Add generic Simulation template for all universality proofs#2
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Add generic Simulation template for all universality proofs#2
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Introduce Simulation and HaltingSimulation structures in SimulationEncoding.lean as a unified template for all simulation proofs. Each proof file now follows the same pattern: standalone lemmas for encode/commutes/halting, then a trivial assembly into the Simulation structure. The type checker guarantees correctness of every simulation statement. Changes: - SimulationEncoding.lean: add Simulation (encode + commutes + halting), HaltingSimulation (encode + preserves_halting), with id/compose/coercions - ComputationalMachine.lean: add Halts_of_step_none helper - All machine Defs.lean: add toComputationalMachine wrappers and iterationStep_eq_exactSteps compatibility lemmas - All proof files: add Simulation/HaltingSimulation instances with standalone lemmas + clean assembly pattern - README.md and Wiki/Status.md: update tables with template info Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
richardassar
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Apr 11, 2026
Merge PR #2 (generic Simulation/HaltingSimulation template) and update proof integrity system to cover the new framework: - Add Simulation, HaltingSimulation, toComputationalMachine to locked definitions (CLAUDE.md Rule 2) - Add all new Simulation instance theorems to keyTheorems in Integrity.lean (tmToGSSimulation, gsToTMSimulation, tagToCTSSimulation, wolfram23HaltingSimulation, rule110/124 simulations, Simulation.compose, Simulation.halting_preserved) - Resolve Status.md merge conflict: keep simulation framework sections, integrate proof integrity section
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Introduce Simulation and HaltingSimulation structures in SimulationEncoding.lean as a unified template for all simulation proofs. Each proof file now follows the same pattern: standalone lemmas for encode/commutes/halting, then a trivial assembly into the Simulation structure. The type checker guarantees correctness of every simulation statement.
Changes: