Another redefinition of Language.

1 files changed, 47 insertions, 0 deletions

diff --git a/src/Cfe/Language/Indexed/Homogeneous.agda b/src/Cfe/Language/Indexed/Homogeneous.agda
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+{-# OPTIONS --without-K --safe #-}
+
+open import Relation.Binary as B using (Setoid)
+
+module Cfe.Language.Indexed.Homogeneous
+  {c ℓ} (over : Setoid c ℓ)
+  where
+
+open import Cfe.Language over
+open import Level
+open import Data.List
+open import Data.Product
+open import Relation.Binary.Indexed.Heterogeneous
+
+open _≈_
+
+open Setoid over using () renaming (Carrier to C)
+
+record IndexedLanguage i iℓ a aℓ : Set (ℓ ⊔ suc (c ⊔ i ⊔ iℓ ⊔ a ⊔ aℓ)) where
+  field
+    Carrierᵢ : Set i
+    _≈ᵢ_ : B.Rel Carrierᵢ iℓ
+    isEquivalenceᵢ : B.IsEquivalence _≈ᵢ_
+    F : Carrierᵢ → Language a aℓ
+    cong : F B.Preserves _≈ᵢ_ ⟶ _≈_
+
+  open B.IsEquivalence isEquivalenceᵢ using () renaming (refl to reflᵢ; sym to symᵢ; trans to transᵢ) public
+
+  Tagged : List C → Set (i ⊔ a)
+  Tagged l = ∃[ i ] l ∈ F i
+
+  _≈ᵗ_ : IRel Tagged (iℓ ⊔ aℓ)
+  _≈ᵗ_ (i , l∈Fi) (j , m∈Fj) = Σ (i ≈ᵢ j) λ i≈j → ≈ᴸ (F j) (f (cong i≈j) l∈Fi) m∈Fj
+
+  -- ≈ᵗ-refl : Reflexive Tagged _≈ᵗ_
+  -- ≈ᵗ-refl {l} {i , l∈Fi} = reflᵢ , {!≈ᴸ-refl!}
+
+  -- ⋃ : Language (i ⊔ a) (iℓ ⊔ aℓ)
+  -- ⋃ = record
+  --   { Carrier = Tagged
+  --   ; _≈_ = _≈ᵗ_
+  --   ; isEquivalence = record
+  --     { refl = λ i≈j → {!!}
+  --     ; sym = {!!}
+  --     ; trans = {!!}
+  --     }
+  --   }