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Proven Library Integration Plan

This document outlines how the proven library's formally verified modules integrate with Valence Shell.

Note: Valence Shell already has extensive formal proofs (256 theorems across 6 proof systems). The proven library provides Idris 2 implementations that complement existing proofs.

Applicable Modules

Core Integration (High Priority)

Module Use Case Formal Guarantee
SafeReversible Operation reversibility inverse . forward = id
SafeStateMachine Shell state transitions Valid filesystem states
SafeProvenance MAA audit trails Hash-chained accountability

Supporting Modules

Module Use Case Formal Guarantee
SafeTree Directory tree operations Coverage proofs
SafeCapability Permission modeling Least privilege
SafeResource File handle lifecycle Valid state transitions

Integration Points

1. Reversible Operations (SafeReversible)

Valence Shell's core guarantee maps directly to proven's SafeReversible:

-- vsh: rmdir(mkdir(p, fs)) = fs
-- proven: inverse . forward = id

SafeReversible.define
  forward  = mkdir path
  inverse  = rmdir path
  proof    = mkdirRmdirIdentity

2. Filesystem State Machine (SafeStateMachine)

:pristine → :modified → :staged → :committed

State transitions for operations:

  • touch: pristine → modified
  • git add: modified → staged
  • git commit: staged → committed
  • undo: * → previous (via reversibility proof)

3. MAA Audit Trail (SafeProvenance)

operation → SafeProvenance.logEntry → hash-chained audit record

Every shell operation creates a tamper-evident audit entry with:

  • Operation type and arguments
  • Before/after filesystem hash
  • User identity and timestamp
  • Previous entry hash (chain link)

Proof System Correspondence

vsh Proof System proven Equivalent Notes
Coq theorems Idris 2 dependent types Direct translation
Lean 4 proofs Idris 2 proofs Similar type theory
Agda proofs Idris 2 native Same language family
Isabelle/HOL SafeThm module Higher-order logic
Mizar SafeProof terms Set-theoretic foundation
Z3 (SMT) SafeProperty module Automated verification

Implementation Strategy

Since vsh already has proven reversibility in 6 systems, the integration focuses on:

  1. Runtime enforcement: Use proven's compiled Idris to enforce proofs at runtime
  2. Audit trail: Add SafeProvenance for MAA framework implementation
  3. Unified API: Expose proven modules as vsh shell builtins

Status

  • Theoretical alignment verified (256 theorems → proven correspondence)
  • Add SafeReversible runtime bindings
  • Integrate SafeProvenance for MAA audit trails
  • Compile proven modules to OCaml for vsh integration