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174 lines
5.9 KiB
Text
174 lines
5.9 KiB
Text
/-!
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# Rainbow Raccoon Compiler Logogram Projection
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This module formalizes the small claim proven by the current Python receipt:
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* a logogram can be type-admissible as a `LogogramProjection`;
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* a torn logogram can be projection-admissible after repair/quarantine;
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* the same torn logogram is not merge-admissible.
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This is intentionally not a proof that the source mathematics is true. It is a
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proof that the routing discipline separates type admission, projection
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admission, and merge admission.
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-/
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namespace Semantics.RRCLogogramProjection
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/-- Lawful RRC type-shapes currently used by the shim. -/
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inductive RRCShape where
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| signalShapedRouteCompiler
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| projectableGeometryTopology
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| cognitiveLoadField
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| cadForceProbeReceipt
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| logogramProjection
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| holdForUnlawfulOrUnderspecifiedShape
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deriving DecidableEq, Repr
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/-- RRC witness status. `candidate` is not a proof; it only admits next-stage checks. -/
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inductive WitnessStatus where
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| candidate
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| hold
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deriving DecidableEq, Repr
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/-- Semantic topology regime for a compiled logogram. -/
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inductive SemanticRegime where
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| beautifulTopologicalFolding
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| uglyAsymmetricPruning
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| horribleManifoldTearing
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deriving DecidableEq, Repr
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/-- Projection lane chosen after semantic-regime gating. -/
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inductive ProjectionLane where
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| normalProjection
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| quarantineProjection
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deriving DecidableEq, Repr
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/-- Receipt core for one compiled logogram projection. -/
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structure LogogramReceipt where
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shape : RRCShape
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status : WitnessStatus
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regime : SemanticRegime
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payloadBound : Bool
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contradictionWitness : Bool
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tearBoundary : Bool
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detachedMass : Bool
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residualLane : Bool
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deriving Repr
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/-- A tear is repaired only when it has all quarantine evidence. -/
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def hasTearRepair (r : LogogramReceipt) : Bool :=
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r.contradictionWitness && r.tearBoundary && r.detachedMass && r.residualLane
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/-- Type admission: the object has the RRC logogram shape and bounded payload. -/
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def typeAdmissible (r : LogogramReceipt) : Bool :=
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r.shape == RRCShape.logogramProjection &&
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r.status == WitnessStatus.candidate &&
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r.payloadBound
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/-- Merge admission: only non-tearing logogram projections may enter ordinary merge space. -/
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def mergeAdmissible (r : LogogramReceipt) : Bool :=
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typeAdmissible r &&
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r.regime != SemanticRegime.horribleManifoldTearing
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/-- Projection admission: non-tears project normally; repaired tears project into quarantine. -/
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def projectionAdmissible (r : LogogramReceipt) : Bool :=
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typeAdmissible r &&
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(r.regime != SemanticRegime.horribleManifoldTearing || hasTearRepair r)
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/-- Lane choice is a pure function of the semantic regime. -/
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def projectionLane (r : LogogramReceipt) : ProjectionLane :=
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if r.regime == SemanticRegime.horribleManifoldTearing then
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ProjectionLane.quarantineProjection
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else
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ProjectionLane.normalProjection
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/-- The repaired `semantic_tear` receipt from the Python bridge, abstracted to booleans. -/
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def semanticTearReceipt : LogogramReceipt :=
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{ shape := RRCShape.logogramProjection
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status := WitnessStatus.candidate
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regime := SemanticRegime.horribleManifoldTearing
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payloadBound := true
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contradictionWitness := true
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tearBoundary := true
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detachedMass := true
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residualLane := true }
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/-- An ordinary logogram projection with no tear. -/
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def ordinaryLogogramReceipt : LogogramReceipt :=
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{ shape := RRCShape.logogramProjection
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status := WitnessStatus.candidate
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regime := SemanticRegime.uglyAsymmetricPruning
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payloadBound := true
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contradictionWitness := false
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tearBoundary := false
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detachedMass := false
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residualLane := false }
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/-- A torn logogram with no repair evidence remains projection-inadmissible. -/
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def unrepairedTearReceipt : LogogramReceipt :=
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{ shape := RRCShape.logogramProjection
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status := WitnessStatus.candidate
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regime := SemanticRegime.horribleManifoldTearing
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payloadBound := true
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contradictionWitness := false
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tearBoundary := false
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detachedMass := false
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residualLane := false }
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/-! ## Executable theorem witnesses -/
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theorem semantic_tear_projects_after_repair :
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projectionAdmissible semanticTearReceipt = true := by
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native_decide
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theorem semantic_tear_does_not_merge :
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mergeAdmissible semanticTearReceipt = false := by
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native_decide
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theorem semantic_tear_uses_quarantine_lane :
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projectionLane semanticTearReceipt = ProjectionLane.quarantineProjection := by
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native_decide
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theorem unrepaired_tear_does_not_project :
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projectionAdmissible unrepairedTearReceipt = false := by
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native_decide
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theorem ordinary_logogram_projects_and_merges :
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projectionAdmissible ordinaryLogogramReceipt = true ∧
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mergeAdmissible ordinaryLogogramReceipt = true ∧
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projectionLane ordinaryLogogramReceipt = ProjectionLane.normalProjection := by
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native_decide
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/-- Any merge-admissible logogram is also projection-admissible. -/
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theorem merge_implies_projection (r : LogogramReceipt) :
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mergeAdmissible r = true -> projectionAdmissible r = true := by
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unfold mergeAdmissible projectionAdmissible
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intro h
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cases hType : typeAdmissible r
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· simp [hType] at h
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· cases hRegime : (r.regime != SemanticRegime.horribleManifoldTearing)
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· simp [hType, hRegime] at h
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· exact rfl
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/-- A repaired tear is projection-admissible but not merge-admissible. -/
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theorem repaired_tear_separates_projection_from_merge
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(r : LogogramReceipt)
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(hType : typeAdmissible r = true)
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(hTear : r.regime = SemanticRegime.horribleManifoldTearing)
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(hRepair : hasTearRepair r = true) :
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projectionAdmissible r = true ∧ mergeAdmissible r = false := by
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constructor
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· unfold projectionAdmissible
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simp [hType, hTear, hRepair]
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· unfold mergeAdmissible
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simp [hType, hTear]
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/-! ## Eval witnesses for script/readback use. -/
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#eval projectionAdmissible semanticTearReceipt
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#eval mergeAdmissible semanticTearReceipt
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#eval projectionLane semanticTearReceipt
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#eval projectionAdmissible unrepairedTearReceipt
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#eval mergeAdmissible ordinaryLogogramReceipt
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end Semantics.RRCLogogramProjection
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