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Prove 'sufficiency' for if-else.

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-28 12:10:12 -07:00
parent 9366ec4a97
commit 07550bc214
2 changed files with 12 additions and 3 deletions
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6
Language/Graphs.agda
View File

@ -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
infixl 5 _∙_ infixr 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)
} }
infixl 5 _↦_ infixr 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)
} }
infixl 5 _skipto_ infixr 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.++

9
Language/Properties.agda
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@ -112,6 +112,7 @@ Trace-loop {idx₁ = idx₁} {idx₁} (Trace-single ρ₁⇒ρ₂) = Trace-singl
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 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
@ -152,3 +153,11 @@ 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