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compare: DanilaFe:69a4e8eb5c6ab2ae4ba323e2ecd883e4ed98434b
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2 changed files with 25 additions and 63 deletions
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6
Language/Graphs.agda
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@ -52,7 +52,7 @@ _↑ˡᵉ_ l m = List.map (_↑ˡ m) l
_↑ʳᵉ_ : ∀ {m} n → List (Fin m × Fin m) → List (Fin (n Nat.+ m) × Fin (n Nat.+ m)) _↑ʳᵉ_ : ∀ {m} n → List (Fin m × Fin m) → List (Fin (n Nat.+ m) × Fin (n Nat.+ m))
_↑ʳᵉ_ n l = List.map (n ↑ʳ_) l _↑ʳᵉ_ n l = List.map (n ↑ʳ_) l
infixr 5 _∙_ infixl 5 _∙_
_∙_ : Graph → Graph → Graph _∙_ : Graph → Graph → Graph
_∙_ g₁ g₂ = record _∙_ g₁ g₂ = record
{ size = Graph.size g₁ Nat.+ Graph.size g₂ { size = Graph.size g₁ Nat.+ Graph.size g₂
@ -65,7 +65,7 @@ _∙_ g₁ g₂ = record
(Graph.size g₁ ↑ʳⁱ Graph.outputs g₂) (Graph.size g₁ ↑ʳⁱ Graph.outputs g₂)
} }
infixr 5 _↦_ infixl 5 _↦_
_↦_ : Graph → Graph → Graph _↦_ : Graph → Graph → Graph
_↦_ g₁ g₂ = record _↦_ g₁ g₂ = record
{ size = Graph.size g₁ Nat.+ Graph.size g₂ { size = Graph.size g₁ Nat.+ Graph.size g₂
@ -84,7 +84,7 @@ loop g = record g
List.cartesianProduct (Graph.outputs g) (Graph.inputs g) List.cartesianProduct (Graph.outputs g) (Graph.inputs g)
} }
infixr 5 _skipto_ infixl 5 _skipto_
_skipto_ : Graph → Graph → Graph _skipto_ : Graph → Graph → Graph
_skipto_ g₁ g₂ = record (g₁ ∙ g₂) _skipto_ g₁ g₂ = record (g₁ ∙ g₂)
{ edges = Graph.edges (g₁ ∙ g₂) List.++ { edges = Graph.edges (g₁ ∙ g₂) List.++

82
Language/Properties.agda
View File

@ -32,87 +32,57 @@ buildCfg-output (if _ then s₁ else s₂) = (_ , refl)
buildCfg-output (while _ repeat s) buildCfg-output (while _ repeat s)
with (idx , p) ← buildCfg-output s rewrite p = (_ , refl) with (idx , p) ← buildCfg-output s rewrite p = (_ , refl)
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 tr') (Trace-∙ˡ g₁ g₂ 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 _ (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 tr') (Trace-∙ʳ g₁ g₂ tr')
EndToEndTrace-∙ˡ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env} → Trace-↦ˡ : ∀ (g₁ g₂ : Graph) {idx₁ idx₂ : Graph.Index g₁} {ρ₁ ρ₂ : Env} →
EndToEndTrace {g₁} ρ₁ ρ₂ →
EndToEndTrace {g₁ ∙ g₂} ρ₁ ρ₂
EndToEndTrace-∙ˡ {g₁} {g₂} etr = record
{ idx₁ = EndToEndTrace.idx₁ etr Fin.↑ˡ Graph.size g₂
; idx₁∈inputs = ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Fin._↑ˡ Graph.size g₂)
(EndToEndTrace.idx₁∈inputs etr))
; idx₂ = EndToEndTrace.idx₂ etr Fin.↑ˡ Graph.size g₂
; idx₂∈outputs = ListMemProp.∈-++⁺ˡ (x∈xs⇒fx∈fxs (Fin._↑ˡ Graph.size g₂)
(EndToEndTrace.idx₂∈outputs etr))
; trace = Trace-∙ˡ (EndToEndTrace.trace etr)
}
EndToEndTrace-∙ʳ : ∀ {g₁ g₂ : Graph} {ρ₁ ρ₂ : Env} →
EndToEndTrace {g₂} ρ₁ ρ₂ →
EndToEndTrace {g₁ ∙ g₂} ρ₁ ρ₂
EndToEndTrace-∙ʳ {g₁} {g₂} etr = record
{ idx₁ = Graph.size g₁ Fin.↑ʳ EndToEndTrace.idx₁ etr
; idx₁∈inputs = ListMemProp.∈-++⁺ʳ (Graph.inputs g₁ ↑ˡⁱ Graph.size g₂)
((x∈xs⇒fx∈fxs (Graph.size g₁ Fin.↑ʳ_)
(EndToEndTrace.idx₁∈inputs etr)))
; idx₂ = Graph.size g₁ Fin.↑ʳ EndToEndTrace.idx₂ etr
; idx₂∈outputs = ListMemProp.∈-++⁺ʳ (Graph.outputs g₁ ↑ˡⁱ Graph.size g₂)
((x∈xs⇒fx∈fxs (Graph.size g₁ Fin.↑ʳ_)
(EndToEndTrace.idx₂∈outputs etr)))
; trace = Trace-∙ʳ (EndToEndTrace.trace etr)
}
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 tr') (Trace-↦ˡ g₁ g₂ 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 {idx₁ = idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-single ρ₁⇒ρ₂ Trace-loop g₁ {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 tr') Trace-edge ρ₁⇒ρ (ListMemProp.∈-++⁺ˡ idx₁→idx) (Trace-loop g₁ tr')
infixr 5 _++_
_++_ : ∀ {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 →
EndToEndTrace {g₁ ↦ g₂} ρ₁ ρ₃ EndToEndTrace {g₁ ↦ g₂} ρ₁ ρ₃
@ -130,8 +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} →
@ -153,11 +123,3 @@ buildCfg-sufficient (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
Trace-singleton (ρ₁,bs⇒ρ₂ ∷ []) Trace-singleton (ρ₁,bs⇒ρ₂ ∷ [])
buildCfg-sufficient (⇒ˢ-then ρ₁ ρ₂ ρ₃ s₁ s₂ ρ₁,s₁⇒ρ₂ ρ₂,s₂⇒ρ₃) = buildCfg-sufficient (⇒ˢ-then ρ₁ ρ₂ ρ₃ s₁ s₂ ρ₁,s₁⇒ρ₂ ρ₂,s₂⇒ρ₃) =
buildCfg-sufficient ρ₁,s₁⇒ρ₂ ++ buildCfg-sufficient ρ₂,s₂⇒ρ₃ buildCfg-sufficient ρ₁,s₁⇒ρ₂ ++ buildCfg-sufficient ρ₂,s₂⇒ρ₃
buildCfg-sufficient (⇒ˢ-if-true ρ₁ ρ₂ _ _ s₁ s₂ _ _ ρ₁,s₁⇒ρ₂) =
Trace-singleton[] ρ₁ ++
(EndToEndTrace-∙ˡ (buildCfg-sufficient ρ₁,s₁⇒ρ₂)) ++
Trace-singleton[] ρ₂
buildCfg-sufficient (⇒ˢ-if-false ρ₁ ρ₂ _ s₁ s₂ _ ρ₁,s₂⇒ρ₂) =
Trace-singleton[] ρ₁ ++
(EndToEndTrace-∙ʳ {buildCfg s₁} (buildCfg-sufficient ρ₁,s₂⇒ρ₂)) ++
Trace-singleton[] ρ₂