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Add a witness for Map being an intersect semilattice

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2023-08-05 12:48:44 -07:00
parent d3e0db449c
commit 990a785463
1 changed files with 11 additions and 0 deletions
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Lattice.agda
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@ -238,6 +238,9 @@ module IsSemilatticeInstances where
_⊔_ : Map → Map → Map _⊔_ : Map → Map → Map
m₁ ⊔ m₂ = union _⊔₂_ m₁ m₂ m₁ ⊔ m₂ = union _⊔₂_ m₁ m₂
_⊓_ : Map → Map → Map
m₁ ⊓ m₂ = intersect _⊔₂_ m₁ m₂
module MapEquiv = IsEquivalenceInstances.ForMap A B ≡-dec-A _≈₂_ (IsSemilattice.≈-equiv sB) module MapEquiv = IsEquivalenceInstances.ForMap A B ≡-dec-A _≈₂_ (IsSemilattice.≈-equiv sB)
MapIsUnionSemilattice : IsSemilattice Map _≈_ _⊔_ MapIsUnionSemilattice : IsSemilattice Map _≈_ _⊔_
@ -248,6 +251,14 @@ module IsSemilatticeInstances where
; ⊔-idemp = union-idemp _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-idemp ; ⊔-idemp = union-idemp _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-idemp
} }
MapIsIntersectSemilattice : IsSemilattice Map _≈_ _⊓_
MapIsIntersectSemilattice = record
{ ≈-equiv = MapEquiv.LiftEquivalence
; ⊔-assoc = intersect-assoc _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-assoc
; ⊔-comm = intersect-comm _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-comm
; ⊔-idemp = intersect-idemp _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-idemp
}
module IsLatticeInstances where module IsLatticeInstances where
module ForNat where module ForNat where
open Nat open Nat