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Reexport VariantList completeness and soundness in LanguageMap
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ibbem committed May 20, 2024
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6 changes: 5 additions & 1 deletion src/Translation/LanguageMap.lagda.md
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Expand Up @@ -36,7 +36,7 @@ open import Util.AuxProofs using (decidableEquality-×)
open import Construct.Artifact as At using () renaming (Syntax to Artifact)
open import Lang.All
open VariantList using (VariantListL; VariantList-is-Complete; VariantList-is-Sound)
open VariantList using (VariantListL)
open CCC using (CCCL)
open NCC using (NCCL)
open 2CC using (2CCL)
Expand Down Expand Up @@ -232,6 +232,8 @@ module Expressiveness {F : 𝔽} (f : F × ℕ → F) (f⁻¹ : F → F × ℕ)
module Completeness {F : 𝔽} (f : F × ℕ → F) (f⁻¹ : F → F × ℕ) (f⁻¹∘f≗id : f⁻¹ ∘ f ≗ id) (D : F) where
open Expressiveness f f⁻¹ f⁻¹∘f≗id
open VariantList using (VariantList-is-Complete) public
CCC-is-complete : Complete (CCCL F)
CCC-is-complete = completeness-by-expressiveness VariantList-is-Complete (CCC≽VariantList D)
Expand Down Expand Up @@ -282,6 +284,8 @@ module Completeness {F : 𝔽} (f : F × ℕ → F) (f⁻¹ : F → F × ℕ) (f
```

```agda
open VariantList using (VariantList-is-Sound) public
ADT-is-sound : ∀ {F : 𝔽} (_==_ : DecidableEquality F) → Sound (ADTL Variant F)
ADT-is-sound {F} _==_ = soundness-by-expressiveness VariantList-is-Sound (ADT-to-VariantList.VariantList≽ADT F Variant _==_)
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