agda-spa/Language.agda

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module Language where
open import Language.Base public
open import Language.Semantics public
open import Language.Traces public
open import Language.Graphs public
open import Language.Properties public
open import Data.Fin using (Fin; suc; zero)
open import Data.Fin.Properties as FinProp using (suc-injective)
open import Data.List as List using (List; []; _∷_)
open import Data.List.Membership.Propositional as ListMem using ()
open import Data.List.Relation.Unary.All using (All; []; _∷_)
open import Data.List.Relation.Unary.Any as RelAny using ()
open import Data.Nat using (; suc)
open import Data.Product using (_,_; Σ; proj₁; proj₂)
open import Data.Product.Properties as ProdProp using ()
open import Data.String using (String) renaming (_≟_ to _≟ˢ_)
open import Relation.Binary.PropositionalEquality using (_≡_; refl)
open import Relation.Nullary using (¬_)
open import Lattice
open import Utils using (Unique; push; Unique-map; x∈xs⇒fx∈fxs)
open import Lattice.MapSet _≟ˢ_ using ()
renaming
( MapSet to StringSet
; to-List to to-Listˢ
)
private
z≢sf : {n : } (f : Fin n) ¬ (zero suc f)
z≢sf f ()
z≢mapsfs : {n : } (fs : List (Fin n)) All (λ sf ¬ zero sf) (List.map suc fs)
z≢mapsfs [] = []
z≢mapsfs (f fs') = z≢sf f z≢mapsfs fs'
indices : (n : ) Σ (List (Fin n)) Unique
indices 0 = ([] , Utils.empty)
indices (suc n') =
let
(inds' , unids') = indices n'
in
( zero List.map suc inds'
, push (z≢mapsfs inds') (Unique-map suc suc-injective unids')
)
indices-complete : (n : ) (f : Fin n) f ListMem.∈ (proj₁ (indices n))
indices-complete (suc n') zero = RelAny.here refl
indices-complete (suc n') (suc f') = RelAny.there (x∈xs⇒fx∈fxs suc (indices-complete n' f'))
record Program : Set where
field
rootStmt : Stmt
graph : Graph
graph = buildCfg rootStmt
State : Set
State = Graph.Index graph
initialState : State
initialState = proj₁ (buildCfg-input rootStmt)
finalState : State
finalState = proj₁ (buildCfg-output rootStmt)
private
vars-Set : StringSet
vars-Set = Stmt-vars rootStmt
vars : List String
vars = to-Listˢ vars-Set
vars-Unique : Unique vars
vars-Unique = proj₂ vars-Set
states : List State
states = proj₁ (indices (Graph.size graph))
states-complete : (s : State) s ListMem.∈ states
states-complete = indices-complete (Graph.size graph)
states-Unique : Unique states
states-Unique = proj₂ (indices (Graph.size graph))
code : State List BasicStmt
code st = graph [ st ]
-- vars-complete : ∀ {k : String} (s : State) → k ∈ᵇ (code s) → k ListMem.∈ vars
-- vars-complete {k} s = ∈⇒∈-Stmts-vars {length} {k} {stmts} {s}
_≟_ : IsDecidable (_≡_ {_} {State})
_≟_ = FinProp._≟_
_≟ᵉ_ : IsDecidable (_≡_ {_} {Graph.Edge graph})
_≟ᵉ_ = ProdProp.≡-dec _≟_ _≟_
open import Data.List.Membership.DecPropositional _≟ᵉ_ using (_∈?_)
incoming : State List State
incoming idx = List.filter (λ idx' (idx' , idx) ∈? (Graph.edges graph)) states