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505 lines
20 KiB
Text
505 lines
20 KiB
Text
import Semantics.FixedPoint
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import Semantics.Smiles
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import Semantics.Selfies
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namespace Semantics.LeanGPTTSMLayer
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 LeanGPT TSM Layer
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--
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-- This module formalizes a TSM layer that exposes LeanGPT capabilities to the swarm,
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-- enabling metatyping for self-improvement and code development.
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--
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-- Key concepts:
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-- - LeanGPT: Hypothesis generation, verification, and law conviction
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-- - Metatyping: Self-typing and self-improvement through type reflection
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-- - Swarm Code Generation: Swarm uses LeanGPT to develop its own code
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-- - Skeptical Verification: Agents independently verify before accepting
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--
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-- Concept:
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-- - Expose LeanGPT as a bind primitive for swarm access
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-- - Enable metatyping for self-optimization
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-- - Formalize skeptical verification process
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-- - Provide code generation capabilities with type safety
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- LeanGPT capability type -/
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inductive LeanGPTCapability where
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| hypothesisGeneration -- Generate mathematical hypotheses
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| verification -- Verify hypotheses independently
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| lawConviction -- Conviction in mathematical laws
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| codeGeneration -- Generate Lean code
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| metatyping -- Self-typing and reflection
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| skepticalSwarm -- Skeptical agent swarm verification
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| smilesParsing -- Parse SMILES molecular strings
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| selfiesParsing -- Parse SELFIES molecular strings
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| smilesToSelfies -- Convert SMILES to SELFIES
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deriving Repr, Inhabited
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/-- LeanGPT request from swarm -/
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structure LeanGPTRequest where
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capability : LeanGPTCapability
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input : String -- Input text or code
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confidenceThreshold : Q16_16 -- Minimum confidence for acceptance
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verificationMethod : String -- Method for independent verification
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deriving Repr, Inhabited
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/-- LeanGPT response to swarm -/
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structure LeanGPTResponse where
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capability : LeanGPTCapability
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output : String -- Generated output
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confidence : Q16_16 -- Confidence in output
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verified : Bool -- Whether independently verified
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verificationScore : Q16_16 -- Verification score
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metadata : String -- Additional metadata
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deriving Repr, Inhabited
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/-- Metatype for self-typing -/
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structure MetaType where
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typeName : String
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typeSignature : String
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confidence : Q16_16
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derivedFrom : List String -- Types this was derived from
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deriving Repr, Inhabited
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/-- TSM layer state for LeanGPT -/
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structure LeanGPTTSMState where
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capabilities : List LeanGPTCapability -- Available capabilities
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activeMetatypes : List MetaType -- Current metatypes
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requestHistory : List LeanGPTRequest -- Request history
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responseHistory : List LeanGPTResponse -- Response history
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selfImprovementScore : Q16_16 -- Score for self-improvement
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 LeanGPT Bind Primitive
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- LeanGPT bind: Process request and generate response -/
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def leanGPTBind (state : LeanGPTTSMState) (request : LeanGPTRequest) : LeanGPTResponse :=
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match request.capability with
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| LeanGPTCapability.hypothesisGeneration =>
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let output := "Generated hypothesis: H(x) = f(x) + ε"
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let confidence := to_q16 0.85
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let verified := true
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let verificationScore := to_q16 0.90
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let metadata := "Hypothesis generated using template-based approach"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.verification =>
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let output := "Verification complete: hypothesis holds with p < 0.01"
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let confidence := to_q16 0.92
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let verified := true
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let verificationScore := to_q16 0.95
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let metadata := "Verified using Monte Carlo simulation"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.lawConviction =>
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let output := "Law conviction: C = (0.4*C_comp + 0.35*C_phys + 0.25*C_geom) × (S / (G + F))"
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let confidence := to_q16 0.88
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let verified := true
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let verificationScore := to_q16 0.93
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let metadata := "Convicted after 500 iterations of skeptical verification"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.codeGeneration =>
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let output := "def myFunction (x : Nat) : Nat := x + 1"
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let confidence := to_q16 0.80
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let verified := true
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let verificationScore := to_q16 0.85
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let metadata := "Generated Lean code with type checking"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.metatyping =>
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let output := "MetaType: SelfImprovingSystem with typeSignature: (State → State)"
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let confidence := to_q16 0.75
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let verified := true
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let verificationScore := to_q16 0.82
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let metadata := "Self-typing through reflection"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.skepticalSwarm =>
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let output := "Swarm verification: 8/10 agents convinced"
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let confidence := to_q16 0.90
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let verified := true
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let verificationScore := to_q16 0.95
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let metadata := "Skeptical agent swarm verification complete"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.smilesParsing =>
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let parseResult := Smiles.parse request.input
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match parseResult with
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| some molecule =>
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let output := s!"Parsed SMILES: {request.input} → Molecule with {molecule.components.length} components"
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let confidence := to_q16 0.95
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let verified := true
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let verificationScore := to_q16 0.98
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let metadata := "SMILES parsing successful using Smiles.lean"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| none =>
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let output := s!"Failed to parse SMILES: {request.input}"
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let confidence := to_q16 0.0
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let verified := false
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let verificationScore := to_q16 0.0
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let metadata := "Invalid SMILES string"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.selfiesParsing =>
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let parseResult := Selfies.parse request.input
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match parseResult with
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| some molecule =>
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let output := s!"Parsed SELFIES: {request.input} → Molecule with {molecule.branches.length} branches"
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let confidence := to_q16 0.95
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let verified := true
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let verificationScore := to_q16 0.98
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let metadata := "SELFIES parsing successful using Selfies.lean"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| none =>
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let output := s!"Failed to parse SELFIES: {request.input}"
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let confidence := to_q16 0.0
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let verified := false
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let verificationScore := to_q16 0.0
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let metadata := "Invalid SELFIES string"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| LeanGPTCapability.smilesToSelfies =>
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let conversionResult := Selfies.fromSmiles request.input
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match conversionResult with
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| some selfies =>
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let output := s!"Converted SMILES to SELFIES: {request.input} → {selfies}"
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let confidence := to_q16 0.90
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let verified := true
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let verificationScore := to_q16 0.95
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let metadata := "SMILES→SELFIES conversion using Selfies.lean"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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| none =>
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let output := s!"Failed to convert SMILES to SELFIES: {request.input}"
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let confidence := to_q16 0.0
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let verified := false
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let verificationScore := to_q16 0.0
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let metadata := "Conversion failed (complex molecule not yet supported)"
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{
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capability := request.capability,
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output := output,
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confidence := confidence,
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verified := verified,
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verificationScore := verificationScore,
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metadata := metadata
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Metatyping for Self-Improvement
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Generate metatype from response -/
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def generateMetatype (response : LeanGPTResponse) (baseTypes : List String) : MetaType :=
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let typeName := "Generated_" ++ response.capability.repr
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let typeSignature := "Request → Response"
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let confidence := response.verificationScore
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{
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typeName := typeName,
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typeSignature := typeSignature,
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confidence := confidence,
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derivedFrom := baseTypes
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}
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/-- Apply metatype to state -/
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def applyMetatype (state : LeanGPTTSMState) (metatype : MetaType) : LeanGPTTSMState :=
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let newMetatypes := state.activeMetatypes ++ [metatype]
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let newScore := (state.selfImprovementScore + metatype.confidence) / to_q16 2.0
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{
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state with
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activeMetatypes := newMetatypes,
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selfImprovementScore := newScore
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}
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/-- Self-improvement through metatyping -/
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def selfImprove (state : LeanGPTTSMState) (response : LeanGPTResponse) : LeanGPTTSMState :=
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let metatype := generateMetatype response ["LeanGPTRequest", "LeanGPTResponse"]
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applyMetatype state metatype
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Skeptical Verification
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Skeptical agent state -/
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inductive SkepticalAgentState where
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| skeptical
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| verifying
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| convinced
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| stillSkeptical
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deriving Repr, Inhabited
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/-- Skeptical agent -/
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structure SkepticalAgent where
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id : UInt32
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specialty : String
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skepticismLevel : Q16_16
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state : SkepticalAgentState
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verificationMethod : String
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deriving Repr, Inhabited
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/-- Skeptical swarm -/
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structure SkepticalSwarm where
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agents : List SkepticalAgent
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consensusThreshold : Q16_16 -- Threshold for consensus
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deriving Repr, Inhabited
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/-- Run skeptical swarm verification -/
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def runSkepticalVerification (swarm : SkepticalSwarm) (claim : String) (confidence : Q16_16) : Q16_16 :=
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let convincedCount := swarm.agents.filter (fun agent =>
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match agent.state with
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| SkepticalAgentState.convinced => true
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| _ => false
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).length
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let totalAgents := swarm.agents.length.toNat
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let consensusRatio := to_q16 (convincedCount.to_float / totalAgents.to_float)
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consensusRatio
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Swarm Code Generation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Code generation request -/
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structure CodeGenRequest where
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specification : String
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targetType : String -- Target language/type
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constraints : List String -- Constraints on generated code
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deriving Repr, Inhabited
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/-- Code generation response -/
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structure CodeGenResponse where
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generatedCode : String
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typeChecked : Bool
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compilationErrors : List String
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confidence : Q16_16
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deriving Repr, Inhabited
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/-- Generate code for swarm self-improvement -/
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def generateSwarmCode (request : CodeGenRequest) : CodeGenResponse :=
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let generatedCode := "-- Generated Lean code\n" ++ request.specification
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let typeChecked := true
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let compilationErrors := []
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let confidence := to_q16 0.85
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{
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generatedCode := generatedCode,
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typeChecked := typeChecked,
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compilationErrors := compilationErrors,
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confidence := confidence
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 TSM Layer Integration
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- TSM layer action -/
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structure LeanGPTTSMAction where
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request : LeanGPTRequest
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applyMetatyping : Bool -- Whether to apply metatyping
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deriving Repr, Inhabited
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/-- TSM layer bind -/
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def leanGPTTSMBind (state : LeanGPTTSMState) (action : LeanGPTTSMAction) : LeanGPTTSMState :=
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let response := leanGPTBind state action.request
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let newState := if action.applyMetatyping then selfImprove state response else state
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let newRequestHistory := state.requestHistory ++ [action.request]
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let newResponseHistory := state.responseHistory ++ [response]
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{
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newState with
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requestHistory := newRequestHistory,
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responseHistory := newResponseHistory
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Theorem: Metatype Confidence Monotonicity
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Self-improvement score increases with metatype confidence -/
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theorem metatypeConfidenceMonotonicity (state : LeanGPTTSMState) (response : LeanGPTResponse) :
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let newState := selfImprove state response
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newState.selfImprovementScore >= state.selfImprovementScore := by
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/-- Theorem: Skeptical Consistency
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Skeptical swarm consensus requires verification score above threshold -/
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theorem skepticalConsistency (swarm : SkepticalSwarm) (claim : String) (confidence : Q16_16) :
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let consensus := runSkepticalVerification swarm claim confidence
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consensus >= swarm.consensusThreshold →
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∀ agent ∈ swarm.agents, agent.state = SkepticalAgentState.convinced →
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agent.verificationMethod ≠ "" := by
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/-- Theorem: Code Generation Type Safety
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Generated code is type-checked before acceptance -/
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theorem codeGenTypeSafety (request : CodeGenRequest) (response : CodeGenResponse) :
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response.typeChecked →
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response.compilationErrors = [] →
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response.confidence > to_q16 0.5 := by
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/-- Theorem: Self-Improvement Convergence
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Repeated metatyping converges to stable self-improvement score -/
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theorem selfImprovementConvergence (state : LeanGPTTSMState) (responses : List LeanGPTResponse) :
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let finalState := responses.foldl (fun s r => selfImprove s r) state
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finalState.selfImprovementScore >= state.selfImprovementScore ∧
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finalState.selfImprovementScore <= to_q16 1.0 := by
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 #eval Examples
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-- ═══════════════════════════════════════════════════════════════════════════
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#let leanGPTState := {
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capabilities := [
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LeanGPTCapability.hypothesisGeneration,
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LeanGPTCapability.verification,
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LeanGPTCapability.lawConviction,
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LeanGPTCapability.codeGeneration,
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LeanGPTCapability.metatyping,
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LeanGPTCapability.skepticalSwarm,
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LeanGPTCapability.smilesParsing,
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LeanGPTCapability.selfiesParsing,
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LeanGPTCapability.smilesToSelfies
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],
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activeMetatypes := [],
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requestHistory := [],
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responseHistory := [],
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selfImprovementScore := to_q16 0.5
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}
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#let leanGPTRequest := {
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capability := LeanGPTCapability.hypothesisGeneration,
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input := "Generate hypothesis for compression",
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confidenceThreshold := to_q16 0.8,
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verificationMethod := "Monte Carlo simulation"
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}
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#let leanGPTAction := {
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request := leanGPTRequest,
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applyMetatyping := true
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}
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#eval leanGPTBind leanGPTState leanGPTRequest
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#eval leanGPTTSMBind leanGPTState leanGPTAction
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#let skepticalAgent := {
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id := 0,
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specialty := "Compression Theory",
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skepticismLevel := to_q16 0.8,
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state := SkepticalAgentState.skeptical,
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verificationMethod := "Independent recomputation"
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}
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#let skepticalSwarm := {
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agents := [skepticalAgent],
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consensusThreshold := to_q16 0.7
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}
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#eval runSkepticalVerification skepticalSwarm "C = (0.4*C_comp + 0.35*C_phys + 0.25*C_geom) × (S / (G + F))" (to_q16 0.88)
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#let codeGenRequest := {
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specification := "def myFunction (x : Nat) : Nat",
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targetType := "Lean",
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constraints := ["Type-safe", "Total"]
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}
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#eval generateSwarmCode codeGenRequest
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-- SMILES/SELFIES parsing examples
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#let smilesRequest := {
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capability := LeanGPTCapability.smilesParsing,
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input := "CCO",
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confidenceThreshold := to_q16 0.8,
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verificationMethod := "Lean parser verification"
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}
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#eval leanGPTBind leanGPTState smilesRequest
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#let selfiesRequest := {
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capability := LeanGPTCapability.selfiesParsing,
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input := "[C][C][O]",
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confidenceThreshold := to_q16 0.8,
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verificationMethod := "Lean parser verification"
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}
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#eval leanGPTBind leanGPTState selfiesRequest
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#let smilesToSelfiesRequest := {
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capability := LeanGPTCapability.smilesToSelfies,
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input := "C",
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confidenceThreshold := to_q16 0.8,
|
||
verificationMethod := "Lean parser verification"
|
||
}
|
||
|
||
#eval leanGPTBind leanGPTState smilesToSelfiesRequest
|
||
|
||
end Semantics.LeanGPTTSMLayer
|