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Do away with implicit arguments in some places where they can't be inferred 

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2023-07-24 23:58:14 -07:00
parent 4aea9a0358
commit 850984ec15
1 changed files with 15 additions and 15 deletions
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Lattice.agda
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@ -90,33 +90,33 @@ module IsEquivalenceInstances where
_⊆_ : Map → Map → Set (Agda.Primitive._⊔_ a b)
_⊆_ = subset _≈₂_
⊆-refl : {m : Map} → m ⊆ m
⊆-refl k v k,v∈m = (v , (≈₂-refl , k,v∈m))
⊆-refl : (m : Map) → m ⊆ m
⊆-refl _ k v k,v∈m = (v , (≈₂-refl , k,v∈m))
⊆-trans : {m₁ m₂ m₃ : Map} → m₁ ⊆ m₂ → m₂ ⊆ m₃ → m₁ ⊆ m₃
⊆-trans m₁⊆m₂ m₂⊆m₃ k v k,v∈m₁ =
⊆-trans : (m₁ m₂ m₃ : Map) → m₁ ⊆ m₂ → m₂ ⊆ m₃ → m₁ ⊆ m₃
⊆-trans _ _ _ m₁⊆m₂ m₂⊆m₃ k v k,v∈m₁ =
let
(v' , (v≈v' , k,v'∈m₂)) = m₁⊆m₂ k v k,v∈m₁
(v'' , (v'≈v'' , k,v''∈m₃)) = m₂⊆m₃ k v' k,v'∈m₂
in (v'' , (≈₂-trans v≈v' v'≈v'' , k,v''∈m₃))
≈-refl : {m : Map} → m ≈ m
≈-refl {m} = (⊆-refl {m}, ⊆-refl {m})
≈-refl : (m : Map) → m ≈ m
≈-refl m = (⊆-refl m , ⊆-refl m)
≈-sym : {m₁ m₂ : Map} → m₁ ≈ m₂ → m₂ ≈ m₁
≈-sym (m₁⊆m₂ , m₂⊆m₁) = (m₂⊆m₁ , m₁⊆m₂)
≈-sym : (m₁ m₂ : Map) → m₁ ≈ m₂ → m₂ ≈ m₁
≈-sym _ _ (m₁⊆m₂ , m₂⊆m₁) = (m₂⊆m₁ , m₁⊆m₂)
≈-trans : {m₁ m₂ m₃ : Map} → m₁ ≈ m₂ → m₂ ≈ m₃ → m₁ ≈ m₃
≈-trans {m₁} {m₂} {m₃} (m₁⊆m₂ , m₂⊆m₁) (m₂⊆m₃ , m₃⊆m₂) =
( ⊆-trans {m₁} {m₂} {m₃} m₁⊆m₂ m₂⊆m₃
, ⊆-trans {m₃} {m₂} {m₁} m₃⊆m₂ m₂⊆m₁
≈-trans : (m₁ m₂ m₃ : Map) → m₁ ≈ m₂ → m₂ ≈ m₃ → m₁ ≈ m₃
≈-trans m₁ m₂ m₃ (m₁⊆m₂ , m₂⊆m₁) (m₂⊆m₃ , m₃⊆m₂) =
( ⊆-trans m₁ m₂ m₃ m₁⊆m₂ m₂⊆m₃
, ⊆-trans m₃ m₂ m₁ m₃⊆m₂ m₂⊆m₁
)
LiftEquivalence : IsEquivalence Map _≈_
LiftEquivalence = record
{ ≈-refl = λ {m₁} → ≈-refl {m₁}
; ≈-sym = λ {m₁} {m₂} → ≈-sym {m₁} {m₂}
; ≈-trans = λ {m₁} {m₂} {m₃} → ≈-trans {m₁} {m₂} {m₃}
{ ≈-refl = λ {m₁} → ≈-refl m₁
; ≈-sym = λ {m₁} {m₂} → ≈-sym m₁ m₂
; ≈-trans = λ {m₁} {m₂} {m₃} → ≈-trans m₁ m₂ m₃
}
module IsSemilatticeInstances where