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07550bc214
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69a4e8eb5c
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@ -52,7 +52,7 @@ _↑ˡᵉ_ l m = List.map (_↑ˡ m) l
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_↑ʳᵉ_ : ∀ {m} n → List (Fin m × Fin m) → List (Fin (n Nat.+ m) × Fin (n Nat.+ m))
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_↑ʳᵉ_ n l = List.map (n ↑ʳ_) l
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infixr 5 _∙_
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infixl 5 _∙_
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_∙_ : Graph → Graph → Graph
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_∙_ g₁ g₂ = record
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{ size = Graph.size g₁ Nat.+ Graph.size g₂
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@ -65,7 +65,7 @@ _∙_ g₁ g₂ = record
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(Graph.size g₁ ↑ʳⁱ Graph.outputs g₂)
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}
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infixr 5 _↦_
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infixl 5 _↦_
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_↦_ : Graph → Graph → Graph
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_↦_ g₁ g₂ = record
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{ size = Graph.size g₁ Nat.+ Graph.size g₂
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@ -84,7 +84,7 @@ loop g = record g
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List.cartesianProduct (Graph.outputs g) (Graph.inputs g)
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}
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infixr 5 _skipto_
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infixl 5 _skipto_
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_skipto_ : Graph → Graph → Graph
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_skipto_ g₁ g₂ = record (g₁ ∙ g₂)
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{ edges = Graph.edges (g₁ ∙ g₂) List.++
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@ -32,87 +32,57 @@ buildCfg-output (if _ then s₁ else s₂) = (_ , refl)
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buildCfg-output (while _ repeat s)
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with (idx , p) ← buildCfg-output s rewrite p = (_ , refl)
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Trace-∙ˡ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace-∙ˡ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ →
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Trace {g₁ ∙ g₂} (idx₁ Fin.↑ˡ Graph.size g₂) (idx₂ Fin.↑ˡ Graph.size g₂) ρ₁ ρ₂
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Trace-∙ˡ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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Trace-∙ˡ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-single ρ₁⇒ρ₂
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Trace-∙ˡ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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Trace-∙ˡ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (_↑ˡ Graph.size g₂) idx₁→idx))
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(Trace-∙ˡ tr')
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(Trace-∙ˡ g₁ g₂ tr')
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Trace-∙ʳ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} →
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Trace-∙ʳ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} →
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Trace {g₂} idx₁ idx₂ ρ₁ ρ₂ →
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Trace {g₁ ∙ g₂} (Graph.size g₁ Fin.↑ʳ idx₁) (Graph.size g₁ Fin.↑ʳ idx₂) ρ₁ ρ₂
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Trace-∙ʳ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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Trace-∙ʳ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-single ρ₁⇒ρ₂
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Trace-∙ʳ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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Trace-∙ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ _ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx))
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(Trace-∙ʳ tr')
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(Trace-∙ʳ g₁ g₂ tr')
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EndToEndTrace-∙ˡ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env} →
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EndToEndTrace {g₁} ρ₁ ρ₂ →
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EndToEndTrace {g₁ ∙ g₂} ρ₁ ρ₂
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EndToEndTrace-∙ˡ {g₁} {g₂} etr = record
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{ idx₁ = EndToEndTrace.idx₁ etr Fin.↑ˡ Graph.size g₂
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; idx₁∈inputs = ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Fin._↑ˡ Graph.size g₂)
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(EndToEndTrace.idx₁∈inputs etr))
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; idx₂ = EndToEndTrace.idx₂ etr Fin.↑ˡ Graph.size g₂
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; idx₂∈outputs = ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Fin._↑ˡ Graph.size g₂)
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(EndToEndTrace.idx₂∈outputs etr))
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; trace = Trace-∙ˡ (EndToEndTrace.trace etr)
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}
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EndToEndTrace-∙ʳ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env} →
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EndToEndTrace {g₂} ρ₁ ρ₂ →
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EndToEndTrace {g₁ ∙ g₂} ρ₁ ρ₂
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EndToEndTrace-∙ʳ {g₁} {g₂} etr = record
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{ idx₁ = Graph.size g₁ Fin.↑ʳ EndToEndTrace.idx₁ etr
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; idx₁∈inputs = ListMemProp.∈-++⁺ʳ (Graph.inputs g₁ ↑ˡⁱ Graph.size g₂)
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((x∈xs⇒fx∈fxs (Graph.size g₁ Fin.↑ʳ_)
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(EndToEndTrace.idx₁∈inputs etr)))
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; idx₂ = Graph.size g₁ Fin.↑ʳ EndToEndTrace.idx₂ etr
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; idx₂∈outputs = ListMemProp.∈-++⁺ʳ (Graph.outputs g₁ ↑ˡⁱ Graph.size g₂)
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((x∈xs⇒fx∈fxs (Graph.size g₁ Fin.↑ʳ_)
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(EndToEndTrace.idx₂∈outputs etr)))
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; trace = Trace-∙ʳ (EndToEndTrace.trace etr)
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}
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Trace-↦ˡ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace-↦ˡ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ →
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Trace {g₁ ↦ g₂} (idx₁ Fin.↑ˡ Graph.size g₂) (idx₂ Fin.↑ˡ Graph.size g₂) ρ₁ ρ₂
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Trace-↦ˡ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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Trace-↦ˡ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-single ρ₁⇒ρ₂
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Trace-↦ˡ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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Trace-↦ˡ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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rewrite sym (lookup-++ˡ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (_↑ˡ Graph.size g₂) idx₁→idx))
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(Trace-↦ˡ tr')
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(Trace-↦ˡ g₁ g₂ tr')
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Trace-↦ʳ : ∀ {g₁ g₂ : Graph} {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} →
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Trace-↦ʳ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₂} {ρ₁ ρ₂ : Env} →
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Trace {g₂} idx₁ idx₂ ρ₁ ρ₂ →
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Trace {g₁ ↦ g₂} (Graph.size g₁ Fin.↑ʳ idx₁) (Graph.size g₁ Fin.↑ʳ idx₂) ρ₁ ρ₂
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Trace-↦ʳ {g₁} {g₂} {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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Trace-↦ʳ g₁ g₂ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂)
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rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-single ρ₁⇒ρ₂
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Trace-↦ʳ {g₁} {g₂} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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Trace-↦ʳ g₁ g₂ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr')
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rewrite sym (lookup-++ʳ (Graph.nodes g₁) (Graph.nodes g₂) idx₁) =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ʳ (Graph.edges g₁ ↑ˡᵉ Graph.size g₂)
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(ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Graph.size g₁ ↑ʳ_) idx₁→idx)))
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(Trace-↦ʳ {g₁} {g₂} tr')
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(Trace-↦ʳ g₁ g₂ tr')
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Trace-loop : ∀ {g₁ : Graph} {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace-loop : ∀ (g₁ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
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Trace {g₁} idx₁ idx₂ ρ₁ ρ₂ → Trace {loop g₁} idx₁ idx₂ ρ₁ ρ₂
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Trace-loop {idx₁ = idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂
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Trace-loop {g₁} {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop tr')
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Trace-loop g₁ {idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂
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Trace-loop g₁ {idx₁} (Trace-edge ρ₁⇒ρ idx₁→idx tr') =
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Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop g₁ tr')
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infixr 5 _++_
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_++_ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ ρ₃ : Env} →
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EndToEndTrace {g₁} ρ₁ ρ₂ → EndToEndTrace {g₂} ρ₂ ρ₃ →
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EndToEndTrace {g₁ ↦ g₂} ρ₁ ρ₃
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@ -130,8 +100,8 @@ _++_ {g₁} {g₂} etr₁ etr₂
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(ListMemProp.∈-++⁺ʳ (Graph.size g₁ ↑ʳᵉ Graph.edges g₂)
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(∈-cartesianProduct o∈tr₁ i∈tr₂))
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in
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(Trace-↦ˡ {g₁} {g₂} (EndToEndTrace.trace etr₁)) ++⟨ oi∈es ⟩
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(Trace-↦ʳ {g₁} {g₂} (EndToEndTrace.trace etr₂))
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(Trace-↦ˡ g₁ g₂ (EndToEndTrace.trace etr₁)) ++⟨ oi∈es ⟩
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(Trace-↦ʳ g₁ g₂ (EndToEndTrace.trace etr₂))
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}
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Trace-singleton : ∀ {bss : List BasicStmt} {ρ₁ ρ₂ : Env} →
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@ -153,11 +123,3 @@ buildCfg-sufficient (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
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Trace-singleton (ρ₁,bs⇒ρ₂ ∷ [])
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buildCfg-sufficient (⇒ˢ-then ρ₁ ρ₂ ρ₃ s₁ s₂ ρ₁,s₁⇒ρ₂ ρ₂,s₂⇒ρ₃) =
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buildCfg-sufficient ρ₁,s₁⇒ρ₂ ++ buildCfg-sufficient ρ₂,s₂⇒ρ₃
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buildCfg-sufficient (⇒ˢ-if-true ρ₁ ρ₂ _ _ s₁ s₂ _ _ ρ₁,s₁⇒ρ₂) =
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Trace-singleton[] ρ₁ ++
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(EndToEndTrace-∙ˡ (buildCfg-sufficient ρ₁,s₁⇒ρ₂)) ++
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Trace-singleton[] ρ₂
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buildCfg-sufficient (⇒ˢ-if-false ρ₁ ρ₂ _ s₁ s₂ _ ρ₁,s₂⇒ρ₂) =
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Trace-singleton[] ρ₁ ++
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(EndToEndTrace-∙ʳ {buildCfg s₁} (buildCfg-sufficient ρ₁,s₂⇒ρ₂)) ++
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Trace-singleton[] ρ₂
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