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Delete more LLM-generated comments from the migration

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Danila Fedorin
2026-06-23 12:29:46 -05:00
parent 21b2e3dd98
commit 7f753a4f38
18 changed files with 1 additions and 427 deletions
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49
lean/Spa/Language/Properties.lean
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@@ -1,36 +1,9 @@
/-
Port of `Language/Properties.agda`.
Correspondence:
↑-≢ (and the whole "ugly" Fin-disjointness block:
idx→f∉↑ʳᵉ, idx→f∉pair, idx→f∉cart, help, helpAll)
↦ Fin.castAdd_ne_natAdd + not_mem_edges_castAdd_link
(mathlib `List.mem_append`/`mem_map`/`mem_product`
replace the hand-rolled membership eliminations)
wrap-preds-∅ ↦ wrap_predecessors_eq_nil
wrap-input, wrap-output ↦ Graph.wrapInput/wrapOutput + wrap_inputs/wrap_outputs
Trace-∙ˡ/ʳ ↦ Trace.comp_left / Trace.comp_right
Trace-↦ˡ/ʳ ↦ Trace.link_left / Trace.link_right
Trace-loop ↦ Trace.loop
EndToEndTrace-∙ˡ/ʳ ↦ EndToEndTrace.comp_left / .comp_right
loop-edge-groups,
loop-edge-help ↦ (inlined: the four edge groups are reached through
`List.mem_append` directly)
EndToEndTrace-loop ↦ EndToEndTrace.loop
EndToEndTrace-loop² ↦ EndToEndTrace.loop_concat
EndToEndTrace-loop⁰ ↦ EndToEndTrace.loop_empty
_++_ ↦ EndToEndTrace.concat
EndToEndTrace-singleton ↦ EndToEndTrace.singleton (+ .singleton_nil)
EndToEndTrace-wrap ↦ EndToEndTrace.wrap
buildCfg-sufficient ↦ buildCfg_sufficient
-/
import Spa.Language.Traces
namespace Spa
open Graph
/-- Agda: `↑-≢`. -/
theorem Fin.castAdd_ne_natAdd {n m : ℕ} (i : Fin n) (j : Fin m) :
Fin.castAdd m i ≠ Fin.natAdd n j := by
intro h
@@ -44,7 +17,6 @@ section Embeddings
variable {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env}
/-- Agda: `Trace-∙ˡ`. -/
theorem Trace.comp_left {idx₁ idx₂ : g₁.Index}
(tr : Trace g₁ idx₁ idx₂ ρ₁ ρ₂) :
Trace (g₁ ∙ g₂) (idx₁.castAdd g₂.size) (idx₂.castAdd g₂.size) ρ₁ ρ₂ := by
@@ -57,7 +29,6 @@ theorem Trace.comp_left {idx₁ idx₂ : g₁.Index}
· rwa [show (g₁ ∙ g₂).nodes = Fin.append g₁.nodes g₂.nodes from rfl, Fin.append_left]
· exact List.mem_append_left _ (List.mem_map_of_mem _ he)
/-- Agda: `Trace-∙ʳ`. -/
theorem Trace.comp_right {idx₁ idx₂ : g₂.Index}
(tr : Trace g₂ idx₁ idx₂ ρ₁ ρ₂) :
Trace (g₁ ∙ g₂) (idx₁.natAdd g₁.size) (idx₂.natAdd g₁.size) ρ₁ ρ₂ := by
@@ -70,7 +41,6 @@ theorem Trace.comp_right {idx₁ idx₂ : g₂.Index}
· rwa [show (g₁ ∙ g₂).nodes = Fin.append g₁.nodes g₂.nodes from rfl, Fin.append_right]
· exact List.mem_append_right _ (List.mem_map_of_mem _ he)
/-- Agda: `Trace-↦ˡ`. -/
theorem Trace.link_left {idx₁ idx₂ : g₁.Index}
(tr : Trace g₁ idx₁ idx₂ ρ₁ ρ₂) :
Trace (g₁ ⤳ g₂) (idx₁.castAdd g₂.size) (idx₂.castAdd g₂.size) ρ₁ ρ₂ := by
@@ -83,7 +53,6 @@ theorem Trace.link_left {idx₁ idx₂ : g₁.Index}
· rwa [show (g₁ ⤳ g₂).nodes = Fin.append g₁.nodes g₂.nodes from rfl, Fin.append_left]
· exact List.mem_append_left _ (List.mem_append_left _ (List.mem_map_of_mem _ he))
/-- Agda: `Trace-↦ʳ`. -/
theorem Trace.link_right {idx₁ idx₂ : g₂.Index}
(tr : Trace g₂ idx₁ idx₂ ρ₁ ρ₂) :
Trace (g₁ ⤳ g₂) (idx₁.natAdd g₁.size) (idx₂.natAdd g₁.size) ρ₁ ρ₂ := by
@@ -97,7 +66,6 @@ theorem Trace.link_right {idx₁ idx₂ : g₂.Index}
· exact List.mem_append_left _
(List.mem_append_right _ (List.mem_map_of_mem _ he))
/-- Agda: `EndToEndTrace-∙ˡ`. -/
theorem EndToEndTrace.comp_left (etr : EndToEndTrace g₁ ρ₁ ρ₂) :
EndToEndTrace (g₁ ∙ g₂) ρ₁ ρ₂ := by
obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := etr
@@ -105,7 +73,6 @@ theorem EndToEndTrace.comp_left (etr : EndToEndTrace g₁ ρ₁ ρ₂) :
i₂.castAdd g₂.size, List.mem_append_left _ (List.mem_map_of_mem _ h₂),
tr.comp_left⟩
/-- Agda: `EndToEndTrace-∙ʳ`. -/
theorem EndToEndTrace.comp_right (etr : EndToEndTrace g₂ ρ₁ ρ₂) :
EndToEndTrace (g₁ ∙ g₂) ρ₁ ρ₂ := by
obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := etr
@@ -113,7 +80,6 @@ theorem EndToEndTrace.comp_right (etr : EndToEndTrace g₂ ρ₁ ρ₂) :
i₂.natAdd g₁.size, List.mem_append_right _ (List.mem_map_of_mem _ h₂),
tr.comp_right⟩
/-- Agda: `_++_` — sequencing end-to-end traces over `⤳`. -/
theorem EndToEndTrace.concat {ρ₃ : Env} (etr₁ : EndToEndTrace g₁ ρ₁ ρ₂)
(etr₂ : EndToEndTrace g₂ ρ₂ ρ₃) : EndToEndTrace (g₁ ⤳ g₂) ρ₁ ρ₃ := by
obtain ⟨i₁, h₁, i₂, h₂, tr₁⟩ := etr₁
@@ -132,7 +98,6 @@ section Loop
variable {g : Graph} {ρ₁ ρ₂ ρ₃ : Env}
/-- Agda: `Trace-loop`. -/
theorem Trace.loop {idx₁ idx₂ : g.Index} (tr : Trace g idx₁ idx₂ ρ₁ ρ₂) :
Trace (Graph.loop g) (idx₁.natAdd 2) (idx₂.natAdd 2) ρ₁ ρ₂ := by
induction tr with
@@ -155,7 +120,6 @@ private theorem loop_nodes_at_out :
(Graph.loop g).nodes g.loopOut = [] :=
Fin.append_left (fun _ : Fin 2 => []) g.nodes 1
/-- Agda: `EndToEndTrace-loop`. -/
theorem EndToEndTrace.loop (etr : EndToEndTrace g ρ₁ ρ₂) :
EndToEndTrace (Graph.loop g) ρ₁ ρ₂ := by
obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := etr
@@ -176,7 +140,6 @@ private theorem loop_edge_out_in :
refine List.mem_append_right _ ?_
exact List.mem_cons_self _ _
/-- Agda: `EndToEndTrace-loop²`. -/
theorem EndToEndTrace.loop_concat (etr₁ : EndToEndTrace (Graph.loop g) ρ₁ ρ₂)
(etr₂ : EndToEndTrace (Graph.loop g) ρ₂ ρ₃) :
EndToEndTrace (Graph.loop g) ρ₁ ρ₃ := by
@@ -187,7 +150,6 @@ theorem EndToEndTrace.loop_concat (etr₁ : EndToEndTrace (Graph.loop g) ρ₁
exact ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _,
Trace.concat tr₁ loop_edge_out_in tr₂⟩
/-- Agda: `EndToEndTrace-loop⁰`. -/
theorem EndToEndTrace.loop_empty {ρ : Env} : EndToEndTrace (Graph.loop g) ρ ρ := by
have hedge : ((g.loopIn, g.loopOut) : (Graph.loop g).Edge) ∈ (Graph.loop g).edges :=
List.mem_append_right _ (List.mem_cons_of_mem _ (List.mem_cons_self _ _))
@@ -199,24 +161,19 @@ end Loop
/-! ### Singletons, wrap, and the main result -/
/-- Agda: `EndToEndTrace-singleton`. -/
theorem EndToEndTrace.singleton {bss : List BasicStmt} {ρ₁ ρ₂ : Env}
(h : EvalBasicStmts ρ₁ bss ρ₂) : EndToEndTrace (Graph.singleton bss) ρ₁ ρ₂ :=
⟨(0 : Fin 1), List.mem_singleton_self _, (0 : Fin 1), List.mem_singleton_self _,
Trace.single h⟩
/-- Agda: `EndToEndTrace-singleton[]`. -/
theorem EndToEndTrace.singleton_nil (ρ : Env) :
EndToEndTrace (Graph.singleton []) ρ ρ :=
EndToEndTrace.singleton EvalBasicStmts.nil
/-- Agda: `EndToEndTrace-wrap`. -/
theorem EndToEndTrace.wrap {g : Graph} {ρ₁ ρ₂ : Env}
(etr : EndToEndTrace g ρ₁ ρ₂) : EndToEndTrace (Graph.wrap g) ρ₁ ρ₂ :=
(EndToEndTrace.singleton_nil ρ₁).concat (etr.concat (EndToEndTrace.singleton_nil ρ₂))
/-- Agda: `buildCfg-sufficient` — every terminating execution is witnessed by
an end-to-end trace through the control-flow graph. -/
theorem buildCfg_sufficient {s : Stmt} {ρ₁ ρ₂ : Env}
(h : EvalStmt ρ₁ s ρ₂) : EndToEndTrace (buildCfg s) ρ₁ ρ₂ := by
induction h with
@@ -235,11 +192,9 @@ theorem buildCfg_sufficient {s : Stmt} {ρ₁ ρ₂ : Env}
/-! ### The wrapped graph's entry has no predecessors (Agda's "ugly" block) -/
/-- The input of `wrap g` (Agda: `wrap-input`). -/
def Graph.wrapInput (g : Graph) : (Graph.wrap g).Index :=
(0 : Fin 1).castAdd ((g ⤳ Graph.singleton []).size)
/-- The output of `wrap g` (Agda: `wrap-output`). -/
def Graph.wrapOutput (g : Graph) : (Graph.wrap g).Index :=
Fin.natAdd 1 ((Fin.natAdd g.size (0 : Fin 1)))
@@ -249,8 +204,6 @@ theorem Graph.wrap_inputs (g : Graph) :
theorem Graph.wrap_outputs (g : Graph) :
(Graph.wrap g).outputs = [g.wrapOutput] := rfl
/-- Agda: `help`/`helpAll` — no edge of `singleton [] ⤳ g₂` ends at a
`castAdd`-injected node (all edge targets are `natAdd`s). -/
private theorem not_mem_edges_castAdd_link {g₂ : Graph} (i : Fin 1)
(idx : (Graph.singleton [] ⤳ g₂).Index) :
((idx, i.castAdd g₂.size) : (Graph.singleton [] ⤳ g₂).Edge)
@@ -268,8 +221,6 @@ private theorem not_mem_edges_castAdd_link {g₂ : Graph} (i : Fin 1)
obtain ⟨j, -, heq⟩ := List.mem_map.mp hb
exact Fin.castAdd_ne_natAdd i j heq.symm
/-- Agda: `wrap-preds-∅` — the entry node of a wrapped graph has no
incoming edges. -/
theorem Graph.wrap_predecessors_eq_nil (g : Graph) (idx : (Graph.wrap g).Index)
(h : idx ∈ (Graph.wrap g).inputs) :
(Graph.wrap g).predecessors idx = [] := by