DanilaFe/agda-spa
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Rename some definitions in Nat and expose bundle

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-02-11 20:56:21 -08:00
parent a920608bef
commit 08f3f49640
1 changed files with 16 additions and 8 deletions
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24
Lattice/Nat.agda
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@ -18,8 +18,8 @@ private
≡-⊓-cong : ∀ {a₁ a₂ a₃ a₄} → a₁ ≡ a₂ → a₃ ≡ a₄ → (a₁ ⊓ a₃) ≡ (a₂ ⊓ a₄) ≡-⊓-cong : ∀ {a₁ a₂ a₃ a₄} → a₁ ≡ a₂ → a₃ ≡ a₄ → (a₁ ⊓ a₃) ≡ (a₂ ⊓ a₄)
≡-⊓-cong a₁≡a₂ a₃≡a₄ rewrite a₁≡a₂ rewrite a₃≡a₄ = refl ≡-⊓-cong a₁≡a₂ a₃≡a₄ rewrite a₁≡a₂ rewrite a₃≡a₄ = refl
NatIsMaxSemilattice : IsSemilattice ℕ _≡_ _⊔_ isMaxSemilattice : IsSemilattice ℕ _≡_ _⊔_
NatIsMaxSemilattice = record isMaxSemilattice = record
{ ≈-equiv = record { ≈-equiv = record
{ ≈-refl = refl { ≈-refl = refl
; ≈-sym = sym ; ≈-sym = sym
@ -31,8 +31,8 @@ NatIsMaxSemilattice = record
; ⊔-idemp = ⊔-idem ; ⊔-idemp = ⊔-idem
} }
NatIsMinSemilattice : IsSemilattice ℕ _≡_ _⊓_ isMinSemilattice : IsSemilattice ℕ _≡_ _⊓_
NatIsMinSemilattice = record isMinSemilattice = record
{ ≈-equiv = record { ≈-equiv = record
{ ≈-refl = refl { ≈-refl = refl
; ≈-sym = sym ; ≈-sym = sym
@ -74,10 +74,18 @@ private
helper : x ⊔ (x ⊓ y) ≤ x ⊔ x → x ⊔ x ≡ x → x ⊔ (x ⊓ y) ≤ x helper : x ⊔ (x ⊓ y) ≤ x ⊔ x → x ⊔ x ≡ x → x ⊔ (x ⊓ y) ≤ x
helper x⊔x⊓y≤x⊔x x⊔x≡x rewrite x⊔x≡x = x⊔x⊓y≤x⊔x helper x⊔x⊓y≤x⊔x x⊔x≡x rewrite x⊔x≡x = x⊔x⊓y≤x⊔x
NatIsLattice : IsLattice ℕ _≡_ _⊔_ _⊓_ isLattice : IsLattice ℕ _≡_ _⊔_ _⊓_
NatIsLattice = record isLattice = record
{ joinSemilattice = NatIsMaxSemilattice { joinSemilattice = isMaxSemilattice
; meetSemilattice = NatIsMinSemilattice ; meetSemilattice = isMinSemilattice
; absorb-⊔-⊓ = λ x y → maxmin-absorb {x} {y} ; absorb-⊔-⊓ = λ x y → maxmin-absorb {x} {y}
; absorb-⊓-⊔ = λ x y → minmax-absorb {x} {y} ; absorb-⊓-⊔ = λ x y → minmax-absorb {x} {y}
} }
lattice : Lattice ℕ
lattice = record
{ _≈_ = _≡_
; _⊔_ = _⊔_
; _⊓_ = _⊓_
; isLattice = isLattice
}