Expose bundles and apply so renames to IterProd
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -21,17 +21,14 @@ IterProd k = iterate k (λ t → A × t) B
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-- records, perform the recursion, and unpackage.
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private module _ where
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BLattice : Lattice B
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BLattice = record
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lattice : ∀ {k : ℕ} → Lattice (IterProd k)
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lattice {0} = record
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{ _≈_ = _≈₂_
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; _⊔_ = _⊔₂_
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; _⊓_ = _⊓₂_
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; isLattice = lB
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}
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IterProdLattice : ∀ {k : ℕ} → Lattice (IterProd k)
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IterProdLattice {0} = BLattice
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IterProdLattice {suc k'} = record
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lattice {suc k'} = record
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{ _≈_ = _≈_
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; _⊔_ = _⊔_
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; _⊓_ = _⊓_
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@ -39,7 +36,7 @@ private module _ where
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}
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where
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Right : Lattice (IterProd k')
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Right = IterProdLattice {k'}
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Right = lattice {k'}
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open import Lattice.Prod
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_≈₁_ (Lattice._≈_ Right)
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@ -48,7 +45,7 @@ private module _ where
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lA (Lattice.isLattice Right)
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module _ (k : ℕ) where
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open Lattice.Lattice (IterProdLattice {k}) public
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open Lattice.Lattice (lattice {k}) public
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module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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(h₁ h₂ : ℕ)
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@ -67,8 +64,8 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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open IsFiniteHeightLattice isFiniteHeightLattice public
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BFiniteHeightLattice : FiniteHeightAndDecEq B
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BFiniteHeightLattice = record
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finiteHeightAndDec : ∀ {k : ℕ} → FiniteHeightAndDecEq (IterProd k)
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finiteHeightAndDec {0} = record
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{ height = h₂
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; _≈_ = _≈₂_
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; _⊔_ = _⊔₂_
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@ -79,10 +76,7 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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}
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; ≈-dec = ≈₂-dec
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}
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IterProdFiniteHeightLattice : ∀ {k : ℕ} → FiniteHeightAndDecEq (IterProd k)
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IterProdFiniteHeightLattice {0} = BFiniteHeightLattice
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IterProdFiniteHeightLattice {suc k'} = record
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finiteHeightAndDec {suc k'} = record
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{ height = h₁ + FiniteHeightAndDecEq.height Right
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; _≈_ = P._≈_
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; _⊔_ = P._⊔_
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@ -94,7 +88,7 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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; ≈-dec = ≈-dec ≈₁-dec (FiniteHeightAndDecEq.≈-dec Right)
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}
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where
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Right = IterProdFiniteHeightLattice {k'}
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Right = finiteHeightAndDec {k'}
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open import Lattice.Prod
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_≈₁_ (FiniteHeightAndDecEq._≈_ Right)
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@ -103,10 +97,10 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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lA (FiniteHeightAndDecEq.isLattice Right) as P
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module _ (k : ℕ) where
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open FiniteHeightAndDecEq (IterProdFiniteHeightLattice {k}) using (isFiniteHeightLattice) public
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open FiniteHeightAndDecEq (finiteHeightAndDec {k}) using (isFiniteHeightLattice) public
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private
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FHD = IterProdFiniteHeightLattice {k}
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FHD = finiteHeightAndDec {k}
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finiteHeightLattice : FiniteHeightLattice (IterProd k)
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finiteHeightLattice = record
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