DanilaFe/agda-spa
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Add some helpers and rewrite code

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2024-04-27 17:43:16 -07:00
parent 4fee16413a
commit 69a4e8eb5c
1 changed files with 15 additions and 8 deletions
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19
Language/Properties.agda
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@ -6,7 +6,7 @@ open import Language.Graphs
open import Language.Traces
open import Data.Fin as Fin using (zero)
open import Data.List using (_∷_; [])
open import Data.List using (List; _∷_; [])
open import Data.List.Relation.Unary.Any using (here)
open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
open import Data.Product using (Σ; _,_; _×_)
@ -104,15 +104,22 @@ _++_ {g₁} {g₂} etr₁ etr₂
(Trace-↦ʳ g₁ g₂ (EndToEndTrace.trace etr₂))
}
buildCfg-sufficient : ∀ {s : Stmt} {ρ₁ ρ₂ : Env} → ρ₁ , s ⇒ˢ ρ₂ →
EndToEndTrace {buildCfg s} ρ₁ ρ₂
buildCfg-sufficient (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs ρ₁,bs⇒ρ₂) =
record
Trace-singleton : ∀ {bss : List BasicStmt} {ρ₁ ρ₂ : Env} →
ρ₁ , bss ⇒ᵇˢ ρ₂ → EndToEndTrace {singleton bss} ρ₁ ρ₂
Trace-singleton ρ₁⇒ρ₂ = record
{ idx₁ = zero
; idx₁∈inputs = here refl
; idx₂ = zero
; idx₂∈outputs = here refl
; trace = Trace-single (ρ₁,bs⇒ρ₂ ∷ [])
; trace = Trace-single ρ₁⇒ρ₂
}
Trace-singleton[] : ∀ (ρ : Env) → EndToEndTrace {singleton []} ρ ρ
Trace-singleton[] env = Trace-singleton []
buildCfg-sufficient : ∀ {s : Stmt} {ρ₁ ρ₂ : Env} → ρ₁ , s ⇒ˢ ρ₂ →
EndToEndTrace {buildCfg s} ρ₁ ρ₂
buildCfg-sufficient (⇒ˢ-⟨⟩ ρ₁ ρ₂ bs 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 ρ₁,s₁⇒ρ₂ ++ buildCfg-sufficient ρ₂,s₂⇒ρ₃