Reorder some definitions
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -104,12 +104,26 @@ module Graphs where
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nodes : Vec (List BasicStmt) size
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edges : List Edge
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castᵉ : ∀ {n m : ℕ} .(p : n ≡ m) → (Fin n × Fin n) → (Fin m × Fin m)
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castᵉ p (idx₁ , idx₂) = (castᶠ p idx₁ , castᶠ p idx₂)
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↑ˡ-Edge : ∀ {n} → (Fin n × Fin n) → ∀ m → (Fin (n +ⁿ m) × Fin (n +ⁿ m))
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↑ˡ-Edge (idx₁ , idx₂) m = (idx₁ ↑ˡ m , idx₂ ↑ˡ m)
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_[_] : ∀ (g : Graph) → Graph.Index g → List BasicStmt
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_[_] g idx = lookup (Graph.nodes g) idx
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record _⊆_ (g₁ g₂ : Graph) : Set where
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constructor Mk-⊆
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field
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n : ℕ
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sg₂≡sg₁+n : Graph.size g₂ ≡ Graph.size g₁ +ⁿ n
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newNodes : Vec (List BasicStmt) n
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nsg₂≡nsg₁++newNodes : cast sg₂≡sg₁+n (Graph.nodes g₂) ≡ Graph.nodes g₁ ++ newNodes
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e∈g₁⇒e∈g₂ : ∀ {e : Graph.Edge g₁} →
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e ∈ˡ (Graph.edges g₁) →
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(↑ˡ-Edge e n) ∈ˡ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂))
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castᵉ : ∀ {n m : ℕ} .(p : n ≡ m) → (Fin n × Fin n) → (Fin m × Fin m)
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castᵉ p (idx₁ , idx₂) = (castᶠ p idx₁ , castᶠ p idx₂)
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↑ˡ-assoc : ∀ {s n₁ n₂} (f : Fin s) (p : s +ⁿ (n₁ +ⁿ n₂) ≡ s +ⁿ n₁ +ⁿ n₂) →
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f ↑ˡ n₁ ↑ˡ n₂ ≡ castᶠ p (f ↑ˡ (n₁ +ⁿ n₂))
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↑ˡ-assoc zero p = refl
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@ -140,20 +154,6 @@ module Graphs where
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rewrite castᶠ-is-id refl idx₁
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rewrite castᶠ-is-id refl idx₂ = e∈es
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_[_] : ∀ (g : Graph) → Graph.Index g → List BasicStmt
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_[_] g idx = lookup (Graph.nodes g) idx
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record _⊆_ (g₁ g₂ : Graph) : Set where
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constructor Mk-⊆
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field
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n : ℕ
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sg₂≡sg₁+n : Graph.size g₂ ≡ Graph.size g₁ +ⁿ n
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newNodes : Vec (List BasicStmt) n
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nsg₂≡nsg₁++newNodes : cast sg₂≡sg₁+n (Graph.nodes g₂) ≡ Graph.nodes g₁ ++ newNodes
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e∈g₁⇒e∈g₂ : ∀ {e : Graph.Edge g₁} →
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e ∈ˡ (Graph.edges g₁) →
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(↑ˡ-Edge e n) ∈ˡ (subst (λ m → List (Fin m × Fin m)) sg₂≡sg₁+n (Graph.edges g₂))
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⊆-trans : ∀ {g₁ g₂ g₃ : Graph} → g₁ ⊆ g₂ → g₂ ⊆ g₃ → g₁ ⊆ g₃
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⊆-trans {MkGraph s₁ ns₁ es₁} {MkGraph s₂ ns₂ es₂} {MkGraph s₃ ns₃ es₃}
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(Mk-⊆ n₁ p₁@refl newNodes₁ nsg₂≡nsg₁++newNodes₁ e∈g₁⇒e∈g₂)
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