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Successfully prove that monotonic updates preserve existing indices

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-04-08 00:24:52 -07:00
parent bc5b4b7d9e
commit 4f14a7b765
1 changed files with 8 additions and 2 deletions
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@ -179,6 +179,14 @@ module Graphs where
) )
} }
open Relaxable {{...}} public
relax-preserves-[]≡ : ∀ (g₁ g₂ : Graph) (g₁⊆g₂ : g₁ ⊆ g₂) (idx : Graph.Index g₁) →
g₁ [ idx ] ≡ g₂ [ relax g₁⊆g₂ idx ]
relax-preserves-[]≡ g₁ g₂ (Mk-⊆ n refl g₁[]≡g₂[] _) idx =
trans (g₁[]≡g₂[] idx) (cong (λ vec → lookup vec (idx ↑ˡ n))
(cast-is-id refl (Graph.nodes g₂)))
MonotonicGraphFunction : (Graph → Set) → Set MonotonicGraphFunction : (Graph → Set) → Set
MonotonicGraphFunction T = (g₁ : Graph) → Σ Graph (λ g₂ → T g₂ × g₁ ⊆ g₂) MonotonicGraphFunction T = (g₁ : Graph) → Σ Graph (λ g₂ → T g₂ × g₁ ⊆ g₂)
@ -259,8 +267,6 @@ module Graphs where
addEdges g ((idx , idx') ∷ (idx₂ , idx) ∷ []) }) addEdges g ((idx , idx') ∷ (idx₂ , idx) ∷ []) })
map (λ { g ((idx₁ , idx₂) , idx , idx') → (idx , idx') }) map (λ { g ((idx₁ , idx₂) , idx , idx') → (idx , idx') })
-- open Relaxable {{...}} public
open import Lattice.MapSet _≟ˢ_ open import Lattice.MapSet _≟ˢ_
renaming renaming
( MapSet to StringSet ( MapSet to StringSet