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Implement graph construction using <*>, map, and update.

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2024-04-07 20:26:38 -07:00
parent d4b0796715
commit 195537fe15
1 changed files with 34 additions and 0 deletions
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@ -182,6 +182,20 @@ module Graphs where
with (g'' , (t₂ , g'⊆g'')) ← f₂ g' =
(g'' , ((Relaxable.relax r g'⊆g'' t₁ , t₂) , ⊆-trans g⊆g' g'⊆g''))
infixl 2 _update_
_update_ : ∀ {T : Graph → Set} {{ TRelaxable : Relaxable T }} →
MonotonicGraphFunction T → (∀ (g : Graph) → T g → Σ Graph (λ g' → g ⊆ g')) →
MonotonicGraphFunction T
_update_ {{r}} f mod g
with (g' , (t , g⊆g')) ← f g
with (g'' , g'⊆g'') ← mod g' t =
(g'' , ((Relaxable.relax r g'⊆g'' t , ⊆-trans g⊆g' g'⊆g'')))
infixl 2 _map_
_map_ : ∀ {T₁ T₂ : Graph → Set} →
MonotonicGraphFunction T₁ → (∀ (g : Graph) → T₁ g → T₂ g) →
MonotonicGraphFunction T₂
_map_ f fn g = let (g' , (t₁ , g⊆g')) = f g in (g' , (fn g' t₁ , g⊆g'))
module Construction where
pushBasicBlock : List BasicStmt → MonotonicGraphFunction Graph.Index
@ -196,9 +210,29 @@ module Graphs where
in
(g₁ ∙ g' , (Graph.size g₁ ↑ʳ zero , (g' , refl)))
addEdges : ∀ (g : Graph) → List (Graph.Edge g) → Σ Graph (λ g' → g ⊆ g')
addEdges g es = {!!}
pushEmptyBlock : MonotonicGraphFunction Graph.Index
pushEmptyBlock = pushBasicBlock []
buildCfg : Stmt → MonotonicGraphFunction (Graph.Index ⊗ Graph.Index)
buildCfg ⟨ bs₁ ⟩ = pushBasicBlock (bs₁ ∷ []) map (λ g idx → (idx , idx))
buildCfg (s₁ then s₂) =
(buildCfg s₁ ⟨⊗⟩ buildCfg s₂)
update (λ { g ((idx₁ , idx₂) , (idx₃ , idx₄)) → addEdges g ((idx₂ , idx₃) ∷ []) })
map (λ { g ((idx₁ , idx₂) , (idx₃ , idx₄)) → (idx₁ , idx₄) })
buildCfg (if _ then s₁ else s₂) =
(buildCfg s₁ ⟨⊗⟩ buildCfg s₂ ⟨⊗⟩ pushEmptyBlock ⟨⊗⟩ pushEmptyBlock)
update (λ { g ((idx₁ , idx₂) , (idx₃ , idx₄) , idx , idx') →
addEdges g ((idx , idx₁) ∷ (idx , idx₃) ∷ (idx₂ , idx') ∷ (idx₄ , idx') ∷ []) })
map (λ { g ((idx₁ , idx₂) , (idx₃ , idx₄) , idx , idx') → (idx , idx') })
buildCfg (while _ repeat s) =
(buildCfg s ⟨⊗⟩ pushEmptyBlock ⟨⊗⟩ pushEmptyBlock)
update (λ { g ((idx₁ , idx₂) , idx , idx') →
addEdges g ((idx , idx') ∷ (idx₂ , idx) ∷ []) })
map (λ { g ((idx₁ , idx₂) , idx , idx') → (idx , idx') })
-- open Relaxable {{...}} public
open import Lattice.MapSet _≟ˢ_