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Switch product to using instances

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2025-01-04 21:33:59 -08:00
parent 70847d51db
commit cf824dc744
2 changed files with 77 additions and 79 deletions
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22
Lattice/IterProd.agda
View File

@ -40,11 +40,11 @@ build a b (suc s) = (a , build a b s)
private
record RequiredForFixedHeight : Set (lsuc a) where
field
≈₁-Decidable : IsDecidable _≈₁_
≈₂-Decidable : IsDecidable _≈₂_
{{≈₁-Decidable}} : IsDecidable _≈₁_
{{≈₂-Decidable}} : IsDecidable _≈₂_
h₁ h₂ : ℕ
fhA : FixedHeight₁ h₁
fhB : FixedHeight₂ h₂
{{fhA}} : FixedHeight₁ h₁
{{fhB}} : FixedHeight₂ h₂
⊥₁ : A
⊥₁ = Height.⊥ fhA
@ -102,10 +102,9 @@ private
{ height = (RequiredForFixedHeight.h₁ req) + IsFiniteHeightWithBotAndDecEq.height fhlRest
; fixedHeight =
P.fixedHeight
(RequiredForFixedHeight.≈₁-Decidable req) (IsFiniteHeightWithBotAndDecEq.≈-Decidable fhlRest)
(RequiredForFixedHeight.h₁ req) (IsFiniteHeightWithBotAndDecEq.height fhlRest)
(RequiredForFixedHeight.fhA req) (IsFiniteHeightWithBotAndDecEq.fixedHeight fhlRest)
; ≈-Decidable = P.≈-Decidable (RequiredForFixedHeight.≈₁-Decidable req) (IsFiniteHeightWithBotAndDecEq.≈-Decidable fhlRest)
{{≈₂-Decidable = IsFiniteHeightWithBotAndDecEq.≈-Decidable fhlRest}}
{{fhB = IsFiniteHeightWithBotAndDecEq.fixedHeight fhlRest}}
; ≈-Decidable = P.≈-Decidable {{≈₂-Decidable = IsFiniteHeightWithBotAndDecEq.≈-Decidable fhlRest}}
; ⊥-correct =
cong ((Height.⊥ (RequiredForFixedHeight.fhA req)) ,_)
(IsFiniteHeightWithBotAndDecEq.⊥-correct fhlRest)
@ -113,12 +112,7 @@ private
}
where
everythingRest = everything k'
import Lattice.Prod
_≈₁_ (Everything._≈_ everythingRest)
_⊔₁_ (Everything._⊔_ everythingRest)
_⊓₁_ (Everything._⊓_ everythingRest)
lA (Everything.isLattice everythingRest) as P
import Lattice.Prod A (IterProd k') {{lB = Everything.isLattice everythingRest}} as P
module _ {k : ℕ} where
open Everything (everything k) using (_≈_; _⊔_; _⊓_) public

20
Lattice/Prod.agda
View File

@ -1,10 +1,10 @@
open import Lattice
module Lattice.Prod {a b} {A : Set a} {B : Set b}
(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set b)
(_⊔₁_ : A → A → A) (_⊔₂_ : B → B → B)
(_⊓₁_ : A → A → A) (_⊓₂_ : B → B → B)
(lA : IsLattice A _≈₁_ _⊔₁_ _⊓₁_) (lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_) where
module Lattice.Prod {a b} (A : Set a) (B : Set b)
{_≈₁_ : A → A → Set a} {_≈₂_ : B → B → Set b}
{_⊔₁_ : A → A → A} {_⊔₂_ : B → B → B}
{_⊓₁_ : A → A → A} {_⊓₂_ : B → B → B}
{{lA : IsLattice A _≈₁_ _⊔₁_ _⊓₁_}} {{lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_}} where
open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔ℓ_)
open import Data.Nat using (ℕ; _≤_; _+_; suc)
@ -40,6 +40,7 @@ open IsLattice lB using () renaming
_≈_ : A × B → A × B → Set (a ⊔ℓ b)
(a₁ , b₁) ≈ (a₂ , b₂) = (a₁ ≈₁ a₂) × (b₁ ≈₂ b₂)
instance
≈-equiv : IsEquivalence (A × B) _≈_
≈-equiv = record
{ ≈-refl = λ {p} → (≈₁-refl , ≈₂-refl)
@ -76,6 +77,7 @@ private module ProdIsSemilattice (f₁ : A → A → A) (f₂ : B → B → B) (
)
}
instance
isJoinSemilattice : IsSemilattice (A × B) _≈_ _⊔_
isJoinSemilattice = ProdIsSemilattice.isSemilattice _⊔₁_ _⊔₂_ joinSemilattice₁ joinSemilattice₂
@ -104,7 +106,7 @@ lattice = record
; isLattice = isLattice
}
module _ (≈₁-Decidable : IsDecidable _≈₁_) (≈₂-Decidable : IsDecidable _≈₂_) where
module _ {{≈₁-Decidable : IsDecidable _≈₁_}} {{≈₂-Decidable : IsDecidable _≈₂_}} where
open IsDecidable ≈₁-Decidable using () renaming (R-dec to ≈₁-dec)
open IsDecidable ≈₂-Decidable using () renaming (R-dec to ≈₂-dec)
@ -115,11 +117,12 @@ module _ (≈₁-Decidable : IsDecidable _≈₁_) (≈₂-Decidable : IsDecidab
... | no a₁̷≈a₂ | _ = no (λ (a₁≈a₂ , _) → a₁̷≈a₂ a₁≈a₂)
... | _ | no b₁̷≈b₂ = no (λ (_ , b₁≈b₂) → b₁̷≈b₂ b₁≈b₂)
instance
≈-Decidable : IsDecidable _≈_
≈-Decidable = record { R-dec = ≈-dec }
module _ (h₁ h₂ : ℕ)
(fhA : FixedHeight₁ h₁) (fhB : FixedHeight₂ h₂) where
module _ {h₁ h₂ : ℕ}
{{fhA : FixedHeight₁ h₁}} {{fhB : FixedHeight₂ h₂}} where
open import Data.Nat.Properties
open IsLattice isLattice using (_≼_; _≺_; ≺-cong)
@ -167,6 +170,7 @@ module _ (≈₁-Decidable : IsDecidable _≈₁_) (≈₂-Decidable : IsDecidab
, m≤n⇒m≤o+n 1 (subst (n ≤_) (sym (+-suc n₁ n₂)) (+-monoʳ-≤ 1 n≤n₁+n₂))
))
instance
fixedHeight : IsLattice.FixedHeight isLattice (h₁ + h₂)
fixedHeight = record
{ ⊥ = (⊥₁ , ⊥₂)