Rei-PL Prover v0.1: A D-FUMT-8-Native Proof Assistant Prototype (Rei-AIOS Paper 137)
Abstract
Introduces Rei-PL Prover v0.1, a prototype D-FUMT-8-native proof assistant that complements Lean 4 / Mathlib by providing native eight-valued propositional semantics. Unlike Lean 4's two-valued Prop, Rei-PL Prover's base judgment carries one of 8 truth values (TRUE / FALSE / BOTH / NEITHER / INFINITY / ZERO / FLOWING / SELF), enabling direct machine verification of D-FUMT-8 laws that Lean 4 can only encode via opaque axioms. 160-line prototype implementation in 4 modules (types, checker, theorems, lean4-export). 3 toy theorems machine-checked: Peace Axiom #196 = TRUE, AND(BOTH, BOTH) = BOTH (Belnap idempotence), AND(FLOWING, FLOWING) = FLOWING (Heraclitus impermanence). 16/16 unit tests pass. One-way Lean 4 export bridge with zero-sorry compilation under Mathlib v4.27. Honest positioning: prototype-grade (160 LOC vs Lean 4 core ~50,000 LOC); Lean 4 export is lossy (D-FUMT-8 non-classical values become opaque Prop axioms); no Mathlib-equivalent library yet (Phase 2); no self-hosting (Phase 3); no neural tactic search (Phase 4). The paper does NOT claim to replace Lean 4; it claims (1) D-FUMT-8 proof assistants are implementable, (2) three toy theorems genuinely require 8-valued semantics, (3) the Lean 4 bridge establishes co-evolution feasibility, (4) Peace Axiom #196 is a first-class structural invariant. Paper 137 was drafted on 2026-04-24 and held for 3 days before publication on 2026-04-27.
Fields of Study & Subjects
Logic
programming
and type systems
Reasoning
and Knowledge
Artificial Intelligence in Games
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 27 April 2026