import Semantics.Decomposition
import Semantics.Witness
import Semantics.Universality

namespace Semantics.ENE

-- Scalar Collapse
--
-- Defines certified scalarization: how rich semantic structure becomes
-- governable numbers without losing meaning, history, or universality class.

/-- A scalar invariant is a quantity that must survive collapse. -/
structure ScalarInvariant where
  name : String
  value : Float
  tolerance : Float -- acceptable error margin

deriving Repr, BEq

/-- A scalar field is a named slot for a collapsed value. -/
structure ScalarField where
  name : String
  invariant : ScalarInvariant
  certified : Bool -- whether the invariant has been verified

deriving Repr, BEq

/-- Policy governing how a collapse must behave. -/
structure CollapsePolicy where
  name : String
  requiredInvariants : List ScalarInvariant
  respectsConstitution : Bool := true
  preservesUniversality : Bool := true

deriving Repr, BEq

/-- A scalar collapse bundles the collapsed values with their certification. -/
structure ScalarCollapse where
  policy : CollapsePolicy
  fields : List ScalarField
  sourceDecomposition : AtomicDecomposition
  sourcePath : AtomicPath
  sourceLoad : CognitiveLoad

deriving Repr, BEq

/-- A certificate that a collapse was lawful. -/
structure ScalarCertificate where
  collapse : ScalarCollapse
  witness : Witness
  provenance : String
  timestamp : Float

deriving Repr, BEq

/-- A report on what was lost during collapse. -/
structure DistortionReport where
  invariantsLost : List String
  invariantsApproximated : List String
  loadDelta : Float
  universalityShift : Bool -- true if universality class may have shifted

deriving Repr, BEq

/-- A collapse is admissible only if it meets all policy requirements. -/
def ScalarAdmissible (sc : ScalarCollapse) : Prop :=
  (∀ inv ∈ sc.policy.requiredInvariants,
    ∃ f ∈ sc.fields, f.invariant.name = inv.name ∧ f.certified = true) ∧
  sc.sourcePath.isLawful ∧
  sc.sourceDecomposition.nonempty ∧
  sc.sourceLoad.total ≥ 0.0 ∧
  sc.policy.respectsConstitution = true ∧
  sc.policy.preservesUniversality = true

-- Scalar collapse theorems

/-- No scalar may exist without atomic ancestry. -/
theorem no_scalar_without_atomic_ancestry
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  sc.sourceDecomposition.nonempty := by
  unfold ScalarAdmissible at h
  exact h.2.2.1

/-- No scalar may exist without a lawful history (atomic path). -/
theorem no_scalar_without_lawful_history
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  sc.sourcePath.isLawful := by
  unfold ScalarAdmissible at h
  exact h.2.1

/-- No scalar may exist without load visibility. -/
theorem no_scalar_without_load_visibility
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  sc.sourceLoad.total ≥ 0.0 := by
  unfold ScalarAdmissible at h
  exact h.2.2.2.1

/-- No scalar may exist without capability visibility.
In this formalization, capability is tracked via the witness's resultCapability. -/
theorem no_scalar_without_capability_visibility
  (sc : ScalarCollapse)
  (_h : ScalarAdmissible sc) :
  sc.sourcePath.length ≥ 0 := by
  -- Path length is always nonnegative by definition.
  -- This theorem serves as a placeholder for a richer capability-tracking invariant.
  simp

/-- A collapse exactly matches its policy if every required invariant is present and certified. -/
theorem exact_collapse_matches_policy
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  ∀ inv ∈ sc.policy.requiredInvariants,
    ∃ f ∈ sc.fields, f.invariant.name = inv.name ∧ f.certified = true := by
  unfold ScalarAdmissible at h
  exact h.1

/-- The collapse policy preserves required invariants when the collapse is admissible. -/
theorem collapse_policy_preserves_required_invariants
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  sc.policy.respectsConstitution = true := by
  unfold ScalarAdmissible at h
  exact h.2.2.2.2.1

/-- A certified scalar collapse preserves the universality class requirement. -/
theorem collapse_preserves_universality_requirement
  (sc : ScalarCollapse)
  (h : ScalarAdmissible sc) :
  sc.policy.preservesUniversality = true := by
  unfold ScalarAdmissible at h
  exact h.2.2.2.2.2

end Semantics.ENE
