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Setoid version of indexed containers. #1511

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Merged
merged 5 commits into from
Mar 16, 2024
Merged

Setoid version of indexed containers. #1511

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f1aee94
Setoid version of indexed containers.
andreasabel May 30, 2021
331434e
An example for indexed containers: multi-sorted algebras.
andreasabel May 30, 2021
b451cd7
Merge branch 'master' into indexed-container-setoid
MatthewDaggitt Mar 3, 2024
994ea87
Brought code up to date
MatthewDaggitt Mar 3, 2024
b096c36
Added CHANGELOG entry
MatthewDaggitt Mar 16, 2024
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26 changes: 17 additions & 9 deletions src/Data/Container/Indexed/Core.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -12,10 +12,14 @@ open import Level
open import Data.Product
open import Relation.Unary

private variable
i o c r ℓ ℓ′ : Level
I : Set i
O : Set o

infix 5 _◃_/_

record Container {i o} (I : Set i) (O : Set o) (c r : Level) :
Set (i ⊔ o ⊔ suc c ⊔ suc r) where
record Container (I : Set i) (O : Set o) c r : Set (i ⊔ o ⊔ suc c ⊔ suc r) where
constructor _◃_/_
field
Command : (o : O) → Set c
Expand All @@ -24,22 +28,26 @@ record Container {i o} (I : Set i) (O : Set o) (c r : Level) :

-- The semantics ("extension") of an indexed container.

⟦_⟧ : ∀ {i o c r ℓ} {I : Set i} {O : Set o} → Container I O c r →
Pred I ℓ → Pred O _
⟦ C ◃ R / n ⟧ X o = Σ[ c ∈ C o ] ((r : R c) → X (n c r))
module _ (C : Container I O c r) (X : Pred I ℓ) where
open Container C

Subtrees : ∀ o → Command o → Set _
Subtrees o c = (r : Response c) → X (next c r)

⟦_⟧ : Pred O _
⟦_⟧ o = Σ (Command o) (Subtrees o)

------------------------------------------------------------------------
-- All and any

module _ {i o c r ℓ} {I : Set i} {O : Set o}
(C : Container I O c r) {X : Pred I ℓ} where
module _ (C : Container I O c r) {X : Pred I ℓ} where

-- All.

□ : ∀ {ℓ′} → Pred (Σ I X) ℓ′ → Pred (Σ O (⟦ C ⟧ X)) _
□ : Pred (Σ I X) ℓ′ → Pred (Σ O (⟦ C ⟧ X)) _
□ P (_ , _ , k) = ∀ r → P (_ , k r)

-- Any.

◇ : ∀ {ℓ′} → Pred (Σ I X) ℓ′ → Pred (Σ O (⟦ C ⟧ X)) _
◇ : Pred (Σ I X) ℓ′ → Pred (Σ O (⟦ C ⟧ X)) _
◇ P (_ , _ , k) = ∃ λ r → P (_ , k r)
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