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Switch maps (and consequently most of the code) 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 21:16:22 -08:00
parent d90b544436
commit d96eb97b69
16 changed files with 257 additions and 240 deletions
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95
Lattice/IterProd.agda
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@@ -1,14 +1,15 @@
open import Lattice
open import Data.Unit using (⊤)
-- Due to universe levels, it becomes relatively annoying to handle the case
-- where the levels of A and B are not the same. For the time being, constrain
-- them to be the same.
module Lattice.IterProd {a} {A B : Set a}
(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set a)
(_⊔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.IterProd {a} (A B : Set a)
{_≈₁_ : A → A → Set a} {_≈₂_ : B → B → Set a}
{_⊔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_}} (dummy : ⊤) where
open import Agda.Primitive using (lsuc)
open import Data.Nat using (ℕ; zero; suc; _+_)
@@ -119,49 +120,55 @@ private
_⊓₁_ (Everything._⊓_ everythingRest)
lA (Everything.isLattice everythingRest) as P
module _ (k : ℕ) where
open Everything (everything k) using (_≈_; _⊔_; _⊓_; isLattice) public
open Lattice.IsLattice isLattice public
module _ {k : ℕ} where
open Everything (everything k) using (_≈_; _⊔_; _⊓_) public
open Lattice.IsLattice (Everything.isLattice (everything k)) public
lattice : Lattice (IterProd k)
lattice = record
{ _≈_ = _≈_
; _⊔_ = _⊔_
; _⊓_ = _⊓_
; isLattice = isLattice
}
instance
isLattice = Everything.isLattice (everything k)
module _ (≈₁-Decidable : IsDecidable _≈₁_) (≈₂-Decidable : IsDecidable _≈₂_)
(h₁ h₂ : ℕ)
(fhA : FixedHeight₁ h₁) (fhB : FixedHeight₂ h₂) where
private
required : RequiredForFixedHeight
required = record
{ ≈₁-Decidable = ≈₁-Decidable
; ≈₂-Decidable = ≈₂-Decidable
; h₁ = h₁
; h₂ = h₂
; fhA = fhA
; fhB = fhB
}
fixedHeight = IsFiniteHeightWithBotAndDecEq.fixedHeight (Everything.isFiniteHeightIfSupported (everything k) required)
isFiniteHeightLattice = record
{ isLattice = isLattice
; fixedHeight = fixedHeight
}
finiteHeightLattice : FiniteHeightLattice (IterProd k)
finiteHeightLattice = record
{ height = IsFiniteHeightWithBotAndDecEq.height (Everything.isFiniteHeightIfSupported (everything k) required)
; _≈_ = _≈_
lattice : Lattice (IterProd k)
lattice = record
{ _≈_ = _≈_
; _⊔_ = _⊔_
; _⊓_ = _⊓_
; isFiniteHeightLattice = isFiniteHeightLattice
; isLattice = isLattice
}
⊥-built : Height.⊥ fixedHeight ≡ (build (Height.⊥ fhA) (Height.⊥ fhB) k)
⊥-built = IsFiniteHeightWithBotAndDecEq.⊥-correct (Everything.isFiniteHeightIfSupported (everything k) required)
module _ {{≈₁-Decidable : IsDecidable _≈₁_}} {{≈₂-Decidable : IsDecidable _≈₂_}}
{h₁ h₂ : ℕ}
{{fhA : FixedHeight₁ h₁}} {{fhB : FixedHeight₂ h₂}} where
private
isFiniteHeightWithBotAndDecEq =
Everything.isFiniteHeightIfSupported (everything k)
record
{ ≈₁-Decidable = ≈₁-Decidable
; ≈₂-Decidable = ≈₂-Decidable
; h₁ = h₁
; h₂ = h₂
; fhA = fhA
; fhB = fhB
}
open IsFiniteHeightWithBotAndDecEq isFiniteHeightWithBotAndDecEq using (height; ⊥-correct)
instance
fixedHeight = IsFiniteHeightWithBotAndDecEq.fixedHeight isFiniteHeightWithBotAndDecEq
isFiniteHeightLattice = record
{ isLattice = isLattice
; fixedHeight = fixedHeight
}
finiteHeightLattice : FiniteHeightLattice (IterProd k)
finiteHeightLattice = record
{ height = height
; _≈_ = _≈_
; _⊔_ = _⊔_
; _⊓_ = _⊓_
; isFiniteHeightLattice = isFiniteHeightLattice
}
⊥-built : Height.⊥ fixedHeight ≡ (build (Height.⊥ fhA) (Height.⊥ fhB) k)
⊥-built = ⊥-correct