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Make graph arguments implicit where possible

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Danila Fedorin 2024-04-28 11:37:08 -07:00
parent 69a4e8eb5c
commit 6b44ac1feb
1 changed files with 14 additions and 14 deletions
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@ -54,34 +54,34 @@ Trace-∙ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ _ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx)) Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ _ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx))
(Trace-∙ʳ g₁ g₂ tr') (Trace-∙ʳ g₁ g₂ tr')
Trace-↦ˡ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} → Trace-↦ˡ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ →
Trace {g₁ ↦ g₂} (idx₁ Fin.↑ˡ Graph.size g₂) (idx₂ Fin.↑ˡ Graph.size g₂) ρ₁ ρ₂ Trace {g₁ ↦ g₂} (idx₁ Fin.↑ˡ Graph.size g₂) (idx₂ Fin.↑ˡ Graph.size g₂) ρ₁ ρ₂
Trace-↦ˡ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) Trace-↦ˡ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
Trace-single ρ₁⇒ρ₂ Trace-single ρ₁⇒ρ₂
Trace-↦ˡ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') Trace-↦ˡ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (_↑ˡ Graph.size g₂) idx₁→idx)) Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (_↑ˡ Graph.size g₂) idx₁→idx))
(Trace-↦ˡ g₁ g₂ tr') (Trace-↦ˡ tr')
Trace-↦ʳ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} → Trace-↦ʳ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} →
Trace {g₂} idx₁ idx₂ ρ₁ ρ₂ → Trace {g₂} idx₁ idx₂ ρ₁ ρ₂ →
Trace {g₁ ↦ g₂} (Graph.size g₁ Fin.↑ʳ idx₁) (Graph.size g₁ Fin.↑ʳ idx₂) ρ₁ ρ₂ Trace {g₁ ↦ g₂} (Graph.size g₁ Fin.↑ʳ idx₁) (Graph.size g₁ Fin.↑ʳ idx₂) ρ₁ ρ₂
Trace-↦ʳ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) Trace-↦ʳ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
Trace-single ρ₁⇒ρ₂ Trace-single ρ₁⇒ρ₂
Trace-↦ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') Trace-↦ʳ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) = rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ (Graph.edges g₁ ↑ˡᵉ Graph.size g₂) Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ (Graph.edges g₁ ↑ˡᵉ Graph.size g₂)
(ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx))) (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx)))
(Trace-↦ʳ g₁ g₂ tr') (Trace-↦ʳ {g₁} {g₂} tr')
Trace-loop : ∀ (g₁ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} → Trace-loop : ∀ {g₁ : Graph} {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → Trace {loop g₁} idx₁ idx₂ ρ₁ ρ₂ Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → Trace {loop g₁} idx₁ idx₂ ρ₁ ρ₂
Trace-loop g₁ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂ Trace-loop {idx₁ = idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂
Trace-loop g₁ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') = Trace-loop {g₁} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') =
Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop g₁ tr') Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop tr')
_++_ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ ρ₃ : Env} → _++_ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ ρ₃ : Env} →
EndToEndTrace {g₁} ρ₁ ρ₂ → EndToEndTrace {g₂} ρ₂ ρ₃ → EndToEndTrace {g₁} ρ₁ ρ₂ → EndToEndTrace {g₂} ρ₂ ρ₃ →
@ -100,8 +100,8 @@ _++_ {g₁} {g₂} etr₁ etr₂
(ListMemProp.∈-++⁺ʳ (Graph.size g₁ ↑ʳᵉ Graph.edges g₂) (ListMemProp.∈-++⁺ʳ (Graph.size g₁ ↑ʳᵉ Graph.edges g₂)
(∈-cartesianProduct o∈tr₁ i∈tr₂)) (∈-cartesianProduct o∈tr₁ i∈tr₂))
in in
(Trace-↦ˡ g₁ g₂ (EndToEndTrace.trace etr₁)) ++⟨ oi∈es ⟩ (Trace-↦ˡ {g₁} {g₂} (EndToEndTrace.trace etr₁)) ++⟨ oi∈es ⟩
(Trace-↦ʳ g₁ g₂ (EndToEndTrace.trace etr₂)) (Trace-↦ʳ {g₁} {g₂} (EndToEndTrace.trace etr₂))
} }
Trace-singleton : ∀ {bss : List BasicStmt} {ρ₁ ρ₂ : Env} → Trace-singleton : ∀ {bss : List BasicStmt} {ρ₁ ρ₂ : Env} →