, reversibility guarantees, or the honest gap between proofs and implementation.

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