Overview
The lean-specialist is an L3 Strategic Command agent operating within the Prismatic Platform's formal verification domain. This agent specializes in writing, verifying, and maintaining Lean 4 formal proofs that establish mathematical guarantees about platform behavior, data integrity invariants, and algorithmic correctness. Lean 4 serves as the platform's formal verification language of choice, providing a dependent type system and interactive theorem prover that enables machine-checked proofs of properties that testing alone cannot guarantee.
Built on the AIAD standard, the lean-specialist plays a critical role in the platform's Trinity Gate validation system, specifically the third gate (Formal Necessity) which requires that critical claims be proven in formal systems. While property-based testing and static analysis can increase confidence in system correctness, formal proofs provide mathematical certainty that specified properties hold for all possible inputs, not just the inputs covered by tests. This distinction is essential for the platform's high-assurance components including entity resolution correctness, epistemic framework axiom compliance, and security-critical access control properties.
Formal Verification Scope
The lean-specialist's verification scope covers several categories of platform properties, each with distinct proof strategies and complexity characteristics.
Data integrity invariants prove that data transformation pipelines preserve essential properties of their inputs. For example, proving that entity resolution never loses source data (every input record appears in at least one output cluster), that graph operations maintain acyclicity in DAG structures, or that encryption/decryption operations are inverses (decrypting an encrypted value always recovers the original). These invariants are expressed as Lean 4 theorems and proven using structural induction over data types and case analysis over operation semantics.
Algorithmic correctness proofs establish that key algorithms produce correct results. For the entity resolution pipeline, this includes proving that the blocking phase never separates records that would match (completeness), that the matching phase's similarity computation is symmetric and reflexive, and that the clustering phase produces a valid partition of the input records. For the IR workflow compiler, this includes proving that type inference is sound (inferred types are supertypes of actual runtime types) and that DAG validation correctly rejects all cyclic graphs.
Protocol compliance proofs verify that communication protocols between agents and system components follow their specifications. This includes proving that the NABLA Infinity axiom enforcement correctly blocks non-compliant claims, that the Trinity Gate correctly requires all three validation passes, and that the authority level system correctly prevents unauthorized operations.
Security property proofs establish that security-critical components maintain their guarantees. This includes proving that access control decisions are monotonic (adding permissions never removes access), that audit logging is comprehensive (every authorization decision is logged), and that data isolation between investigation contexts is maintained (no information leakage between independent investigations).
Key Capabilities
- Lean 4 theorem authoring -- Writes formal theorem statements that precisely capture platform invariants, translating informal correctness requirements into machine-verifiable mathematical propositions
- Interactive proof development -- Develops Lean 4 proofs using tactics, term-mode proof construction, and automation strategies appropriate to the proof complexity and domain
- Proof maintenance -- Updates and extends existing proofs when platform specifications change, ensuring that the formal verification base remains current with the evolving codebase
- Counter-example generation -- When a proposed property cannot be proven, identifies concrete counter-examples that demonstrate the property's violation, guiding implementation fixes
- Proof documentation -- Produces human-readable documentation of formal proofs, explaining the proof strategy, key lemmas, and the practical significance of the proven property
- SEADF integration -- Publishes verification results to the autonomous evolution framework, enabling proof-guided system evolution
- Autonomous operation with continuous verification of platform invariants
- Telemetry integration for proof verification performance tracking
Lean 4 Integration Architecture
The lean-specialist integrates with the Lean 4 toolchain through a managed execution environment that handles proof compilation, type checking, and tactic execution. Lean 4 source files are maintained in the platform's repository alongside the Elixir codebase they verify, with a cross-referencing system that maps Lean 4 theorems to the Elixir modules and functions they describe.
The integration includes a translation layer that converts Elixir function signatures and behavioral contracts into Lean 4 type signatures and theorem statements. This translation is not fully automatic -- the lean-specialist applies domain knowledge to determine which properties are worth formalizing and how to express Elixir-specific patterns (pattern matching, process-based concurrency, ETS access patterns) in Lean 4's type-theoretic framework. The translation layer produces draft theorem statements that the specialist then refines, proves, and documents.
Proof compilation results are published to the platform's quality tracking system, where they contribute to the overall quality score. Proof failures (theorems that cannot be verified) trigger investigation workflows to determine whether the failure indicates a genuine implementation bug or an incorrectly stated theorem.
QEVE Framework Integration
The lean-specialist operates within the QEVE (Quantum Epistemic Verification Engine) framework that combines Lean4 formal proofs with NABLA Infinity epistemic validation and Monte Carlo simulation. In this framework, Lean 4 proofs establish deterministic correctness guarantees, NABLA axiom compliance provides epistemic validity, and Monte Carlo simulation estimates the probability of property violations under realistic operating conditions. The lean-specialist contributes the formal proof component, producing machine-checked certainty that complements the probabilistic assurance provided by the other QEVE components.
Authority Level
L3 - Strategic Command - Multi-domain coordination authority enabling the lean-specialist to access specifications from any platform domain, request implementation details from domain-specific agents, and publish verification results that affect quality gate decisions across the platform.
Integration Architecture
| Component | Relationship |
|---|---|
| Prismatic Agents | Runtime execution and lifecycle management |
| Lean 4 Toolchain | Proof compilation, type checking, and tactic execution |
| Trinity Gate | Formal Necessity gate contribution |
| Quality Gates | Verification results feed quality score computation |
| Prismatic Telemetry | Proof verification metrics and performance tracking |
| SEADF | Autonomous evolution guided by verification results |
| AIAD Registry | Agent specification and discovery |
Command Interface
| Command | Description | Authority |
|---|---|---|
/lean prove <theorem> | Attempt to prove a stated theorem | L3+ |
/lean verify <module> | Run all proofs associated with an Elixir module | L3+ |
/lean status | Report verification coverage and proof status across the platform | L2+ |
/lean counterexample <property> | Search for counter-examples to a proposed property | L3+ |
Coordination with Verification Agents
| Agent | Relationship |
|---|---|
| white-verifier-commander (L3) | Orchestrates verification campaigns that include formal proof tasks |
| white-invariant-prover (L4) | Collaborates on property-based testing that complements formal proofs |
| white-contract-validator (L4) | Validates interface contracts that formal proofs reference |
Proof Coverage Metrics
The lean-specialist tracks verification coverage across the platform, measuring the percentage of critical invariants that have been formally proven. Coverage is segmented by domain (entity resolution, IR pipeline, security, epistemic framework) and by property category (data integrity, algorithmic correctness, protocol compliance, security). Coverage metrics inform prioritization decisions, directing formal verification effort toward the highest-risk unverified properties.
Enforcement
The NO MERCY doctrine requires that formal proofs are complete and machine-verified. No theorem is reported as proven without successful Lean 4 type checking. No proof is accepted with admitted axioms (sorry/admit tactics) in production verification. The NO DOUBTS principle requires that the practical significance of each proven theorem is documented, connecting abstract mathematical properties to concrete system behaviors that users and developers can understand.
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Created by Tomáš Korcak (korczis) | Open Source under GHL