    {-# OPTIONS_GHC -Wunused-imports #-}

    {- | Checking for recursion:

       - We detect truly (co)recursive definitions by computing the
         dependency graph and checking for cycles.

       - This is inexpensive and let us skip the termination check
         when there's no (co)recursion

       Original contribution by Andrea Vezzosi (sanzhiyan).
       This implementation by Andreas.
    -}

    module Agda.Termination.RecCheck
        ( MutualNames
        , recursive
        , anyDefs
        )
     where

    import Control.Monad (forM)
    import Data.Foldable
    import Data.Graph
    import Data.IntMap (IntMap)
    import qualified Data.IntMap as IntMap
    import qualified Data.Map as Map
    import qualified Data.Map.Strict as MapS
    import Data.Maybe
    import Data.Set (Set)
    import qualified Data.Set as Set

    import Agda.Syntax.Internal
    import Agda.Syntax.Internal.Defs
    import Agda.Syntax.Common.Pretty  (prettyShow)

    import Agda.TypeChecking.Monad

    import Agda.Utils.Impossible

    -- | The mutual block we are checking.
    --
    --   The functions are numbered according to their order of appearance
    --   in this set.

    type MutualNames = Set QName

    -- | We compute for each clause the set of potentially recursive names.
    type NamesPerClause = IntMap (Set QName)

    -- | Given a list of formally mutually recursive functions,
    --   check for actual recursive calls in the bodies of these functions.
    --   Returns the actually recursive functions as strongly connected components.
    --
    --   As a side effect, update the 'clauseRecursive' field in the
    --   clauses belonging to the given functions.
    recursive :: Set QName -> TCM [MutualNames]
    recursive :: Set QName -> TCM [Set QName]
    recursive Set QName
    names = do
      let names' :: [QName]
    names' = Set QName -> [QName]
    forall a. Set a -> [a]
    forall (t :: * -> *) a. Foldable t => t a -> [a]
    toList Set QName
    names
      -- For each function, get names per clause and total.
      (perClauses, nss) <- [(IntMap (Set QName), Set QName)]
    -> ([IntMap (Set QName)], [Set QName])
    forall a b. [(a, b)] -> ([a], [b])
    unzip ([(IntMap (Set QName), Set QName)]
     -> ([IntMap (Set QName)], [Set QName]))
    -> TCMT IO [(IntMap (Set QName), Set QName)]
    -> TCMT IO ([IntMap (Set QName)], [Set QName])
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (QName -> TCMT IO (IntMap (Set QName), Set QName))
    -> [QName] -> TCMT IO [(IntMap (Set QName), Set QName)]
    forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    (a -> m b) -> t a -> m (t b)
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
    mapM ((QName -> Bool) -> QName -> TCMT IO (IntMap (Set QName), Set QName)
    recDef (QName -> Set QName -> Bool
    forall a. Ord a => a -> Set a -> Bool
    `Set.member` Set QName
    names)) [QName]
    names'
      -- Create graph suitable for stronglyConnComp.
      -- Nodes are identical to node keys.
      let graph  = (QName -> Set QName -> (QName, QName, [QName]))
    -> [QName] -> [Set QName] -> [(QName, QName, [QName])]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith (\ QName
    x Set QName
    ns -> (QName
    x, QName
    x, Set QName -> [QName]
    forall a. Set a -> [a]
    Set.toList Set QName
    ns)) [QName]
    names' [Set QName]
    nss
      let sccs   = [(QName, QName, [QName])] -> [SCC QName]
    forall key node. Ord key => [(node, key, [key])] -> [SCC node]
    stronglyConnComp [(QName, QName, [QName])]
    graph
      let nonRec = (SCC QName -> Maybe QName) -> [SCC QName] -> [QName]
    forall a b. (a -> Maybe b) -> [a] -> [b]
    mapMaybe (\case AcyclicSCC QName
    x -> QName -> Maybe QName
    forall a. a -> Maybe a
    Just QName
    x
                                   SCC QName
    _            -> Maybe QName
    forall a. Maybe a
    Nothing)
                     [SCC QName]
    sccs
      let recs   = (SCC QName -> Maybe (Set QName)) -> [SCC QName] -> [Set QName]
    forall a b. (a -> Maybe b) -> [a] -> [b]
    mapMaybe (\case CyclicSCC [QName]
    xs -> Set QName -> Maybe (Set QName)
    forall a. a -> Maybe a
    Just ([QName] -> Set QName
    forall a. Ord a => [a] -> Set a
    Set.fromList [QName]
    xs)
                                   SCC QName
    _            -> Maybe (Set QName)
    forall a. Maybe a
    Nothing)
                     [SCC QName]
    sccs

      reportSLn "rec.graph" 60 $ show graph

      -- Mark all non-recursive functions and their clauses as such.
      mapM_ markNonRecursive nonRec

      -- Mark individual clauses of recursive functions:
      --------------------------------------------------
      -- Map names to clause numbers to sets of mentioned names.
      let clMap = (IntMap (Set QName) -> IntMap (Set QName) -> IntMap (Set QName))
    -> [(QName, IntMap (Set QName))] -> Map QName (IntMap (Set QName))
    forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
    Map.fromListWith IntMap (Set QName) -> IntMap (Set QName) -> IntMap (Set QName)
    forall a. HasCallStack => a
    __IMPOSSIBLE__ ([(QName, IntMap (Set QName))] -> Map QName (IntMap (Set QName)))
    -> [(QName, IntMap (Set QName))] -> Map QName (IntMap (Set QName))
    forall a b. (a -> b) -> a -> b
    $ [QName] -> [IntMap (Set QName)] -> [(QName, IntMap (Set QName))]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [QName]
    names' [IntMap (Set QName)]
    perClauses
      -- Walk through SCCs.
      forM_ recs $ \ Set QName
    scc -> do
        -- Does a set of names have an overlap with the current scc?
        let overlap :: Set QName -> Bool
    overlap Set QName
    s = (QName -> Bool) -> Set QName -> Bool
    forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
    any (QName -> Set QName -> Bool
    forall a. Ord a => a -> Set a -> Bool
    `Set.member` Set QName
    s) Set QName
    scc
        -- Walk through members of SCC.
        Set QName -> (QName -> TCMT IO ()) -> TCMT IO ()
    forall (t :: * -> *) (m :: * -> *) a b.
    (Foldable t, Monad m) =>
    t a -> (a -> m b) -> m ()
    forM_ Set QName
    scc ((QName -> TCMT IO ()) -> TCMT IO ())
    -> (QName -> TCMT IO ()) -> TCMT IO ()
    forall a b. (a -> b) -> a -> b
    $ \ QName
    x -> do
          -- Get the NamesPerClause for the current function x.
          let perClause :: IntMap (Set QName)
    perClause  = IntMap (Set QName)
    -> QName -> Map QName (IntMap (Set QName)) -> IntMap (Set QName)
    forall k a. Ord k => a -> k -> Map k a -> a
    Map.findWithDefault IntMap (Set QName)
    forall a. HasCallStack => a
    __IMPOSSIBLE__ QName
    x Map QName (IntMap (Set QName))
    clMap
          -- A clause is recursive if its calls overlap with its scc.
          let recClause :: Key -> Bool
    recClause Key
    i = Set QName -> Bool
    overlap (Set QName -> Bool) -> Set QName -> Bool
    forall a b. (a -> b) -> a -> b
    $ Set QName -> Key -> IntMap (Set QName) -> Set QName
    forall a. a -> Key -> IntMap a -> a
    IntMap.findWithDefault Set QName
    forall a. HasCallStack => a
    __IMPOSSIBLE__ Key
    i IntMap (Set QName)
    perClause
          (Key -> Bool) -> QName -> TCMT IO ()
    markRecursive Key -> Bool
    recClause QName
    x

      -- Return recursive SCCs.
      return recs

    -- | Mark a function as terminating and all its clauses as non-recursive.
    markNonRecursive :: QName -> TCM ()
    markNonRecursive :: QName -> TCMT IO ()
    markNonRecursive QName
    q = (Signature -> Signature) -> TCMT IO ()
    forall (m :: * -> *).
    MonadTCState m =>
    (Signature -> Signature) -> m ()
    modifySignature ((Signature -> Signature) -> TCMT IO ())
    -> (Signature -> Signature) -> TCMT IO ()
    forall a b. (a -> b) -> a -> b
    $ QName -> (Definition -> Definition) -> Signature -> Signature
    updateDefinition QName
    q ((Definition -> Definition) -> Signature -> Signature)
    -> (Definition -> Definition) -> Signature -> Signature
    forall a b. (a -> b) -> a -> b
    $ (Defn -> Defn) -> Definition -> Definition
    updateTheDef ((Defn -> Defn) -> Definition -> Definition)
    -> (Defn -> Defn) -> Definition -> Definition
    forall a b. (a -> b) -> a -> b
    $ \case
      def :: Defn
    def@Function{} -> Defn
    def
       { funTerminates = Just True
       , funClauses    = map (\ Clause
    cl -> Clause
    cl { clauseRecursive = Just False }) $ funClauses def
       }
      def :: Defn
    def@Record{} -> Defn
    def
       { recTerminates = Just True
       }
      Defn
    def -> Defn
    def

    -- | Mark all clauses of a function as recursive or non-recursive.
    markRecursive
      :: (Int -> Bool)  -- ^ Which clauses are recursive?
      -> QName -> TCM ()
    markRecursive :: (Key -> Bool) -> QName -> TCMT IO ()
    markRecursive Key -> Bool
    f QName
    q = (Signature -> Signature) -> TCMT IO ()
    forall (m :: * -> *).
    MonadTCState m =>
    (Signature -> Signature) -> m ()
    modifySignature ((Signature -> Signature) -> TCMT IO ())
    -> (Signature -> Signature) -> TCMT IO ()
    forall a b. (a -> b) -> a -> b
    $ QName -> (Definition -> Definition) -> Signature -> Signature
    updateDefinition QName
    q ((Definition -> Definition) -> Signature -> Signature)
    -> (Definition -> Definition) -> Signature -> Signature
    forall a b. (a -> b) -> a -> b
    $ (Defn -> Defn) -> Definition -> Definition
    updateTheDef ((Defn -> Defn) -> Definition -> Definition)
    -> (Defn -> Defn) -> Definition -> Definition
    forall a b. (a -> b) -> a -> b
    $ \case
      def :: Defn
    def@Function{} -> Defn
    def
       { funClauses    = zipWith (\ Key
    i Clause
    cl -> Clause
    cl { clauseRecursive = Just (f i) }) [0..] $ funClauses def
       }
      Defn
    def -> Defn
    def

    -- | @recDef names name@ returns all definitions from @names@
    --   that are used in the type and body of @name@.
    recDef :: (QName -> Bool) -> QName -> TCM (NamesPerClause, Set QName)
    recDef :: (QName -> Bool) -> QName -> TCMT IO (IntMap (Set QName), Set QName)
    recDef QName -> Bool
    include QName
    name = do
      -- Retrieve definition
      def <- QName -> TCMT IO Definition
    forall (m :: * -> *). HasConstInfo m => QName -> m Definition
    getConstInfo QName
    name

      -- Get names in type
      ns1 <- anyDefs include (defType def)

      -- Get names in body
      (perClause, ns2) <- case theDef def of

        Function{ funClauses :: Defn -> [Clause]
    funClauses = [Clause]
    cls } -> do
          perClause <- do
            [(Key, Clause)]
    -> ((Key, Clause) -> TCMT IO (Key, Set QName))
    -> TCMT IO [(Key, Set QName)]
    forall (t :: * -> *) (m :: * -> *) a b.
    (Traversable t, Monad m) =>
    t a -> (a -> m b) -> m (t b)
    forM ([Key] -> [Clause] -> [(Key, Clause)]
    forall a b. [a] -> [b] -> [(a, b)]
    zip [Key
    0..] [Clause]
    cls) (((Key, Clause) -> TCMT IO (Key, Set QName))
     -> TCMT IO [(Key, Set QName)])
    -> ((Key, Clause) -> TCMT IO (Key, Set QName))
    -> TCMT IO [(Key, Set QName)]
    forall a b. (a -> b) -> a -> b
    $ \ (Key
    i, Clause
    cl) ->
              (Key
    i,) (Set QName -> (Key, Set QName))
    -> TCM (Set QName) -> TCMT IO (Key, Set QName)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> (QName -> Bool) -> Clause -> TCM (Set QName)
    forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
    anyDefs QName -> Bool
    include Clause
    cl
          return (IntMap.fromList perClause, mconcat $ map snd perClause)

        Datatype{ dataClause :: Defn -> Maybe Clause
    dataClause = Just Clause
    cl } -> do
          ns <- (QName -> Bool) -> Clause -> TCM (Set QName)
    forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
    anyDefs QName -> Bool
    include Clause
    cl
          return (IntMap.singleton 0 ns, ns)

        Record{ Maybe Clause
    recClause :: Maybe Clause
    recClause :: Defn -> Maybe Clause
    recClause, Telescope
    recTel :: Telescope
    recTel :: Defn -> Telescope
    recTel } -> do
          ns1 <- (QName -> Bool) -> Maybe Clause -> TCM (Set QName)
    forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
    anyDefs QName -> Bool
    include Maybe Clause
    recClause
          ns2 <- anyDefs include recTel
          let ns = Set QName
    ns1 Set QName -> Set QName -> Set QName
    forall a. Monoid a => a -> a -> a
    `mappend` Set QName
    ns2
          return (IntMap.singleton 0 ns, ns)

        Defn
    _ -> (IntMap (Set QName), Set QName)
    -> TCMT IO (IntMap (Set QName), Set QName)
    forall a. a -> TCMT IO a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (IntMap (Set QName)
    forall a. Monoid a => a
    mempty, Set QName
    forall a. Monoid a => a
    mempty)

      reportS "rec.graph" 20
        [ "recDef " ++ prettyShow name
        , "  names in the type: " ++ prettyShow ns1
        , "  names in the def:  " ++ prettyShow ns2
        ]
      return (perClause, ns1 `mappend` ns2)

    -- | @anysDef names a@ returns all definitions from @names@
    --   that are used in @a@.
    anyDefs :: GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
    anyDefs :: forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
    anyDefs QName -> Bool
    include a
    a = do
      -- Prepare function to lookup metas outside of TCM
      st <- Lens' TCState (Map MetaId MetaVariable)
    -> TCMT IO (Map MetaId MetaVariable)
    forall (m :: * -> *) a. ReadTCState m => Lens' TCState a -> m a
    useR (Map MetaId MetaVariable -> f (Map MetaId MetaVariable))
    -> TCState -> f TCState
    Lens' TCState (Map MetaId MetaVariable)
    stSolvedMetaStore
      let lookup MetaId
    x = MetaInstantiation -> Term
    inst (MetaInstantiation -> Term)
    -> (MetaVariable -> MetaInstantiation) -> MetaVariable -> Term
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . MetaVariable -> MetaInstantiation
    mvInstantiation (MetaVariable -> Term) -> Maybe MetaVariable -> Maybe Term
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> MetaId -> Map MetaId MetaVariable -> Maybe MetaVariable
    forall k a. Ord k => k -> Map k a -> Maybe a
    MapS.lookup MetaId
    x Map MetaId MetaVariable
    st
          -- we collect only those used definitions that are in @names@
          emb QName
    d = if QName -> Bool
    include QName
    d then QName -> Set QName
    forall a. a -> Set a
    Set.singleton QName
    d else Set QName
    forall a. Set a
    Set.empty
      -- get all the Defs that are in names
      return $ getDefs' lookup emb a
      where
      -- TODO: Is it bad to ignore the lambdas?
      inst :: MetaInstantiation -> Term
    inst (InstV Instantiation
    i)                      = Instantiation -> Term
    instBody Instantiation
    i
      inst OpenMeta{}                     = Term
    forall a. HasCallStack => a
    __IMPOSSIBLE__
      inst BlockedConst{}                 = Term
    forall a. HasCallStack => a
    __IMPOSSIBLE__
      inst PostponedTypeCheckingProblem{} = Term
    forall a. HasCallStack => a
    __IMPOSSIBLE__