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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
|