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Update comments in Graph and make map be a Functor instance

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2026-06-25 17:01:27 -05:00
parent a5235f6fbc
commit c2ad0db668
2 changed files with 122 additions and 51 deletions
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26
lean/Spa/Language/Properties.lean
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@@ -17,7 +17,7 @@ section Embeddings
variable {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env}
lemma Trace.comp_left {idx₁ idx₂ : g₁.Index}
lemma Trace.overlay_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
induction tr with
@@ -29,7 +29,7 @@ lemma 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)
lemma Trace.comp_right {idx₁ idx₂ : g₂.Index}
lemma Trace.overlay_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
induction tr with
@@ -41,7 +41,7 @@ lemma 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)
lemma Trace.link_left {idx₁ idx₂ : g₁.Index}
lemma Trace.sequence_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
induction tr with
@@ -53,7 +53,7 @@ lemma 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))
lemma Trace.link_right {idx₁ idx₂ : g₂.Index}
lemma Trace.sequence_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
induction tr with
@@ -66,19 +66,19 @@ lemma Trace.link_right {idx₁ idx₂ : g₂.Index}
· exact List.mem_append_left _
(List.mem_append_right _ (List.mem_map_of_mem _ he))
lemma EndToEndTrace.comp_left (etr : EndToEndTrace g₁ ρ₁ ρ₂) :
lemma EndToEndTrace.overlay_left (etr : EndToEndTrace g₁ ρ₁ ρ₂) :
EndToEndTrace (g₁ ∙ g₂) ρ₁ ρ₂ := by
obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := etr
exact ⟨i₁.castAdd g₂.size, List.mem_append_left _ (List.mem_map_of_mem _ h₁),
i₂.castAdd g₂.size, List.mem_append_left _ (List.mem_map_of_mem _ h₂),
tr.comp_left⟩
tr.overlay_left⟩
lemma EndToEndTrace.comp_right (etr : EndToEndTrace g₂ ρ₁ ρ₂) :
lemma EndToEndTrace.overlay_right (etr : EndToEndTrace g₂ ρ₁ ρ₂) :
EndToEndTrace (g₁ ∙ g₂) ρ₁ ρ₂ := by
obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := etr
exact ⟨i₁.natAdd g₁.size, List.mem_append_right _ (List.mem_map_of_mem _ h₁),
i₂.natAdd g₁.size, List.mem_append_right _ (List.mem_map_of_mem _ h₂),
tr.comp_right⟩
tr.overlay_right⟩
lemma EndToEndTrace.concat {ρ₃ : Env} (etr₁ : EndToEndTrace g₁ ρ₁ ρ₂)
(etr₂ : EndToEndTrace g₂ ρ₂ ρ₃) : EndToEndTrace (g₁ ⤳ g₂) ρ₁ ρ₃ := by
@@ -86,7 +86,7 @@ lemma EndToEndTrace.concat {ρ₃ : Env} (etr₁ : EndToEndTrace g₁ ρ₁ ρ
obtain ⟨j₁, k₁, j₂, k₂, tr₂⟩ := etr₂
refine ⟨i₁.castAdd g₂.size, List.mem_map_of_mem _ h₁,
j₂.natAdd g₁.size, List.mem_map_of_mem _ k₂,
Trace.concat tr₁.link_left ?_ tr₂.link_right⟩
Trace.concat tr₁.sequence_left ?_ tr₂.sequence_right⟩
exact List.mem_append_right _
(List.mem_product.mpr ⟨List.mem_map_of_mem _ h₂, List.mem_map_of_mem _ k₁⟩)
@@ -182,9 +182,9 @@ theorem Stmt.cfg_sufficient {s : Stmt} {ρ₁ ρ₂ : Env}
| andThen ρ₁ ρ₂ ρ₃ s₁ s₂ _ _ ih₁ ih₂ =>
exact ih₁.concat ih₂
| ifTrue ρ₁ ρ₂ e z s₁ s₂ _ _ _ ih =>
exact ih.comp_left
exact ih.overlay_left
| ifFalse ρ₁ ρ₂ e s₁ s₂ _ _ ih =>
exact ih.comp_right
exact ih.overlay_right
| whileTrue ρ₁ ρ₂ ρ₃ e z s _ _ _ _ ih₁ ih₂ =>
exact (ih₁.loop).loop_concat ih₂
| whileFalse ρ e s _ =>
@@ -204,7 +204,7 @@ lemma Graph.wrap_inputs (g : Graph) :
lemma Graph.wrap_outputs (g : Graph) :
(Graph.wrap g).outputs = [g.wrapOutput] := rfl
private lemma not_mem_edges_castAdd_link {g₂ : Graph} (i : Fin 1)
private lemma not_mem_edges_castAdd_sequence {g₂ : Graph} (i : Fin 1)
(idx : (Graph.singleton [] ⤳ g₂).Index) :
((idx, i.castAdd g₂.size) : (Graph.singleton [] ⤳ g₂).Edge)
∉ (Graph.singleton [] ⤳ g₂).edges := by
@@ -228,6 +228,6 @@ lemma Graph.wrap_predecessors_eq_nil (g : Graph) (idx : (Graph.wrap g).Index)
subst h
rw [GGraph.predecessors, List.filter_eq_nil_iff]
intro idx' _
simpa using not_mem_edges_castAdd_link (g₂ := g ⤳ Graph.singleton []) 0 idx'
simpa using not_mem_edges_castAdd_sequence (g₂ := g ⤳ Graph.singleton []) 0 idx'
end Spa