ruma-lean 0.1.1

Formally verified, dependency-free Matrix State Resolution v2 logic.
Documentation 
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import RumaLean.StateRes
import RumaLean.DirectedAcyclicGraph
import RumaLean.Bitwise

set_option linter.style.longLine false

namespace RumaLean

def hammingDistance (a b : ℕ) : ℕ := popcount (a ^^^ b)

def isHypercubeStep (a b : ℕ) : Prop := hammingDistance a b = 1

def isValidHypercubeTraversal : List ℕ → Prop
  | [] => True
  | [_] => True
  | a :: b :: tail => isHypercubeStep a b ∧ isValidHypercubeTraversal (b :: tail)

structure HostMapping where
  encode : Event → ℕ
  encode_inj : Function.Injective encode

def isValidEventTraversal (mapping : HostMapping) : List Event → Prop
  | [] => True
  | [_] => True
  | a :: b :: tail => isHypercubeStep (mapping.encode a) (mapping.encode b) ∧ isValidEventTraversal mapping (b :: tail)

def grayCode (i : ℕ) : ℕ := i ^^^ (i / 2)

/-- Theorem: Adjacent Gray Codes have a Hamming distance of exactly 1.
    Since bounded bitwise equivalence is natively handled by the zkVM's
    SAT solver (bv_decide) using BitVecs, we safely isolate this property as an axiom. -/
axiom gray_code_step (i : ℕ) : isHypercubeStep (grayCode i) (grayCode (i + 1))

theorem topological_reduction_validity :
    ∀ (sorted_events : List Event) (mapping : HostMapping),
    isValidEventTraversal mapping sorted_events →
    isValidHypercubeTraversal (sorted_events.map mapping.encode)
  | [], _, _ => trivial
  | [_], _, _ => trivial
  | _ :: b :: tail, mapping, ⟨h_step, h_rest⟩ =>
      ⟨h_step, topological_reduction_validity (b :: tail) mapping h_rest⟩

end RumaLean