{- | 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, 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.TypeChecking.Monad

import Agda.Utils.List    (hasElem)
import Agda.Utils.Pretty  (prettyShow)

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' = forall (t :: * -> *) a. Foldable t => t a -> [a]
toList Set QName
names
  -- For each function, get names per clause and total.
  ([IntMap (Set QName)]
perClauses, [Set QName]
nss) <- forall a b. [(a, b)] -> ([a], [b])
unzip forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM ((QName -> Bool) -> QName -> TCM (IntMap (Set QName), Set QName)
recDef (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, QName, [QName])]
graph  = forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\ QName
x Set QName
ns -> (QName
x, QName
x, forall a. Set a -> [a]
Set.toList Set QName
ns)) [QName]
names' [Set QName]
nss
  let sccs :: [SCC QName]
sccs   = forall key node. Ord key => [(node, key, [key])] -> [SCC node]
stronglyConnComp [(QName, QName, [QName])]
graph
  let nonRec :: [QName]
nonRec = forall a b. (a -> Maybe b) -> [a] -> [b]
mapMaybe (\case AcyclicSCC QName
x -> forall a. a -> Maybe a
Just QName
x
                               SCC QName
_            -> forall a. Maybe a
Nothing)
                 [SCC QName]
sccs
  let recs :: [Set QName]
recs   = forall a b. (a -> Maybe b) -> [a] -> [b]
mapMaybe (\case CyclicSCC [QName]
xs -> forall a. a -> Maybe a
Just (forall a. Ord a => [a] -> Set a
Set.fromList [QName]
xs)
                               SCC QName
_            -> forall a. Maybe a
Nothing)
                 [SCC QName]
sccs

  forall (m :: * -> *).
MonadDebug m =>
[Char] -> Key -> [Char] -> m ()
reportSLn [Char]
"rec.graph" Key
60 forall a b. (a -> b) -> a -> b
$ forall a. Show a => a -> [Char]
show [(QName, QName, [QName])]
graph

  -- Mark all non-recursive functions and their clauses as such.
  forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
(a -> m b) -> t a -> m ()
mapM_ QName -> TCMT IO ()
markNonRecursive [QName]
nonRec

  -- Mark individual clauses of recursive functions:
  --------------------------------------------------
  -- Map names to clause numbers to sets of mentioned names.
  let clMap :: Map QName (IntMap (Set QName))
clMap = forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
Map.fromListWith forall a. HasCallStack => a
__IMPOSSIBLE__ forall a b. (a -> b) -> a -> b
$ forall a b. [a] -> [b] -> [(a, b)]
zip [QName]
names' [IntMap (Set QName)]
perClauses
  -- Walk through SCCs.
  forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
t a -> (a -> m b) -> m ()
forM_ [Set QName]
recs forall a b. (a -> b) -> a -> b
$ \ 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 = forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
any (forall a. Ord a => a -> Set a -> Bool
`Set.member` Set QName
s) Set QName
scc
    -- Walk through members of SCC.
    forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
t a -> (a -> m b) -> m ()
forM_ Set QName
scc forall a b. (a -> b) -> a -> b
$ \ QName
x -> do
      -- Get the NamesPerClause for the current function x.
      let perClause :: IntMap (Set QName)
perClause  = forall k a. Ord k => a -> k -> Map k a -> a
Map.findWithDefault 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 forall a b. (a -> b) -> a -> b
$ forall a. a -> Key -> IntMap a -> a
IntMap.findWithDefault 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.
  forall (m :: * -> *) a. Monad m => a -> m a
return [Set QName]
recs

-- | Mark a function as terminating and all its clauses as non-recursive.
markNonRecursive :: QName -> TCM ()
markNonRecursive :: QName -> TCMT IO ()
markNonRecursive QName
q = forall (m :: * -> *).
MonadTCState m =>
(Signature -> Signature) -> m ()
modifySignature forall a b. (a -> b) -> a -> b
$ QName -> (Definition -> Definition) -> Signature -> Signature
updateDefinition QName
q forall a b. (a -> b) -> a -> b
$ (Defn -> Defn) -> Definition -> Definition
updateTheDef forall a b. (a -> b) -> a -> b
$ \case
  def :: Defn
def@Function{} -> Defn
def
   { funTerminates :: Maybe Bool
funTerminates = forall a. a -> Maybe a
Just Bool
True
   , funClauses :: [Clause]
funClauses    = forall a b. (a -> b) -> [a] -> [b]
map (\ Clause
cl -> Clause
cl { clauseRecursive :: Maybe Bool
clauseRecursive = forall a. a -> Maybe a
Just Bool
False }) forall a b. (a -> b) -> a -> b
$ Defn -> [Clause]
funClauses Defn
def
   }
  def :: Defn
def@Record{} -> Defn
def
   { recTerminates :: Maybe Bool
recTerminates = forall a. a -> Maybe a
Just Bool
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 = forall (m :: * -> *).
MonadTCState m =>
(Signature -> Signature) -> m ()
modifySignature forall a b. (a -> b) -> a -> b
$ QName -> (Definition -> Definition) -> Signature -> Signature
updateDefinition QName
q forall a b. (a -> b) -> a -> b
$ (Defn -> Defn) -> Definition -> Definition
updateTheDef forall a b. (a -> b) -> a -> b
$ \case
  def :: Defn
def@Function{} -> Defn
def
   { funClauses :: [Clause]
funClauses    = forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\ Key
i Clause
cl -> Clause
cl { clauseRecursive :: Maybe Bool
clauseRecursive = forall a. a -> Maybe a
Just (Key -> Bool
f Key
i) }) [Key
0..] forall a b. (a -> b) -> a -> b
$ Defn -> [Clause]
funClauses Defn
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 -> TCM (IntMap (Set QName), Set QName)
recDef QName -> Bool
include QName
name = do
  -- Retrieve definition
  Definition
def <- forall (m :: * -> *). HasConstInfo m => QName -> m Definition
getConstInfo QName
name

  -- Get names in type
  Set QName
ns1 <- forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
anyDefs QName -> Bool
include (Definition -> Type
defType Definition
def)

  -- Get names in body
  (IntMap (Set QName)
perClause, Set QName
ns2) <- case Definition -> Defn
theDef Definition
def of

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

    Record{ Telescope
recTel :: Defn -> Telescope
recTel :: Telescope
recTel } -> do
      Set QName
ns <- forall a. GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
anyDefs QName -> Bool
include Telescope
recTel
      forall (m :: * -> *) a. Monad m => a -> m a
return (forall a. Key -> a -> IntMap a
IntMap.singleton Key
0 Set QName
ns, Set QName
ns)

    Defn
_ -> forall (m :: * -> *) a. Monad m => a -> m a
return (forall a. Monoid a => a
mempty, forall a. Monoid a => a
mempty)

  forall a (m :: * -> *).
(ReportS a, MonadDebug m) =>
[Char] -> Key -> a -> m ()
reportS [Char]
"rec.graph" Key
20
    [ [Char]
"recDef " forall a. [a] -> [a] -> [a]
++ forall a. Pretty a => a -> [Char]
prettyShow QName
name
    , [Char]
"  names in the type: " forall a. [a] -> [a] -> [a]
++ forall a. Pretty a => a -> [Char]
prettyShow Set QName
ns1
    , [Char]
"  names in the def:  " forall a. [a] -> [a] -> [a]
++ forall a. Pretty a => a -> [Char]
prettyShow Set QName
ns2
    ]
  forall (m :: * -> *) a. Monad m => a -> m a
return (IntMap (Set QName)
perClause, Set QName
ns1 forall a. Monoid a => a -> a -> a
`mappend` Set QName
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
  Map MetaId MetaVariable
st <- forall (m :: * -> *) a. ReadTCState m => Lens' a TCState -> m a
useR Lens' (Map MetaId MetaVariable) TCState
stSolvedMetaStore
  let lookup :: MetaId -> Maybe Term
lookup MetaId
x = MetaInstantiation -> Term
inst forall b c a. (b -> c) -> (a -> b) -> a -> c
. MetaVariable -> MetaInstantiation
mvInstantiation forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> 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 -> Set QName
emb QName
d = if QName -> Bool
include QName
d then forall a. a -> Set a
Set.singleton QName
d else forall a. Set a
Set.empty
  -- get all the Defs that are in names
  forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ forall a b.
(GetDefs a, Monoid b) =>
(MetaId -> Maybe Term) -> (QName -> b) -> a -> b
getDefs' MetaId -> Maybe Term
lookup QName -> Set QName
emb a
a
  where
  -- TODO: Is it bad to ignore the lambdas?
  inst :: MetaInstantiation -> Term
inst (InstV Instantiation
i)                      = Instantiation -> Term
instBody Instantiation
i
  inst MetaInstantiation
Open                           = forall a. HasCallStack => a
__IMPOSSIBLE__
  inst MetaInstantiation
OpenInstance                   = forall a. HasCallStack => a
__IMPOSSIBLE__
  inst BlockedConst{}                 = forall a. HasCallStack => a
__IMPOSSIBLE__
  inst PostponedTypeCheckingProblem{} = forall a. HasCallStack => a
__IMPOSSIBLE__