25 lines
1.3 KiB
Agda
25 lines
1.3 KiB
Agda
module Language.Traces where
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open import Language.Base public
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open import Language.Semantics public
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open import Language.Graphs public
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open import Data.Product using (_,_)
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open import Data.List.Membership.Propositional as MemProp using ()
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module _ {g : Graph} where
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open Graph g using (Index; edges)
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data Trace : Index → Index → Env → Env → Set where
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Trace-single : ∀ {ρ₁ ρ₂ : Env} {idx : Index} →
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ρ₁ , (g [ idx ]) ⇒ᵇˢ ρ₂ → Trace idx idx ρ₁ ρ₂
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Trace-edge : ∀ {ρ₁ ρ₂ ρ₃ : Env} {idx₁ idx₂ idx₃ : Index} →
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ρ₁ , (g [ idx₁ ]) ⇒ᵇˢ ρ₂ → (idx₁ , idx₂) MemProp.∈ edges →
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Trace idx₂ idx₃ ρ₂ ρ₃ → Trace idx₁ idx₃ ρ₁ ρ₃
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_++⟨_⟩_ : ∀ {idx₁ idx₂ idx₃ idx₄ : Index} {ρ₁ ρ₂ ρ₃ : Env} →
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Trace idx₁ idx₂ ρ₁ ρ₂ → (idx₂ , idx₃) MemProp.∈ edges →
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Trace idx₃ idx₄ ρ₂ ρ₃ → Trace idx₁ idx₄ ρ₁ ρ₃
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_++⟨_⟩_ (Trace-single ρ₁⇒ρ₂) idx₂→idx₃ tr = Trace-edge ρ₁⇒ρ₂ idx₂→idx₃ tr
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_++⟨_⟩_ (Trace-edge ρ₁⇒ρ₂ idx₁→idx' tr') idx₂→idx₃ tr = Trace-edge ρ₁⇒ρ₂ idx₁→idx' (tr' ++⟨ idx₂→idx₃ ⟩ tr)
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