{-# LANGUAGE CPP #-}
{-# LANGUAGE NondecreasingIndentation #-}

module Agda.TypeChecking.InstanceArguments
  ( findInstance
  , isInstanceConstraint
  , isConsideringInstance
  , postponeInstanceConstraints
  ) where

#if MIN_VERSION_base(4,11,0)
import Prelude hiding ((<>))
#endif

import Control.Applicative hiding (empty)
import Control.Monad.Reader
import Control.Monad.State
import qualified Data.Map as Map
import qualified Data.Set as Set
import qualified Data.List as List

import Agda.Interaction.Options (optOverlappingInstances)

import Agda.Syntax.Common
import Agda.Syntax.Internal as I
import Agda.Syntax.Scope.Base (isNameInScope)

import Agda.TypeChecking.Errors ()
import Agda.TypeChecking.Implicit (implicitArgs)
import Agda.TypeChecking.Monad
import Agda.TypeChecking.Monad.Builtin
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Reduce
import Agda.TypeChecking.Records
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import Agda.TypeChecking.Free

import {-# SOURCE #-} Agda.TypeChecking.Constraints
import {-# SOURCE #-} Agda.TypeChecking.MetaVars
import {-# SOURCE #-} Agda.TypeChecking.Conversion

import qualified Agda.Benchmarking as Benchmark
import Agda.TypeChecking.Monad.Benchmark (billTo)

import Agda.Utils.Either
import Agda.Utils.Except
import Agda.Utils.Lens
import Agda.Utils.Maybe
import Agda.Utils.Monad
import Agda.Utils.Functor
import Agda.Utils.Pretty (prettyShow)
import Agda.Utils.Null (empty)

#include "undefined.h"
import Agda.Utils.Impossible

-- | Compute a list of instance candidates.
--   'Nothing' if target type or any context type is a meta, error if
--   type is not eligible for instance search.
initialInstanceCandidates :: Type -> TCM (Maybe [Candidate])
initialInstanceCandidates t = do
  (_ , otn) <- getOutputTypeName t
  case otn of
    NoOutputTypeName -> typeError $ GenericError $
      "Instance search can only be used to find elements in a named type"
    OutputTypeNameNotYetKnown -> do
      reportSDoc "tc.instance.cands" 30 $ "Instance type is not yet known. "
      return Nothing
    OutputTypeVar    -> do
      reportSDoc "tc.instance.cands" 30 $ "Instance type is a variable. "
      maybeRight <$> runExceptT getContextVars
    OutputTypeName n -> do
      reportSDoc "tc.instance.cands" 30 $ "Found instance type head: " <+> prettyTCM n
      runExceptT getContextVars >>= \case
        Left b -> return Nothing
        Right ctxVars -> Just . (ctxVars ++) <$> getScopeDefs n
  where
    -- get a list of variables with their type, relative to current context
    getContextVars :: ExceptT Blocked_ TCM [Candidate]
    getContextVars = do
      ctx <- getContext
      reportSDoc "tc.instance.cands" 40 $ hang "Getting candidates from context" 2 (inTopContext $ prettyTCM $ PrettyContext ctx)
          -- Context variables with their types lifted to live in the full context
      let varsAndRaisedTypes = [ (var i, raise (i + 1) t) | (i, t) <- zip [0..] ctx ]
          vars = [ Candidate x t (isOverlappable info)
                 | (x, Dom{domInfo = info, unDom = (_, t)}) <- varsAndRaisedTypes
                 , isInstance info
                 , usableRelevance info
                 , usableQuantity info
                 ]

      -- {{}}-fields of variables are also candidates
      let cxtAndTypes = [ (x, t) | (x, Dom{unDom = (_, t)}) <- varsAndRaisedTypes ]
      fields <- concat <$> mapM instanceFields (reverse cxtAndTypes)
      reportSDoc "tc.instance.fields" 30 $
        if null fields then "no instance field candidates" else
          "instance field candidates" $$ do
            nest 2 $ vcat
              [ sep [ (if overlap then "overlap" else empty) <+> prettyTCM v <+> ":"
                    , nest 2 $ prettyTCM t
                    ]
              | Candidate v t overlap <- fields
              ]

      -- get let bindings
      env <- asksTC envLetBindings
      env <- mapM (getOpen . snd) $ Map.toList env
      let lets = [ Candidate v t False
                 | (v, Dom{domInfo = info, unDom = t}) <- env
                 , isInstance info
                 , usableRelevance info
                 , usableQuantity info
                 ]
      return $ vars ++ fields ++ lets

    etaExpand :: (MonadTCM m, MonadReduce m, HasConstInfo m)
              => Bool -> Type -> m (Maybe (QName, Args))
    etaExpand etaOnce t =
      isEtaRecordType t >>= \case
        Nothing | etaOnce -> do
          isRecordType t >>= \case
            Nothing         -> return Nothing
            Just (r, vs, _) -> do
              m <- currentModule
              -- Are we inside the record module? If so it's safe and desirable
              -- to eta-expand once (issue #2320).
              if qnameToList r `List.isPrefixOf` mnameToList m
                then return (Just (r, vs))
                else return Nothing
        r -> return r

    instanceFields :: (Term,Type) -> ExceptT Blocked_ TCM [Candidate]
    instanceFields = instanceFields' True

    instanceFields' :: Bool -> (Term,Type) -> ExceptT Blocked_ TCM [Candidate]
    instanceFields' etaOnce (v, t) =
      ifBlockedType t (\m _ -> throwError $ Blocked m ()) $ \ _ t -> do
      caseMaybeM (etaExpand etaOnce t) (return []) $ \ (r, pars) -> do
        (tel, args) <- forceEtaExpandRecord r pars v
        let types = map unDom $ applySubst (parallelS $ reverse $ map unArg args) (flattenTel tel)
        fmap concat $ forM (zip args types) $ \ (arg, t) ->
          ([ Candidate (unArg arg) t (isOverlappable arg)
           | isInstance arg ] ++) <$>
          instanceFields' False (unArg arg, t)

    getScopeDefs :: QName -> TCM [Candidate]
    getScopeDefs n = do
      instanceDefs <- getInstanceDefs
      rel          <- asksTC envRelevance
      let qs = maybe [] Set.toList $ Map.lookup n instanceDefs
      catMaybes <$> mapM (candidate rel) qs

    candidate :: Relevance -> QName -> TCM (Maybe Candidate)
    candidate rel q = ifNotM (isNameInScope q <$> getScope) (return Nothing) $ do
      -- Andreas, 2012-07-07:
      -- we try to get the info for q
      -- while opening a module, q may be in scope but not in the signature
      -- in this case, we just ignore q (issue 674)
      flip catchError handle $ do
        def <- getConstInfo q
        if not (defRelevance def `moreRelevant` rel) then return Nothing else do
          -- Andreas, 2017-01-14: instantiateDef is a bit of an overkill
          -- if we anyway get the freeVarsToApply
          -- WAS: t <- defType <$> instantiateDef def
          args <- freeVarsToApply q
          let t = defType def `piApply` args
          let v = case theDef def of
               -- drop parameters if it's a projection function...
               Function{ funProjection = Just p } -> projDropParsApply p ProjSystem args
               -- Andreas, 2014-08-19: constructors cannot be declared as
               -- instances (at least as of now).
               -- I do not understand why the Constructor case is not impossible.
               -- Ulf, 2014-08-20: constructors are always instances.
               Constructor{ conSrcCon = c }       -> Con c ConOSystem []
               _                                  -> Def q $ map Apply args
          return $ Just $ Candidate v t False
      where
        -- unbound constant throws an internal error
        handle (TypeError _ (Closure {clValue = InternalError _})) = return Nothing
        handle err                                                 = throwError err

-- | @findInstance m (v,a)s@ tries to instantiate on of the types @a@s
--   of the candidate terms @v@s to the type @t@ of the metavariable @m@.
--   If successful, meta @m@ is solved with the instantiation of @v@.
--   If unsuccessful, the constraint is regenerated, with possibly reduced
--   candidate set.
--   The list of candidates is equal to @Nothing@ when the type of the meta
--   wasn't known when the constraint was generated. In that case, try to find
--   its type again.
findInstance :: MetaId -> Maybe [Candidate] -> TCM ()
findInstance m Nothing = do
  -- Andreas, 2015-02-07: New metas should be created with range of the
  -- current instance meta, thus, we set the range.
  mv <- lookupMeta m
  setCurrentRange mv $ do
    reportSLn "tc.instance" 20 $ "The type of the FindInstance constraint isn't known, trying to find it again."
    t <- instantiate =<< getMetaTypeInContext m
    reportSLn "tc.instance" 70 $ "findInstance 1: t: " ++ prettyShow t

    -- Issue #2577: If the target is a function type the arguments are
    -- potential candidates, so we add them to the context to make
    -- initialInstanceCandidates pick them up.
    TelV tel t <- telView t
    cands <- addContext tel $ initialInstanceCandidates t
    case cands of
      Nothing -> do
        reportSLn "tc.instance" 20 "Can't figure out target of instance goal. Postponing constraint."
        addConstraint $ FindInstance m Nothing Nothing
      Just {} -> findInstance m cands

findInstance m (Just cands) =
  whenJustM (findInstance' m cands) $ (\ (cands, b) -> addConstraint $ FindInstance m b $ Just cands)

-- | Result says whether we need to add constraint, and if so, the set of
--   remaining candidates and an eventual blocking metavariable.
findInstance' :: MetaId -> [Candidate] -> TCM (Maybe ([Candidate], Maybe MetaId))
findInstance' m cands = ifM (isFrozen m) (do
    reportSLn "tc.instance" 20 "Refusing to solve frozen instance meta."
    return (Just (cands, Nothing))) $ do
  ifM isConsideringInstance (do
    reportSLn "tc.instance" 20 "Postponing possibly recursive instance search."
    return $ Just (cands, Nothing)) $ billTo [Benchmark.Typing, Benchmark.InstanceSearch] $ do
  -- Andreas, 2015-02-07: New metas should be created with range of the
  -- current instance meta, thus, we set the range.
  mv <- lookupMeta m
  setCurrentRange mv $ do
      reportSLn "tc.instance" 15 $
        "findInstance 2: constraint: " ++ prettyShow m ++ "; candidates left: " ++ show (length cands)
      reportSDoc "tc.instance" 60 $ nest 2 $ vcat
        [ sep [ (if overlap then "overlap" else empty) <+> prettyTCM v <+> ":"
              , nest 2 $ prettyTCM t ] | Candidate v t overlap <- cands ]
      reportSDoc "tc.instance" 70 $ "raw" $$ do
       nest 2 $ vcat
        [ sep [ (if overlap then "overlap" else empty) <+> pretty v <+> ":"
              , nest 2 $ pretty t ] | Candidate v t overlap <- cands ]
      t <- normalise =<< getMetaTypeInContext m
      reportSLn "tc.instance" 70 $ "findInstance 2: t: " ++ prettyShow t
      insidePi t $ \ t -> do
      reportSDoc "tc.instance" 15 $ "findInstance 3: t =" <+> prettyTCM t
      reportSLn "tc.instance" 70 $ "findInstance 3: t: " ++ prettyShow t

      mcands <- checkCandidates m t cands
      debugConstraints
      case mcands of

        Just ([(_, err)], []) -> do
          reportSDoc "tc.instance" 15 $
            "findInstance 5: the only viable candidate failed..."
          throwError err
        Just (errs, []) -> do
          if null errs then reportSDoc "tc.instance" 15 $ "findInstance 5: no viable candidate found..."
                       else reportSDoc "tc.instance" 15 $ "findInstance 5: all viable candidates failed..."
          typeError $ InstanceNoCandidate t [ (candidateTerm c, err) | (c, err) <- errs ]

        Just (_, [Candidate term t' _]) -> do
          reportSDoc "tc.instance" 15 $ vcat
            [ "findInstance 5: solved by instance search using the only candidate"
            , nest 2 $ prettyTCM term
            , "of type " <+> prettyTCM t'
            , "for type" <+> prettyTCM t
            ]

          -- If we actually solved the constraints we should wake up any held
          -- instance constraints, to make sure we don't forget about them.
          wakeupInstanceConstraints
          return Nothing  -- We’re done

        _ -> do
          let cs = maybe cands snd mcands -- keep the current candidates if Nothing
          reportSDoc "tc.instance" 15 $
            text ("findInstance 5: refined candidates: ") <+>
            prettyTCM (List.map candidateTerm cs)
          return (Just (cs, Nothing))

-- | Precondition: type is spine reduced and ends in a Def or a Var.
insidePi :: Type -> (Type -> TCM a) -> TCM a
insidePi t ret =
  case unEl t of
    Pi a b     -> addContext (absName b, a) $ insidePi (absBody b) ret
    Def{}      -> ret t
    Var{}      -> ret t
    Sort{}     -> __IMPOSSIBLE__
    Con{}      -> __IMPOSSIBLE__
    Lam{}      -> __IMPOSSIBLE__
    Lit{}      -> __IMPOSSIBLE__
    Level{}    -> __IMPOSSIBLE__
    MetaV{}    -> __IMPOSSIBLE__
    DontCare{} -> __IMPOSSIBLE__
    Dummy s    -> __IMPOSSIBLE_VERBOSE__ s

-- | Apply the computation to every argument in turn by reseting the state every
--   time. Return the list of the arguments giving the result True.
--
--   If the resulting list contains exactly one element, then the state is the
--   same as the one obtained after running the corresponding computation. In
--   all the other cases, the state is reset.
--
--   Also returns the candidates that pass type checking but fails constraints,
--   so that the error messages can be reported if there are no successful
--   candidates.
filterResetingState :: MetaId -> [Candidate] -> (Candidate -> TCM YesNoMaybe) -> TCM ([(Candidate, TCErr)], [Candidate])
filterResetingState m cands f = do
  ctxArgs  <- getContextArgs
  let ctxElims = map Apply ctxArgs
      tryC c = do
        ok <- f c
        v  <- instantiateFull (MetaV m ctxElims)
        a  <- instantiateFull =<< (`piApplyM` ctxArgs) =<< getMetaType m
        return (ok, v, a)
  result <- mapM (\c -> do bs <- localTCStateSaving (tryC c); return (c, bs)) cands

  -- Check that there aren't any hard failures
  case [ err | (_, ((HellNo err, _, _), _)) <- result ] of
    err : _ -> throwError err
    []      -> return ()

  let result' = [ (c, v, a, s) | (c, ((r, v, a), s)) <- result, not (isNo r) ]
  result'' <- dropSameCandidates m result'
  case result'' of
    [(c, _, _, s)] -> ([], [c]) <$ putTC s
    _              -> do
      let bad  = [ (c, err) | (c, ((NoBecause err, _, _), _)) <- result ]
          good = [ c | (c, _, _, _) <- result'' ]
      return (bad, good)

-- Drop all candidates which are judgmentally equal to the first one.
-- This is sufficient to reduce the list to a singleton should all be equal.
dropSameCandidates :: MetaId -> [(Candidate, Term, Type, a)] -> TCM [(Candidate, Term, Type, a)]
dropSameCandidates m cands0 = verboseBracket "tc.instance" 30 "dropSameCandidates" $ do
  metas <- Set.fromList . Map.keys <$> getMetaStore
  let freshMetas x = not $ Set.null $ Set.difference (Set.fromList $ allMetas x) metas

  -- Take overlappable candidates into account
  let cands =
        case List.partition (\ (c, _, _, _) -> candidateOverlappable c) cands0 of
          (cand : _, []) -> [cand]  -- only overlappable candidates: pick the first one
          _              -> cands0  -- otherwise require equality

  reportSDoc "tc.instance" 50 $ vcat
    [ "valid candidates:"
    , nest 2 $ vcat [ if freshMetas (v, a) then "(redacted)" else
                      sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM a ]
                    | (_, v, a, _) <- cands ] ]
  rel <- getMetaRelevance <$> lookupMeta m
  case cands of
    []            -> return cands
    cvd : _ | isIrrelevant rel -> do
      reportSLn "tc.instance" 30 "Meta is irrelevant so any candidate will do."
      return [cvd]
    (_, MetaV m' _, _, _) : _ | m == m' ->  -- We didn't instantiate, so can't compare
      return cands
    cvd@(_, v, a, _) : vas -> do
        if freshMetas (v, a)
          then return (cvd : vas)
          else (cvd :) <$> dropWhileM equal vas
      where
        equal (_, v', a', _)
            | freshMetas (v', a') = return False  -- If there are fresh metas we can't compare
            | otherwise           =
          verboseBracket "tc.instance" 30 "comparingCandidates" $ do
          reportSDoc "tc.instance" 30 $ sep [ prettyTCM v <+> "==", nest 2 $ prettyTCM v' ]
          localTCState $ dontAssignMetas $ ifNoConstraints_ (equalType a a' >> equalTerm a v v')
                             {- then -} (return True)
                             {- else -} (\ _ -> return False)
                             `catchError` (\ _ -> return False)

data YesNoMaybe = Yes | No | NoBecause TCErr | Maybe | HellNo TCErr
  deriving (Show)

isNo :: YesNoMaybe -> Bool
isNo No          = True
isNo NoBecause{} = True
isNo HellNo{}    = True
isNo _           = False

-- | Given a meta @m@ of type @t@ and a list of candidates @cands@,
-- @checkCandidates m t cands@ returns a refined list of valid candidates and
-- candidates that failed some constraints.
checkCandidates :: MetaId -> Type -> [Candidate] -> TCM (Maybe ([(Candidate, TCErr)], [Candidate]))
checkCandidates m t cands =
  verboseBracket "tc.instance.candidates" 20 ("checkCandidates " ++ prettyShow m) $
  ifM (anyMetaTypes cands) (return Nothing) $ Just <$> do
    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ "target:" <+> prettyTCM t
    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ vcat
      [ "candidates"
      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM v <+> ":" <+> prettyTCM t
             | Candidate v t overlap <- cands ] ]
    cands' <- filterResetingState m cands (checkCandidateForMeta m t)
    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ vcat
      [ "valid candidates"
      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM v <+> ":" <+> prettyTCM t
             | Candidate v t overlap <- snd cands' ] ]
    return cands'
  where
    anyMetaTypes :: [Candidate] -> TCM Bool
    anyMetaTypes [] = return False
    anyMetaTypes (Candidate _ a _ : cands) = do
      a <- instantiate a
      case unEl a of
        MetaV{} -> return True
        _       -> anyMetaTypes cands

    checkDepth :: Term -> Type -> TCM YesNoMaybe -> TCM YesNoMaybe
    checkDepth c a k = locallyTC eInstanceDepth succ $ do
      d        <- viewTC eInstanceDepth
      maxDepth <- maxInstanceSearchDepth
      when (d > maxDepth) $ typeError $ InstanceSearchDepthExhausted c a maxDepth
      k

    checkCandidateForMeta :: MetaId -> Type -> Candidate -> TCM YesNoMaybe
    checkCandidateForMeta m t (Candidate term t' _) = checkDepth term t' $ do
      -- Andreas, 2015-02-07: New metas should be created with range of the
      -- current instance meta, thus, we set the range.
      mv <- lookupMeta m
      setCurrentRange mv $ do
        debugConstraints
        verboseBracket "tc.instance" 20 ("checkCandidateForMeta " ++ prettyShow m) $
          liftTCM $ runCandidateCheck $ do
            reportSLn "tc.instance" 70 $ "  t: " ++ prettyShow t ++ "\n  t':" ++ prettyShow t' ++ "\n  term: " ++ prettyShow term ++ "."
            reportSDoc "tc.instance" 20 $ vcat
              [ "checkCandidateForMeta"
              , "t    =" <+> prettyTCM t
              , "t'   =" <+> prettyTCM t'
              , "term =" <+> prettyTCM term
              ]

            -- Apply hidden and instance arguments (recursive inst. search!).
            (args, t'') <- implicitArgs (-1) (\h -> notVisible h) t'

            reportSDoc "tc.instance" 20 $
              "instance search: checking" <+> prettyTCM t''
              <+> "<=" <+> prettyTCM t
            reportSDoc "tc.instance" 70 $ vcat
              [ "instance search: checking (raw)"
              , nest 4 $ pretty t''
              , nest 2 $ "<="
              , nest 4 $ pretty t
              ]
            v <- (`applyDroppingParameters` args) =<< reduce term
            reportSDoc "tc.instance" 15 $ vcat
              [ "instance search: attempting"
              , nest 2 $ prettyTCM m <+> ":=" <+> prettyTCM v
              ]
            reportSDoc "tc.instance" 70 $ nest 2 $
              "candidate v = " <+> pretty v
            -- if constraints remain, we abort, but keep the candidate
            -- Jesper, 05-12-2014: When we abort, we should add a constraint to
            -- instantiate the meta at a later time (see issue 1377).
            ctxElims <- map Apply <$> getContextArgs
            guardConstraint (ValueCmp CmpEq t'' (MetaV m ctxElims) v) $ leqType t'' t
            -- make a pass over constraints, to detect cases where some are made
            -- unsolvable by the assignment, but don't do this for FindInstance's
            -- to prevent loops.
            debugConstraints

            let debugSolution = verboseS "tc.instance" 15 $ do
                  sol <- instantiateFull (MetaV m ctxElims)
                  case sol of
                    MetaV m' _ | m == m' ->
                      reportSDoc "tc.instance" 15 $
                        sep [ "instance search: maybe solution for" <+> prettyTCM m <> ":"
                            , nest 2 $ prettyTCM v ]
                    _ ->
                      reportSDoc "tc.instance" 15 $
                        sep [ "instance search: found solution for" <+> prettyTCM m <> ":"
                            , nest 2 $ prettyTCM sol ]

            do solveAwakeConstraints' True
               Yes <$ debugSolution
              `catchError` (return . NoBecause)

        where
          runCandidateCheck check =
            flip catchError handle $
            nowConsideringInstance $
            ifNoConstraints check
              (\ r -> case r of
                  Yes           -> r <$ debugSuccess
                  NoBecause why -> r <$ debugConstraintFail why
                  _             -> __IMPOSSIBLE__
              )
              (\ _ r -> case r of
                  Yes           -> Maybe <$ debugInconclusive
                  NoBecause why -> r <$ debugConstraintFail why
                  _             -> __IMPOSSIBLE__
              )

          debugSuccess            = reportSLn "tc.instance" 50 "assignment successful" :: TCM ()
          debugInconclusive       = reportSLn "tc.instance" 50 "assignment inconclusive" :: TCM ()
          debugConstraintFail why = reportSDoc "tc.instance" 50 $ "candidate failed constraints:" <+> prettyTCM why
          debugTypeFail err       = reportSDoc "tc.instance" 50 $ "candidate failed type check:" <+> prettyTCM err

          hardFailure :: TCErr -> Bool
          hardFailure (TypeError _ err) =
            case clValue err of
              InstanceSearchDepthExhausted{} -> True
              _                              -> False
          hardFailure _ = False

          handle :: TCErr -> TCM YesNoMaybe
          handle err
            | hardFailure err = return $ HellNo err
            | otherwise       = No <$ debugTypeFail err

isInstanceConstraint :: Constraint -> Bool
isInstanceConstraint FindInstance{} = True
isInstanceConstraint _              = False

isConsideringInstance :: (ReadTCState m, HasOptions m) => m Bool
isConsideringInstance =
  and2M ((^. stConsideringInstance) <$> getTCState)
        (not . optOverlappingInstances <$> pragmaOptions)

nowConsideringInstance :: (MonadTCState m) => m a -> m a
nowConsideringInstance = locallyTCState stConsideringInstance $ const True

wakeupInstanceConstraints :: TCM ()
wakeupInstanceConstraints =
  unlessM isConsideringInstance $ do
    wakeConstraints (return . isInstance)
    solveSomeAwakeConstraints isInstance False
  where
    isInstance = isInstanceConstraint . clValue . theConstraint

postponeInstanceConstraints :: TCM a -> TCM a
postponeInstanceConstraints m =
  nowConsideringInstance m <* wakeupInstanceConstraints

-- | To preserve the invariant that a constructor is not applied to its
--   parameter arguments, we explicitly check whether function term
--   we are applying to arguments is a unapplied constructor.
--   In this case we drop the first 'conPars' arguments.
--   See Issue670a.
--   Andreas, 2013-11-07 Also do this for projections, see Issue670b.
applyDroppingParameters :: Term -> Args -> TCM Term
applyDroppingParameters t vs = do
  let fallback = return $ t `apply` vs
  case t of
    Con c ci [] -> do
      def <- theDef <$> getConInfo c
      case def of
        Constructor {conPars = n} -> return $ Con c ci (map Apply $ drop n vs)
        _ -> __IMPOSSIBLE__
    Def f [] -> do
      mp <- isProjection f
      case mp of
        Just Projection{projIndex = n} -> do
          case drop n vs of
            []     -> return t
            u : us -> (`apply` us) <$> applyDef ProjPrefix f u
        _ -> fallback
    _ -> fallback
