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