{-# LANGUAGE UnicodeSyntax, TypeSynonymInstances, FlexibleInstances, MultiParamTypeClasses, FlexibleContexts #-} -- | Rewrite rules are represented as nested monads: a 'Rule' is a 'Pattern' that returns a 'Rewrite' the latter directly defining the transformation of the graph. -- -- For rule construction a few functions a provided: The most basic one is 'rewrite'. But in most cases 'erase', 'rewire', and 'replace*' should be more convenient. These functions express rewrites that /replace/ the matched nodes of the 'Pattern', which comes quite close to the @L -> R@ form in which graph rewriting rules are usually expressed. module GraphRewriting.Rule where import Prelude.Unicode import GraphRewriting.Graph import GraphRewriting.Graph.Internal (Port (Edge)) import GraphRewriting.Graph.Write import GraphRewriting.Rule.Internal import GraphRewriting.Pattern import Control.Monad.State import Control.Monad.Reader import Data.List (nub) import Data.Either -- | A rewriting rule is defined as a 'Pattern' that returns a 'Rewrite' type Rule n = Pattern n (Rewrite n ()) -- | Apply rule at an arbitrary position if applicable apply ∷ Rule n → Rewrite n () apply r = do contractions ← liftM (evalPattern r) ask when (not $ null contractions) (head contractions >> return ()) -- rule construction --------------------------------------------------------- -- | primitive rule construction with the matched nodes of the left hand side as a parameter rewrite ∷ (Match → Rewrite n a) → Rule n rewrite r = do h ← history return $ r h >> return () -- | constructs a rule that deletes all of the matched nodes from the graph erase ∷ View [Port] n ⇒ Rule n erase = rewrite $ mapM_ deleteNode . nub -- | Constructs a rule from a list of rewirings. Each rewiring specifies a list of hyperedges that are to be merged into a single hyperedge. All matched nodes of the left-hand side are removed. rewire ∷ View [Port] n ⇒ [[Edge]] → Rule n rewire ess = rewrite $ \hist → do mapM_ mergeEs $ joinEdges ess mapM_ deleteNode $ nub hist data RHS v = Node v | Wire Edge Edge | Merge [Edge] -- | Constructs a rule that replaces the matched nodes of the left-hand side by new nodes and rewirings. It generates an amount of new edges specified by the 'Int'. In most cases the functions below named @replace*@ should be sufficient. replace ∷ (View [Port] n, View v n) ⇒ Int → ([Edge] → [RHS v]) → Rule n replace n rhs = do let vs = fst $ partition (replicate n $ Edge 0) lhsNodes ← liftM nub history when (null lhsNodes ∧ not (null vs)) (fail "need at least one matching node to clone new nodes from") return $ do es ← replicateM n newEdge let (vs,ess) = partition es zipWithM_ copyNode (cycle lhsNodes) vs mapM_ mergeEs $ joinEdges ess mapM_ deleteNode lhsNodes where partition es = partitionEithers $ map splitRHS (rhs es) where splitRHS (Node v) = Left v splitRHS (Wire e1 e2) = Right [e1,e2] splitRHS (Merge es) = if length es < 2 then error "Merge requires list length >= 2" else Right es -- | Replaces the matched nodes by a list of new nodes and rewirings. replace0 vs = replace 0 $ \[] → vs -- | Replaces the matched nodes by a list of new nodes and rewirings. It also generates one new edge. replace1 vs = replace 1 $ \[e1] → vs e1 -- | Replaces the matched nodes by a list of new nodes and rewirings. It also generates two new edges. replace2 vs = replace 2 $ \[e1,e2] → vs e1 e2 -- | You get the idea. replace3 vs = replace 3 $ \[e1,e2,e3] → vs e1 e2 e3 replace4 vs = replace 4 $ \[e1,e2,e3,e4] → vs e1 e2 e3 e4 replace5 vs = replace 5 $ \[e1,e2,e3,e4,e5] → vs e1 e2 e3 e4 e5 replace6 vs = replace 6 $ \[e1,e2,e3,e4,e5,e6] → vs e1 e2 e3 e4 e5 e6 replace7 vs = replace 7 $ \[e1,e2,e3,e4,e5,e6,e7] → vs e1 e2 e3 e4 e5 e6 e7 replace8 vs = replace 8 $ \[e1,e2,e3,e4,e5,e6,e7,e8] → vs e1 e2 e3 e4 e5 e6 e7 e8 -- combinators --------------------------------------------------------------- -- | Apply two rules consecutively. Second rule is only applied if first one succeeds. Fails if (and only if) first rule fails. (>>>) ∷ Rule n → Rule n → Rule n r1 >>> r2 = do rw1 ← r1 return $ rw1 >> apply r2 -- | Make a rule exhaustive, i.e. such that (when applied) it reduces redexes until no redexes are occur in the graph. exhaustive ∷ Rule n → Rule n exhaustive = foldr1 (>>>) . repeat -- | Make a rule parallel, i.e. such that (when applied) all current redexes are contracted one by one. Neither new redexes or destroyed redexes are reduced. everywhere ∷ Rule n → Rule n everywhere r = do ms ← amnesia $ matches r exhaustive $ restrictOverlap (\hist future → future ∈ ms) r