108 lines
4.0 KiB
Plaintext
108 lines
4.0 KiB
Plaintext
module Language.Graphs where
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open import Language.Base using (Expr; Stmt; BasicStmt; ⟨_⟩; _then_; if_then_else_; while_repeat_)
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open import Data.Fin as Fin using (Fin; suc; zero)
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open import Data.Fin.Properties as FinProp using (suc-injective)
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open import Data.List as List using (List; []; _∷_)
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open import Data.List.Membership.Propositional as ListMem using ()
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open import Data.List.Membership.Propositional.Properties as ListMemProp using ()
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open import Data.Nat as Nat using (ℕ; suc)
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open import Data.Nat.Properties using (+-assoc; +-comm)
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open import Data.Product using (_×_; Σ; _,_)
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open import Data.Vec using (Vec; []; _∷_; lookup; cast; _++_)
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open import Data.Vec.Properties using (cast-is-id; ++-assoc; lookup-++ˡ; cast-sym; ++-identityʳ; lookup-++ʳ)
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open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; refl; subst; trans)
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open import Lattice
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open import Utils using (x∈xs⇒fx∈fxs; _⊗_; _,_; ∈-cartesianProduct)
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record Graph : Set where
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constructor MkGraph
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field
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size : ℕ
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Index : Set
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Index = Fin size
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Edge : Set
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Edge = Index × Index
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field
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nodes : Vec (List BasicStmt) size
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edges : List Edge
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inputs : List Index
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outputs : List Index
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_↑ˡ_ : ∀ {n} → (Fin n × Fin n) → ∀ m → (Fin (n Nat.+ m) × Fin (n Nat.+ m))
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_↑ˡ_ (idx₁ , idx₂) m = (idx₁ Fin.↑ˡ m , idx₂ Fin.↑ˡ m)
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_↑ʳ_ : ∀ {m} n → (Fin m × Fin m) → Fin (n Nat.+ m) × Fin (n Nat.+ m)
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_↑ʳ_ n (idx₁ , idx₂) = (n Fin.↑ʳ idx₁ , n Fin.↑ʳ idx₂)
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_↑ˡⁱ_ : ∀ {n} → List (Fin n) → ∀ m → List (Fin (n Nat.+ m))
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_↑ˡⁱ_ l m = List.map (Fin._↑ˡ m) l
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_↑ʳⁱ_ : ∀ {m} n → List (Fin m) → List (Fin (n Nat.+ m))
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_↑ʳⁱ_ n l = List.map (n Fin.↑ʳ_) l
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_↑ˡᵉ_ : ∀ {n} → List (Fin n × Fin n) → ∀ m → List (Fin (n Nat.+ m) × Fin (n Nat.+ m))
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_↑ˡᵉ_ l m = List.map (_↑ˡ m) l
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_↑ʳᵉ_ : ∀ {m} n → List (Fin m × Fin m) → List (Fin (n Nat.+ m) × Fin (n Nat.+ m))
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_↑ʳᵉ_ n l = List.map (n ↑ʳ_) l
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infixl 5 _∙_
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_∙_ : Graph → Graph → Graph
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_∙_ g₁ g₂ = record
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{ size = Graph.size g₁ Nat.+ Graph.size g₂
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; nodes = Graph.nodes g₁ ++ Graph.nodes g₂
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; edges = (Graph.edges g₁ ↑ˡᵉ Graph.size g₂) List.++
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(Graph.size g₁ ↑ʳᵉ Graph.edges g₂)
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; inputs = (Graph.inputs g₁ ↑ˡⁱ Graph.size g₂) List.++
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(Graph.size g₁ ↑ʳⁱ Graph.inputs g₂)
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; outputs = (Graph.outputs g₁ ↑ˡⁱ Graph.size g₂) List.++
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(Graph.size g₁ ↑ʳⁱ Graph.outputs g₂)
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}
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infixl 5 _↦_
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_↦_ : Graph → Graph → Graph
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_↦_ g₁ g₂ = record
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{ size = Graph.size g₁ Nat.+ Graph.size g₂
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; nodes = Graph.nodes g₁ ++ Graph.nodes g₂
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; edges = (Graph.edges g₁ ↑ˡᵉ Graph.size g₂) List.++
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(Graph.size g₁ ↑ʳᵉ Graph.edges g₂) List.++
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(List.cartesianProduct (Graph.outputs g₁ ↑ˡⁱ Graph.size g₂)
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(Graph.size g₁ ↑ʳⁱ Graph.inputs g₂))
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; inputs = Graph.inputs g₁ ↑ˡⁱ Graph.size g₂
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; outputs = Graph.size g₁ ↑ʳⁱ Graph.outputs g₂
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}
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loop : Graph → Graph
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loop g = record
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{ size = Graph.size g
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; nodes = Graph.nodes g
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; edges = Graph.edges g List.++
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List.cartesianProduct (Graph.outputs g) (Graph.inputs g)
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; inputs = Graph.inputs g
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; outputs = Graph.outputs g
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}
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_[_] : ∀ (g : Graph) → Graph.Index g → List BasicStmt
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_[_] g idx = lookup (Graph.nodes g) idx
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singleton : List BasicStmt → Graph
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singleton bss = record
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{ size = 1
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; nodes = bss ∷ []
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; edges = []
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; inputs = zero ∷ []
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; outputs = zero ∷ []
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}
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buildCfg : Stmt → Graph
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buildCfg ⟨ bs₁ ⟩ = singleton (bs₁ ∷ [])
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buildCfg (s₁ then s₂) = buildCfg s₁ ↦ buildCfg s₂
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buildCfg (if _ then s₁ else s₂) = singleton [] ↦ (buildCfg s₁ ∙ buildCfg s₂) ↦ singleton []
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buildCfg (while _ repeat s) = loop (buildCfg s ↦ singleton [])
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