import HyperKitty.QLG
import HyperKitty.QRA
import HyperKitty.SLA
import HyperKitty.TripartiteIsomorphism

/-! # Routing Pipeline Formalization

This module formalizes the 11-stage routing pipeline.
-/

-- Stage 1: RegexParser - Tokenization
structure RegexParser : Type where
  parse : String → Option (List String)

-- Stage 2: ASTBuilder - Construct typed AST
inductive ASTNode : Type where
  | Structural : String → ASTNode
  | Payload : String → ASTNode
  
structure AST : Type where
  nodes : List ASTNode
  
structure ASTBuilder : Type where
  build : List String → Option AST

-- Stage 3: SymbolicGraph - Weighted adjacency matrix
def WeightedGraph := List (List Float)

structure SymbolicGraph : Type where
  fromAST : AST → Option WeightedGraph

-- Stage 4: JordanTransformer - Spectral analysis
structure SpectralResults : Type where
  radius : Float
  features : List Float
  
structure JordanTransformer : Type where
  transform : WeightedGraph → Option SpectralResults

-- Stage 5: JacobianLens - Sensitivity analysis
structure Sensitivity : Type where
  deadPaths : List Nat
  condition : Float
  
structure JacobianLens : Type where
  analyze : SpectralResults → Option Sensitivity

-- Stage 6: ConstraintEval - Validity predicates
structure ConstraintEval : Type where
  evaluate : AST → Bool

-- Stage 7: SparseActivation - Candidate experts
type ExpertId := Nat

structure SparseActivation : Type where
  activate : AST → List ExpertId

-- Stage 8: RoutingNodes - Convert to routing nodes
structure RoutingNode : Type where
  expert : ExpertId
  weight : Float
  
structure RoutingNodes : Type where
  convert : List ExpertId → List RoutingNode

-- Stage 9: NANDFilter - Remove incompatible routes
structure NANDFilter : Type where
  filter : List RoutingNode → List RoutingNode

-- Stage 10: AgentDispatch - Execute experts
structure AgentDispatch : Type where
  dispatch : List RoutingNode → Option (List (ExpertId × String))

-- Stage 11: MergeOutput - Recombine output
structure MergeOutput : Type where
  merge : List String → String

-- Full pipeline
structure RoutingPipeline : Type where
  parser : RegexParser
  astBuilder : ASTBuilder
  graph : SymbolicGraph
  jordan : JordanTransformer
  jacobian : JacobianLens
  constraints : ConstraintEval
  activation : SparseActivation
  nodes : RoutingNodes
  nandFilter : NANDFilter
  dispatch : AgentDispatch
  merge : MergeOutput

-- Pipeline execution
def route (pipeline : RoutingPipeline) (input : String) : Option String :=
  let tokens := pipeline.parser.parse input else none;
  let ast := pipeline.astBuilder.build tokens else none;
  let graph := pipeline.graph.fromAST ast else none;
  let spectral := pipeline.jordan.transform graph else none;
  let sensitivity := pipeline.jacobian.analyze spectral else none;
  let _valid := pipeline.constraints.evaluate ast;
  let experts := pipeline.activation.activate ast;
  let nodes := pipeline.nodes.convert experts;
  let filtered := pipeline.nandFilter.filter nodes;
  let results := pipeline.dispatch.dispatch filtered else none;
  let output := pipeline.merge.merge results;
  some output

-- Determinism property
theorem pipeline_deterministic (pipeline : RoutingPipeline) (input : String) :
    route pipeline input = route pipeline input := by
  rfl