37 lines
1.6 KiB
Plaintext
37 lines
1.6 KiB
Plaintext
module Language.Traces where
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open import Language.Base
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open import Language.Semantics using (Env; _,_⇒ᵇˢ_)
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open import Language.Graphs
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open import Data.Product using (_,_)
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open import Data.List.Membership.Propositional using (_∈_)
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module _ {g : Graph} where
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open Graph g using (Index; edges; inputs; outputs)
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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) ∈ edges →
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Trace idx₂ idx₃ ρ₂ ρ₃ → Trace idx₁ idx₃ ρ₁ ρ₃
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infixr 5 _++⟨_⟩_
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_++⟨_⟩_ : ∀ {idx₁ idx₂ idx₃ idx₄ : Index} {ρ₁ ρ₂ ρ₃ : Env} →
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Trace idx₁ idx₂ ρ₁ ρ₂ → (idx₂ , idx₃) ∈ 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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record EndToEndTrace (ρ₁ ρ₂ : Env) : Set where
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constructor MkEndToEndTrace
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field
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idx₁ : Index
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idx₁∈inputs : idx₁ ∈ inputs
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idx₂ : Index
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idx₂∈outputs : idx₂ ∈ outputs
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trace : Trace idx₁ idx₂ ρ₁ ρ₂
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