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Prove monotonicity of eval

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2024-03-10 20:29:05 -07:00
parent 96f3ceaeb2
commit 8964ba59a1
2 changed files with 50 additions and 3 deletions
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9
Lattice/FiniteMap.agda
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@@ -12,7 +12,7 @@ module Lattice.FiniteMap {a b : Level} {A : Set a} {B : Set b}
open IsLattice lB using () renaming (_≼_ to _≼₂_)
open import Lattice.Map ≡-dec-A lB as Map
using (Map; ⊔-equal-keys; ⊓-equal-keys; ∈k-dec; m₁≼m₂⇒m₁[k]≼m₂[k])
using (Map; ⊔-equal-keys; ⊓-equal-keys; ∈k-dec)
renaming
( _≈_ to _≈ᵐ_
; _⊔_ to _⊔ᵐ_
@@ -30,6 +30,7 @@ open import Lattice.Map ≡-dec-A lB as Map
; absorb-⊓-⊔ to absorb-⊓ᵐ-⊔ᵐ
; ≈-dec to ≈ᵐ-dec
; _[_] to _[_]ᵐ
; m₁≼m₂⇒m₁[k]≼m₂[k] to m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ
; locate to locateᵐ
; keys to keysᵐ
; _updating_via_ to _updatingᵐ_via_
@@ -138,6 +139,10 @@ module WithKeys (ks : List A) where
; isLattice = isLattice
}
m₁≼m₂⇒m₁[k]≼m₂[k] : ∀ (fm₁ fm₂ : FiniteMap) {k : A} {v₁ v₂ : B} →
fm₁ ≼ fm₂ → (k , v₁) ∈ fm₁ → (k , v₂) ∈ fm₂ → v₁ ≼₂ v₂
m₁≼m₂⇒m₁[k]≼m₂[k] (m₁ , _) (m₂ , _) m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂ = m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ m₁ m₂ m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂
module GeneralizedUpdate
{l} {L : Set l}
{_≈ˡ_ : L → L → Set l} {_⊔ˡ_ : L → L → L} {_⊓ˡ_ : L → L → L}
@@ -177,7 +182,7 @@ module WithKeys (ks : List A) where
(v₁ , k,v₁∈m₁) = locateᵐ {m = m₁} k∈km₁
(v₂ , k,v₂∈m₂) = locateᵐ {m = m₂} k∈km₂
in
(m₁≼m₂⇒m₁[k]≼m₂[k] m₁ m₂ m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂) ∷ m₁≼m₂⇒m₁[ks]≼m₂[ks] fm₁ fm₂ ks'' m₁≼m₂
(m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ m₁ m₂ m₁≼m₂ k,v₁∈m₁ k,v₂∈m₂) ∷ m₁≼m₂⇒m₁[ks]≼m₂[ks] fm₁ fm₂ ks'' m₁≼m₂
... | no k∉km₁ | no k∉km₂ = m₁≼m₂⇒m₁[ks]≼m₂[ks] fm₁ fm₂ ks'' m₁≼m₂
... | yes k∈km₁ | no k∉km₂ = ⊥-elim (∈k-exclusive fm₁ fm₂ (k∈km₁ , k∉km₂))
... | no k∉km₁ | yes k∈km₂ = ⊥-elim (∈k-exclusive fm₂ fm₁ (k∈km₂ , k∉km₁))