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mrwulf
24a9fb653a
Reusable infrastructure for the scalar Range-loop reductions (sub_loop, add_loop, conditional_add_l). Re-stated standalone so scalar proofs stay independent of the field gen tree. Compiles axiom-clean. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
62 lines
3.1 KiB
Text
62 lines
3.1 KiB
Text
/- ──────────────────────────────────────────────────────────────────────────────
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Proofs/ScalarLoop.lean — generic loop-combinator lemmas for the scalar
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layer's `for i in 0..5` reductions (sub_loop, add_loop, conditional_add_l).
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These three lemmas are identical in statement to the field layer's
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(Proofs/AddSpec.lean); they are about `Aeneas.Std.loop` and the transpiled
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`core::iter::range` iterator, NOT about any field/scalar specifics, so they
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are re-stated here to keep the scalar proofs independent of the field gen.
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────────────────────────────────────────────────────────────────────────────── -/
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import Proofs.ScalarDenote
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open Aeneas Aeneas.Std Result ControlFlow
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open curve25519_dalek
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namespace ScalarProofs
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open Aeneas.Std.WP
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/-- Peel one iteration of the `Aeneas.Std.loop` fixed point under a `spec` goal. -/
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theorem loop_step {α : Type u} {β : Type v}
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{body : α → Result (ControlFlow α β)} {x : α} {post : β → Prop}
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(h : body x ⦃ r => match r with
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| .cont x' => Aeneas.Std.loop body x' ⦃ post ⦄
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| .done y => post y ⦄) :
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Aeneas.Std.loop body x ⦃ post ⦄ := by
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obtain ⟨r, hr, hpost⟩ := spec_imp_exists h
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rw [Aeneas.Std.loop.eq_def, hr]
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cases r <;> simpa using hpost
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/-- `Iterator::next` on a not-yet-finished `usize` range: yields `some start`
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and advances `start`. -/
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theorem range_next_lt_spec (r : core.ops.range.Range Usize)
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(h : r.start.val < r.«end».val) :
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core.iter.range.IteratorRange.next core.iter.range.StepUsize r
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⦃ (o, r') => o = some r.start ∧ r'.start.val = r.start.val + 1 ∧
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r'.«end» = r.«end» ⦄ := by
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have hmax : r.start.val + 1 ≤ Usize.max := by scalar_tac
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have hca := Usize.checked_add_bv_spec r.start 1#usize
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unfold core.iter.range.IteratorRange.next
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simp only [core.cmp.impls.PartialOrdUsize.lt,
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core.clone.impls.CloneUsize.clone, core.iter.range.StepUsize.forward_checked,
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liftFun1, liftFun2, bind_tc_ok]
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simp only [h, decide_true, if_true]
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cases hadd : Usize.checked_add r.start 1#usize with
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| none => rw [hadd] at hca; simp at hca; scalar_tac
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| some n =>
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rw [hadd] at hca
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simp at hca
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simp [spec_ok, hca]
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/-- `Iterator::next` on a finished `usize` range: yields `none`, range unchanged. -/
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theorem range_next_ge_spec (r : core.ops.range.Range Usize)
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(h : r.«end».val ≤ r.start.val) :
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core.iter.range.IteratorRange.next core.iter.range.StepUsize r
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⦃ (o, r') => o = none ∧ r' = r ⦄ := by
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unfold core.iter.range.IteratorRange.next
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simp only [core.cmp.impls.PartialOrdUsize.lt,
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core.clone.impls.CloneUsize.clone, core.iter.range.StepUsize.forward_checked,
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liftFun1, liftFun2, bind_tc_ok]
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have : ¬ (r.start.val < r.«end».val) := by omega
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simp [this]
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end ScalarProofs
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