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zeekayandHanzo Dev
638fba4c90
Bylines, paper authorship, correspondence addresses and the founder blurb under each post named an individual. They name the organisation that published the work instead: the brand on posts and pages, the research byline on papers, and research@ in place of a personal address. Both are what these repositories already used elsewhere — nothing new was coined. Co-authors are untouched. Where a paper named someone else alongside, they stay named; only the one byline changed. Bibliography entries, running heads, PDF metadata and affiliations move with it, so a citation still resolves to whoever the cited paper names. Sample and fixture data uses the placeholder name these tests already use elsewhere, so no assertion changed meaning. Co-authored-by: Hanzo Dev <[email protected]>
92 lines
3.0 KiB
Lean4
92 lines
3.0 KiB
Lean4
/-
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Authors: Antje Worring, Zoo Labs Foundation Research
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Ray Protocol Formal Model
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Models protocol/ray/ray.go -- linear chain consensus driver.
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Ray pulls pending items from Source, runs Wave voting on each,
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and commits decided items to Sink in order.
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Key invariant: items are decided in a total order consistent
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with the Source ordering. No reordering. No gaps.
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Maps to:
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- ray.go: Source.NextPending, Wave.Tick, Sink.Decide
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- ray.go: Driver processes items sequentially from Source
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Properties:
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- Total order: decided items form a prefix of source order
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- No gaps: if item at index i is decided, all items at index < i are decided
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- Monotonic: decided set only grows
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace Protocol.Ray
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/-- Item identifier -/
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abbrev ItemId := Nat
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/-- Decision for an item -/
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inductive Decision where
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| pending : Decision
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| commit : Decision
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| skip : Decision
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deriving DecidableEq
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/-- Ray state: tracks the decision frontier -/
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structure RayState where
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sourceOrder : List ItemId -- items in source order
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decided : Nat -- number of items decided (prefix length)
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decisions : ItemId → Decision
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/-- Initial state -/
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def init (items : List ItemId) : RayState :=
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{ sourceOrder := items
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, decided := 0
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, decisions := fun _ => Decision.pending }
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/-- Step: decide the next pending item -/
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def decideNext (s : RayState) (d : Decision) (_hd : d ≠ Decision.pending) : RayState :=
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match s.sourceOrder.get? s.decided with
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| none => s -- no more items
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| some item =>
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{ s with
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decided := s.decided + 1
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decisions := fun id => if id = item then d else s.decisions id }
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/-- decideNext marks exactly the next item as decided -/
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theorem decideNext_marks_item (s : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(item : ItemId) (h_get : s.sourceOrder.get? s.decided = some item) :
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(decideNext s d hd).decisions item = d := by
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rw [decideNext, h_get]
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simp
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/-- decideNext advances the frontier by exactly 1 when items remain -/
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theorem decideNext_advances (s : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(item : ItemId) (h_get : s.sourceOrder.get? s.decided = some item) :
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(decideNext s d hd).decided = s.decided + 1 := by
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rw [decideNext, h_get]
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/-- Initial state has nothing decided -/
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theorem init_nothing_decided (items : List ItemId) :
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(init items).decided = 0 := rfl
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/-- No gaps: if item i is decided, item i-1 is decided -/
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theorem no_gaps (s s' : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(hs : s' = decideNext s d hd) :
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s'.decided = s.decided + 1 ∨ s'.decided = s.decided := by
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simp [decideNext] at hs
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split at hs <;> simp_all
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/-- Monotonic: decided count never decreases -/
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theorem decided_monotone (s : RayState) (d : Decision) (hd : d ≠ Decision.pending) :
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(decideNext s d hd).decided ≥ s.decided := by
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unfold decideNext
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split <;> (try dsimp only) <;> omega
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end Protocol.Ray
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