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Add Trace.concat notation and apply at call sites

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Introduce `tr₁ ++< he >++ tr₂` scoped notation for `Trace.concat`
(precedence 65, right-associative, mirroring `++`) and use it
throughout Properties.lean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-27 19:45:45 -05:00
parent 1a49689edc
commit 445187837c
2 changed files with 8 additions and 6 deletions
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12
lean/Spa/Language/Properties.lean
View File

@@ -120,7 +120,7 @@ noncomputable def EndToEndTrace.concat {ρ₃ : Env} (etr₁ : EndToEndTrace g
obtain ⟨j₁, k₁, j₂, k₂, tr₂⟩ := etr₂ obtain ⟨j₁, k₁, j₂, k₂, tr₂⟩ := etr₂
refine ⟨i₁.castAdd g₂.size, List.mem_map_of_mem _ h₁, refine ⟨i₁.castAdd g₂.size, List.mem_map_of_mem _ h₁,
j₂.natAdd g₁.size, List.mem_map_of_mem _ k₂, j₂.natAdd g₁.size, List.mem_map_of_mem _ k₂,
Trace.concat tr₁.sequence_left ?_ tr₂.sequence_right⟩ tr₁.sequence_left ++< ?_ >++ tr₂.sequence_right⟩
exact List.mem_append_right _ exact List.mem_append_right _
(List.mem_product.mpr ⟨List.mem_map_of_mem _ h₂, List.mem_map_of_mem _ k₁⟩) (List.mem_product.mpr ⟨List.mem_map_of_mem _ h₂, List.mem_map_of_mem _ k₁⟩)
@@ -168,8 +168,8 @@ noncomputable def EndToEndTrace.loop (etr : EndToEndTrace g ρ₁ ρ₂) :
refine List.mem_append_left _ (List.mem_append_right _ ?_) refine List.mem_append_left _ (List.mem_append_right _ ?_)
exact List.mem_map_of_mem _ (List.mem_map_of_mem _ h₂) exact List.mem_map_of_mem _ (List.mem_map_of_mem _ h₂)
refine ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _, ?_⟩ refine ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _, ?_⟩
exact Trace.concat (Trace.single (loop_nodes_at_in ▸ EvalBasicStmtOpt.none)) hin exact Trace.single (loop_nodes_at_in ▸ EvalBasicStmtOpt.none) ++< hin >++
(Trace.concat tr.loop hout (Trace.single (loop_nodes_at_out ▸ EvalBasicStmtOpt.none))) tr.loop ++< hout >++ Trace.single (loop_nodes_at_out ▸ EvalBasicStmtOpt.none)
/-- The zero-or-more times loop has an edge to return back to the top, to continue after an iteration. -/ /-- The zero-or-more times loop has an edge to return back to the top, to continue after an iteration. -/
private lemma loop_edge_out_in : private lemma loop_edge_out_in :
@@ -186,15 +186,15 @@ noncomputable def EndToEndTrace.loop_concat (etr₁ : EndToEndTrace (Graph.loop
simp only [Graph.loop_inputs, Graph.loop_outputs, List.mem_singleton] at h₁ h₂ k₁ k₂ simp only [Graph.loop_inputs, Graph.loop_outputs, List.mem_singleton] at h₁ h₂ k₁ k₂
subst h₁; subst h₂; subst k₁; subst k₂ subst h₁; subst h₂; subst k₁; subst k₂
exact ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _, exact ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _,
Trace.concat tr₁ loop_edge_out_in tr₂⟩ tr₁ ++< loop_edge_out_in >++ tr₂⟩
/-- A loop can be executed zero times. -/ /-- A loop can be executed zero times. -/
noncomputable def EndToEndTrace.loop_empty {ρ : Env} : EndToEndTrace (Graph.loop g) ρ ρ := by noncomputable def 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 := 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 _ _)) List.mem_append_right _ (List.mem_cons_of_mem _ (List.mem_cons_self _ _))
exact ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _, exact ⟨g.loopIn, List.mem_singleton_self _, g.loopOut, List.mem_singleton_self _,
Trace.concat (Trace.single (loop_nodes_at_in ▸ EvalBasicStmtOpt.none)) hedge Trace.single (loop_nodes_at_in ▸ EvalBasicStmtOpt.none) ++< hedge >++
(Trace.single (loop_nodes_at_out ▸ EvalBasicStmtOpt.none))⟩ Trace.single (loop_nodes_at_out ▸ EvalBasicStmtOpt.none)⟩
end Loop end Loop

2
lean/Spa/Language/Traces.lean
View File

@@ -48,6 +48,8 @@ noncomputable def Trace.concat {g : Graph} {idx₁ idx₂ idx₃ idx₄ : g.Inde
| single hbs => exact Trace.edge hbs he tr₂ | single hbs => exact Trace.edge hbs he tr₂
| edge hbs he' _ ih => exact Trace.edge hbs he' (ih he tr₂) | edge hbs he' _ ih => exact Trace.edge hbs he' (ih he tr₂)
scoped notation:65 tr₁:66 " ++< " he " >++ " tr₂:65 => Trace.concat tr₁ he tr₂
/-- A beginning-to-end trace corresponding to the CFG `g`. -/ /-- A beginning-to-end trace corresponding to the CFG `g`. -/
inductive EndToEndTrace (g : Graph) (ρ₁ ρ₂ : Env) : Type inductive EndToEndTrace (g : Graph) (ρ₁ ρ₂ : Env) : Type
| intro (idx₁ : g.Index) (idx₁_mem : idx₁ ∈ g.inputs) | intro (idx₁ : g.Index) (idx₁_mem : idx₁ ∈ g.inputs)