content: {-# LANGUAGE NondecreasingIndentation #-}
  
  -- | Solving size constraints under hypotheses.
  --
  -- The size solver proceeds as follows:
  --
  -- 1. Get size constraints, cluster into connected components.
  --
  --    All size constraints that mention the same metas go into the same
  --    cluster.  Each cluster can be solved by itself.
  --
  --    Constraints that do not fit our format are ignored.
  --    We check whether our computed solution fulfills them as well
  --    in the last step.
  --
  -- 2. Find a joint context for each cluster.
  --
  --    Each constraint comes with its own typing context, which
  --    contains size hypotheses @j : Size< i@.  We need to find a
  --    common super context in which all constraints of a cluster live,
  --    and raise all constraints to this context.
  --
  --    There might not be a common super context.  Then we are screwed,
  --    since our solver is not ready to deal with such a situation.  We
  --    will blatantly refuse to solve this cluster and blame it on the
  --    user.
  --
  -- 3. Convert the joint context into a hypothesis graph.
  --
  --    This is straightforward.  Each de Bruijn index becomes a
  --    rigid variable, each typing assumption @j : Size< i@ becomes an
  --    arc.
  --
  -- 4. Convert the constraints into a constraint graph.
  --
  --    Here we need to convert @MetaV@s into flexible variables.
  --
  -- 5. Run the solver
  --
  -- 6. Convert the solution into meta instantiations.
  --
  -- 7. Double-check whether the constraints are solved.
  
  -- Opportunities for optimization:
  --
  -- - NamedRigids has some cost to retrieve variable names
  --   just for the sake of debug printing.
  
  module Agda.TypeChecking.SizedTypes.Solve where
  
  import Prelude hiding (null)
  
  import Control.Monad.Except ( catchError )
  import Control.Monad.Trans.Maybe
  
  import Data.Either
  import Data.Foldable (forM_)
  import qualified Data.Foldable as Fold
  import Data.Function (on)
  import qualified Data.List as List
  import Data.Monoid
  import qualified Data.Map as Map
  import Data.Set (Set)
  import qualified Data.Set as Set
  import Data.Traversable (forM)
  
  import Agda.Syntax.Common
  import Agda.Syntax.Internal
  import Agda.Syntax.Internal.MetaVars
  
  import Agda.TypeChecking.Monad as TCM hiding (Offset)
  import Agda.TypeChecking.Pretty
  import Agda.TypeChecking.Free
  import Agda.TypeChecking.Reduce
  import Agda.TypeChecking.MetaVars
  import Agda.TypeChecking.Substitute
  import Agda.TypeChecking.Telescope
  import Agda.TypeChecking.Constraints as C
  
  import qualified Agda.TypeChecking.SizedTypes as S
  import Agda.TypeChecking.SizedTypes.Pretty
  import Agda.TypeChecking.SizedTypes.Syntax as Size
  import Agda.TypeChecking.SizedTypes.Utils
  import Agda.TypeChecking.SizedTypes.WarshallSolver as Size hiding (simplify1)
  
  import Agda.Utils.Cluster
  import Agda.Utils.Function
  import Agda.Utils.Functor
  import Agda.Utils.Lens
  import Agda.Utils.List1 (List1, pattern (:|), nonEmpty, (<|))
  import qualified Agda.Utils.List as List
  import qualified Agda.Utils.List1 as List1
  import Agda.Utils.Maybe
  import Agda.Utils.Monad
  import Agda.Utils.Null
  import Agda.Syntax.Common.Pretty (Pretty, prettyShow)
  import qualified Agda.Syntax.Common.Pretty as P
  import Agda.Utils.Singleton
  import Agda.Utils.Size
  import qualified Agda.Utils.VarSet as VarSet
  import Agda.Utils.VarSet (VarSet)
  
  import Agda.Utils.Impossible
  
  -- | Flag to control the behavior of size solver.
  data DefaultToInfty
    = DefaultToInfty      -- ^ Instantiate all unconstrained size variables to ∞.
    | DontDefaultToInfty  -- ^ Leave unconstrained size variables unsolved.
    deriving (Eq, Ord, Show)
  
  -- | Solve size constraints involving hypotheses.
  
  solveSizeConstraints :: DefaultToInfty -> TCM ()
  solveSizeConstraints flag =  do
  
    -- 1. Take out the size constraints normalised.
  
    -- NOTE: this deletes the size constraints from the constraint set!
    cs0 :: [ProblemConstraint]
      <- forMM (S.takeSizeConstraints (== CmpLeq)) $ \ (c :: ProblemConstraint) -> do
        mapClosure normalise (theConstraint c) <&> \ cl -> c { theConstraint = cl }
  
    unless (null cs0) $
      reportSDoc "tc.size.solve" 40 $ vcat $
        text ( "Solving constraints (" ++ show flag ++ ")" ) : map prettyTCM cs0
  
    -- 2. Cluster the constraints by common size metas.
  
    -- Get all size metas.
    sizeMetaSet <- Set.fromList . map (\ (x, _t, _tel) -> x) <$> S.getSizeMetas True
  
    -- Pair each constraint with its list of size metas occurring in it.
    cms <- forM cs0 $ \ cl -> enterClosure (theConstraint cl) $ \ c -> do
  
      -- @allMetas@ does not reduce or instantiate;
      -- this is why we require the size constraints to be normalised.
      return (cl, Set.toList $
        sizeMetaSet `Set.intersection` allMetas singleton c)
  
    -- Now, some constraints may have no metas (clcs), the others have at least one (othercs).
    let classify :: (a, [b]) -> Either a (a, List1 b)
        classify (cl, [])     = Left  cl
        classify (cl, (x:xs)) = Right (cl, x :| xs)
    let (clcs, othercs) = partitionEithers $ map classify cms
  
    -- We cluster the constraints by their metas.
    let ccs = cluster' othercs
  
    -- 3. Solve each cluster
  
    -- Solve the closed constraints, one by one.
  
    forM_ clcs $ \ c -> () <$ solveSizeConstraints_ flag [c]
  
    -- Solve the clusters.
  
    constrainedMetas <- Set.unions <$> do
      forM  (ccs) $ \ (cs :: List1 ProblemConstraint) -> do
  
        reportSDoc "tc.size.solve" 60 $ vcat $
          "size constraint cluster:" <| fmap (text . show) cs
  
        -- Convert each constraint in the cluster to the largest context.
        -- (Keep fingers crossed).
  
        enterClosure (Fold.maximumBy (compare `on` (length . envContext . clEnv)) $ fmap theConstraint cs) $ \ _ -> do
          -- Get all constraints that can be cast to the longest context.
          cs' :: [ProblemConstraint] <- List1.catMaybes <$> do
            mapM (runMaybeT . castConstraintToCurrentContext) cs
  
          reportSDoc "tc.size.solve" 20 $ vcat $
            ( "converted size constraints to context: " <+> do
                tel <- getContextTelescope
                inTopContext $ prettyTCM tel
            ) : map (nest 2 . prettyTCM) cs'
  
          -- Solve the converted constraints.
          solveSizeConstraints_ flag cs'
  
    -- 4. Possibly set remaining metas to infinity.
  
    -- Andreas, issue 1862: do not default to ∞ always, could be too early.
    when (flag == DefaultToInfty) $ do
  
      -- let constrainedMetas = Set.fromList $ concat $
      --       for cs0 $ \ Closure{ clValue = ValueCmp _ _ u v } ->
      --         allMetas u ++ allMetas v
  
      -- Set the unconstrained, open size metas to ∞.
      ms <- S.getSizeMetas False -- do not get interaction metas
      unless (null ms) $ do
        inf <- primSizeInf
        forM_ ms $ \ (m, t, tel) -> do
          unless (m `Set.member` constrainedMetas) $ do
          unlessM (isFrozen m) $ do
          reportSDoc "tc.size.solve" 20 $
            "solution " <+> prettyTCM (MetaV m []) <+>
            " := "      <+> prettyTCM inf
          assignMeta 0 m t (List.downFrom $ size tel) inf
  
    -- -- Double check.
    -- let -- Error for giving up
    --     cannotSolve :: TCM a
    --     cannotSolve = typeError . GenericDocError =<<
    --       vcat ("Cannot solve size constraints" : map prettyTCM cs0)
    -- unless (null cs0 && null ms) $ do
    --   flip catchError (const cannotSolve) $
    --     noConstraints $
    --       forM_ cs0 $ \ cl -> enterClosure cl solveConstraint
  
    -- 5. Make sure we did not lose any constraints.
  
    -- This is necessary since we have removed the size constraints.
    forM_ cs0 $ withConstraint solveConstraint
  
  
  -- | TODO: this does not actually work!
  --
  --   We would like to use a constraint @c@ created in context @Δ@ from module @N@
  --   in the current context @Γ@ and current module @M@.
  --
  --   @Δ@ is module tel @Δ₁@ of @N@ extended by some local bindings @Δ₂@.
  --   @Γ@ is the current context.
  --   The module parameter substitution from current @M@ to @N@ be
  --   @Γ ⊢ σ : Δ₁@.
  --
  --   If @M == N@, we do not need the parameter substitution.  We try raising.
  --
  --   We first strengthen @Δ ⊢ c@ to live in @Δ₁@ and obtain @c₁ = strengthen Δ₂ c@.
  --   We then transport @c₁@ to @Γ@ and obtain @c₂ = applySubst σ c₁@.
  --
  --   This works for different modules, but if @M == N@ we should not strengthen
  --   and then weaken, because strengthening is a partial operation.
  --   We should rather lift the substitution @σ@ by @Δ₂@ and then
  --   raise by @Γ₂ - Δ₂@.
  --   This "raising" might be a strengthening if @Γ₂@ is shorter than @Δ₂@.
  --
  --   (TODO: If the module substitution does not exist, because @N@ is not
  --   a parent of @M@, we cannot use the constraint, as it has been created
  --   in an unrelated context.)
  
  castConstraintToCurrentContext' :: Closure TCM.Constraint -> MaybeT TCM TCM.Constraint
  castConstraintToCurrentContext' cl = do
    let modN  = envCurrentModule $ clEnv cl
        delta = envContext $ clEnv cl
    -- The module telescope of the constraint.
    -- The constraint could come from the module telescope of the top level module.
    -- In this case, it does not live in any module!
    -- Thus, getSection can return Nothing.
    delta1 <- liftTCM $ maybe empty (^. secTelescope) <$> getSection modN
    -- The number of locals of the constraint.
    let delta2 = size delta - size delta1
    unless (delta2 >= 0) __IMPOSSIBLE__
  
    -- The current module M and context Γ.
    modM  <- currentModule
    gamma <- liftTCM $ getContextSize
    -- The current module telescope.
    -- Could also be empty, if we are in the front matter or telescope of the top-level module.
    gamma1 <-liftTCM $ maybe empty (^. secTelescope) <$> getSection modM
    -- The current locals.
    let gamma2 = gamma - size gamma1
  
    -- Γ ⊢ σ : Δ₁
    sigma <- liftTCM $ fromMaybe idS <$> getModuleParameterSub modN
  
    -- Debug printing.
    reportSDoc "tc.constr.cast" 40 $ "casting constraint" $$ do
      tel <- getContextTelescope
      inTopContext $ nest 2 $ vcat $
        [ "current module                = " <+> prettyTCM modM
        , "current module telescope      = " <+> prettyTCM gamma1
        , "current context               = " <+> prettyTCM tel
        , "constraint module             = " <+> prettyTCM modN
        , "constraint module telescope   = " <+> prettyTCM delta1
        , "constraint context            = " <+> (prettyTCM =<< enterClosure cl (const $ getContextTelescope))
        , "constraint                    = " <+> enterClosure cl prettyTCM
        , "module parameter substitution = " <+> prettyTCM sigma
        ]
  
    -- If gamma2 < 0, we must be in the wrong context.
    -- E.g. we could have switched to the empty context even though
    -- we are still inside a module with parameters.
    -- In this case, we cannot safely convert the constraint,
    -- since the module parameter substitution may be wrong.
    guard (gamma2 >= 0)
  
    -- Shortcut for modN == modM:
    -- Raise constraint from Δ to Γ, if possible.
    -- This might save us some strengthening.
    if modN == modM then raiseMaybe (gamma - size delta) $ clValue cl else do
  
    -- Strengthen constraint to Δ₁ ⊢ c
    c <- raiseMaybe (-delta2) $ clValue cl
  
    -- Ulf, 2016-11-09: I don't understand what this function does when M and N
    -- are not related. Certainly things can go terribly wrong (see
    -- test/Succeed/Issue2223b.agda)
    fv <- liftTCM $ getModuleFreeVars modN
    guard $ fv == size delta1
  
    -- Γ ⊢ c[σ]
    return $ applySubst sigma c
    where
      raiseMaybe n c
        -- We are always fine to weaken.
        | n >= 0 = pure $ raise n c
        | otherwise =
          case VarSet.lookupMin $ allFreeVars c of
            Nothing -> pure $ raise n c
            Just k | -n < k -> pure $ raise n c
                   | otherwise -> mzero
  
  
  -- | A hazardous hack, may the Gods have mercy on us.
  --
  --   To cast to the current context, we match the context of the
  --   given constraint by 'CtxId', and as fallback, by variable name (douh!).
  --
  --   This hack lets issue 2046 go through.
  
  castConstraintToCurrentContext :: ProblemConstraint -> MaybeT TCM ProblemConstraint
  castConstraintToCurrentContext c = do
    -- The checkpoint of the contraint
    let cl = theConstraint c
        cp = envCurrentCheckpoint $ clEnv cl
    sigma <- caseMaybeM (viewTC $ eCheckpoints . key cp)
            (do
              -- We are not in a descendant of the constraint checkpoint.
              -- Here be dragons!!
              gamma <- getContext -- The target context
              let findInGamma ce =
                    -- match by name (hazardous)
                    -- This is one of the seven deadly sins (not respecting alpha).
                    List.findIndex (((==) `on` ctxEntryName) ce) gamma
              let delta = envContext $ clEnv cl
                  cand  = map findInGamma delta
              -- The domain of our substitution
              let coveredVars = VarSet.fromList $ catMaybes $ zipWith ($>) cand [0..]
              -- Check that all the free variables of the constraint are contained in
              -- coveredVars.
              -- We ignore the free variables occurring in sorts.
              guard $ getAll $ runFree (All . (`VarSet.member` coveredVars)) IgnoreAll (clValue cl)
              -- Turn cand into a substitution.
              -- Since we ignored the free variables in sorts, we better patch up
              -- the substitution with some dummy term rather than __IMPOSSIBLE__.
              return $ parallelS $ map (maybe __DUMMY_TERM__ var) cand
            ) return -- Phew, we've got the checkpoint! All is well.
    -- Apply substitution to constraint and pray that the Gods are merciful on us.
    cl' <- buildClosure $ applySubst sigma (clValue cl)
    return $ c { theConstraint = cl' }
    -- Note: the resulting constraint may not well-typed.
    -- Even if it is, it may map variables to their wrong counterpart.
  
  -- | Return the size metas occurring in the simplified constraints.
  --   A constraint like @↑ _j =< ∞ : Size@ simplifies to nothing,
  --   so @_j@ would not be in this set.
  solveSizeConstraints_ :: DefaultToInfty -> [ProblemConstraint] -> TCM (Set MetaId)
  solveSizeConstraints_ flag cs0 = do
    -- Pair constraints with their representation as size constraints.
    -- Discard constraints that do not have such a representation.
    ccs :: [(ProblemConstraint, HypSizeConstraint)] <- catMaybes <$> do
      forM cs0 $ \ c0 -> fmap (c0,) <$> computeSizeConstraint c0
  
    -- Simplify constraints and check for obvious inconsistencies.
    ccs' :: [(ProblemConstraint, HypSizeConstraint)] <- concat <$> do
      forM ccs $ \ cc@(c0 :: ProblemConstraint, HypSizeConstraint cxt hids hs sc) -> do
        case simplify1 (\ sc -> return [sc]) sc of
          Nothing -> typeError $ ContradictorySizeConstraint cc
          Just cs -> return $ (c0,) . HypSizeConstraint cxt hids hs <$> cs
  
    -- Cluster constraints according to the meta variables they mention.
    -- @csNoM@ are the constraints that do not mention any meta.
    let (csNoM, csMs) = (`List.partitionMaybe` ccs') $ \ p@(c0, c) ->
          fmap (p,) $ nonEmpty $ map sizeMetaId $ Set.toList $ flexs c
    -- @css@ are the clusters of constraints.
        css :: [List1 (ProblemConstraint, HypSizeConstraint)]
        css = cluster' csMs
  
    -- Check that the closed constraints are valid.
    whenJust (nonEmpty csNoM) $ solveCluster flag
  
    -- Now, process the clusters.
    forM_ css $ solveCluster flag
  
    return $ Set.mapMonotonic sizeMetaId $ flexs $ map (snd . fst) csMs
  
  -- | Solve a cluster of constraints sharing some metas.
  --
  solveCluster :: DefaultToInfty -> List1 (ProblemConstraint, HypSizeConstraint) -> TCM ()
  solveCluster flag ccs = do
    let
      err :: TCM Doc -> TCM a
      err mdoc = typeError . CannotSolveSizeConstraints ccs =<< mdoc
      cs :: List1 HypSizeConstraint
      cs = fmap snd ccs
    reportSDoc "tc.size.solve" 20 $ vcat $
      "Solving constraint cluster" <| fmap prettyTCM cs
  
    -- Find the super context of all contexts.
  {-
    -- We use the @'ctxId'@s.
    let cis@(ci:cis') = for cs $ \ c -> (c, reverse $ map ctxId $ sizeContext c)
  --  let cis@(ci:cis') = for cs $ \ c -> (c, reverse $ sizeHypIds c)
        max a@Left{}            _            = a
        max a@(Right ci@(c,is)) ci'@(c',is') =
          case preOrSuffix is is' of
            -- No common context:
            IsNofix    -> Left (ci, ci')
            IsPrefix{} -> Right ci'
            _          -> a
        res = foldl' max (Right ci) cis'
        noContext ((c,is),(c',is')) = typeError . GenericDocError =<< vcat
          [ "Cannot solve size constraints; the following constraints have no common typing context:"
          , prettyTCM c
          , prettyTCM c'
          ]
    flip (either noContext) res $ \ (HypSizeConstraint gamma hids hs _, _) -> do
  -}
    -- We rely on the fact that contexts are only extended...
    -- Just take the longest context.
    let HypSizeConstraint gamma hids hs _ = Fold.maximumBy (compare `on` (length . sizeContext)) cs
    -- Length of longest context.
    let n = size gamma
  
    -- Now convert all size constraints to the largest context.
        csL = for cs $ \ (HypSizeConstraint cxt _ _ c) -> raise (n - size cxt) c
    -- Canonicalize the constraints.
    -- This is unsound in the presence of hypotheses.
        csC :: [SizeConstraint]
        csC = applyWhen (null hs) (mapMaybe canonicalizeSizeConstraint) $ List1.toList csL
    reportSDoc "tc.size.solve" 30 $ vcat $
      [ "Size hypotheses" ] ++
      map (prettyTCM . HypSizeConstraint gamma hids hs) hs ++
      [ "Canonicalized constraints" ] ++
      map (prettyTCM . HypSizeConstraint gamma hids hs) csC
  
    -- -- ALT:
    -- -- Now convert all size constraints to de Bruijn levels.
  
    -- -- To get from indices in a context of length m <= n
    -- -- to levels into the target context of length n,
    -- -- we apply the following substitution:
    -- -- Index m-1 needs to be mapped to level 0,
    -- -- index m-2 needs to be mapped to level 1,
    -- -- index 0 needs to be mapped to level m-1,
    -- -- so the desired substitution is @downFrom m@.
    -- let sub m = applySubst $ parallelS $ map var $ downFrom m
  
    -- -- We simply reverse the context to get to de Bruijn levels.
    -- -- Of course, all types in the context are broken, but
    -- -- only need it for pretty printing constraints.
    -- gamma <- return $ reverse gamma
  
    -- -- We convert the hypotheses to de Bruijn levels.
    -- hs <- return $ sub n hs
  
    -- -- We get a form for pretty-printing
    -- let prettyC = prettyTCM . HypSizeConstraint gamma hids hs
  
    -- -- We convert the constraints to de Bruijn level format.
    -- let csC :: [SizeConstraint]
    --     csC = for cs $ \ (HypSizeConstraint cxt _ _ c) -> sub (size cxt) c
  
    -- reportSDoc "tc.size.solve" 30 $ vcat $
    --   [ "Size hypotheses" ]           ++ map prettyC hs ++
    --   [ "Canonicalized constraints" ] ++ map prettyC csC
  
    -- Convert size metas to flexible vars.
    let metas :: [SizeMeta]
        metas = concatMap (foldMap (:[])) csC
        csF   :: [Size.Constraint' NamedRigid MetaId]
        csF   = map (fmap sizeMetaId) csC
  
    -- Construct the hypotheses graph.
    let hyps = map (fmap sizeMetaId) hs
    -- There cannot be negative cycles in hypotheses graph due to scoping.
    let hg = either __IMPOSSIBLE__ id $ hypGraph (rigids csF) hyps
  
    -- -- Construct the constraint graph.
    -- --    g :: Size.Graph NamedRigid Int Label
    -- g <- either err return $ constraintGraph csF hg
    -- reportSDoc "tc.size.solve" 40 $ vcat $
    --   [ "Constraint graph"
    --   , text (show g)
    --   ]
  
    -- sol :: Solution NamedRigid Int <- either err return $ solveGraph Map.empty hg g
    -- either err return $ verifySolution hg csF sol
  
    -- Andreas, 2016-07-13, issue 2096.
    -- Running the solver once might result in unsolvable left-over constraints.
    -- We need to iterate the solver to detect this.
    sol :: Solution NamedRigid MetaId <- either err return $
      iterateSolver Map.empty hg csF emptySolution
  
    -- Convert solution to meta instantiation.
    solved <- fmap Set.unions $ forM (Map.assocs $ theSolution sol) $ \ (m, a) -> do
      unless (validOffset a) __IMPOSSIBLE__
      -- Solution does not contain metas
      u <- unSizeExpr $ fmap __IMPOSSIBLE__ a
      let SizeMeta _ xs = fromMaybe __IMPOSSIBLE__ $
            List.find ((m ==) . sizeMetaId) metas
      -- Check that solution is well-scoped
      let ys = rigidIndex <$> Set.toList (rigids a)
          ok = all (`elem` xs) ys -- TODO: more efficient
      -- unless ok $ err "ill-scoped solution for size meta variable"
      u <- if ok then return u else primSizeInf
      t <- getMetaType m
      reportSDoc "tc.size.solve" 20 $ unsafeModifyContext (const gamma) $ do
        let args = map (Apply . defaultArg . var) xs
        "solution " <+> prettyTCM (MetaV m args) <+> " := " <+> prettyTCM u
      reportSDoc "tc.size.solve" 60 $ vcat
        [ text $ "  xs = " ++ show xs
        , text $ "  u  = " ++ show u
        ]
      ifM (isFrozen m `or2M` (not <$> asksTC envAssignMetas)) (return Set.empty) $ do
        assignMeta n m t xs u
        return $ Set.singleton m
      -- WRONG:
      -- let partialSubst = List.sort $ zip xs $ map var $ downFrom n
      -- assignMeta' n m t (length xs) partialSubst u
      -- WRONG: assign DirEq m (map (defaultArg . var) xs) u
  
    -- Possibly set remaining size metas to ∞ (issue 1862)
    -- unless we have an interaction meta in the cluster (issue 2095).
  
    ims <- Set.fromList <$> getInteractionMetas
  
    --  ms = unsolved size metas from cluster
    let ms = Set.fromList (map sizeMetaId metas) Set.\\ solved
    --  Make sure they do not contain an interaction point
    let noIP = Set.disjoint ims ms
  
    unless (null ms) $ reportSDoc "tc.size.solve" 30 $ fsep $
      "cluster did not solve these size metas: " : map prettyTCM (Set.toList ms)
  
    solvedAll <- do
      -- If no metas are left, we have solved this cluster completely.
      if Set.null ms                then return True  else do
      -- Otherwise, we can solve it completely if we are allowed to set to ∞.
      if flag == DontDefaultToInfty then return False else do
      -- Which is only the case when we have no interaction points in the cluster.
      if not noIP                   then return False else do
      -- Try to set all unconstrained size metas to ∞.
      inf <- primSizeInf
      and <$> do
        forM (Set.toList ms) $ \ m -> do
          -- If one variable is frozen, we cannot set it (and hence not all) to ∞
          let no = do
                reportSDoc "tc.size.solve" 30 $
                  prettyTCM (MetaV m []) <+> "is frozen, cannot set it to ∞"
                return False
          ifM (isFrozen m `or2M` do not <$> asksTC envAssignMetas) no $ {-else-} do
            reportSDoc "tc.size.solve" 20 $
              "solution " <+> prettyTCM (MetaV m []) <+>
              " := "      <+> prettyTCM inf
            t <- metaType m
            TelV tel core <- telView t
            unlessM (isJust <$> isSizeType core) __IMPOSSIBLE__
            assignMeta 0 m t (List.downFrom $ size tel) inf
            return True
  
    -- Double check.
    when solvedAll $ do
        noConstraints $ mapM_ (withConstraint solveConstraint . fst) ccs
      `catchError` \ _ ->
        typeError $ CannotSolveSizeConstraints ccs empty
  
  -- | Collect constraints from a typing context, looking for SIZELT hypotheses.
  getSizeHypotheses :: Context -> TCM [(Nat, SizeConstraint)]
  getSizeHypotheses gamma = unsafeModifyContext (const gamma) $ do
    (_, msizelt) <- getBuiltinSize
    caseMaybe msizelt (return []) $ \ sizelt -> do
      -- Traverse the context from newest to oldest de Bruijn Index
      catMaybes <$> do
        forM (zip [0..] gamma) $ \case
          (i, CtxVar x a) -> do
            -- Get name and type of variable i.
            let s = prettyShow x
            t <- reduce . raise (1 + i) . unEl . unDom $ a
            case t of
              Def d [Apply u] | d == sizelt -> do
                caseMaybeM (sizeExpr $ unArg u) (return Nothing) $ \ a ->
                  return $ Just $ (i, Constraint (Rigid (NamedRigid s i) 0) Lt a)
              _ -> return Nothing
  
  -- | Convert size constraint into form where each meta is applied
  --   to indices @n-1,...,1,0@ where @n@ is the arity of that meta.
  --
  --   @X[σ] <= t@ becomes @X[id] <= t[σ^-1]@
  --
  --   @X[σ] ≤ Y[τ]@ becomes @X[id] ≤ Y[τ[σ^-1]]@ or @X[σ[τ^1]] ≤ Y[id]@
  --   whichever is defined.  If none is defined, we give up.
  --
  --   Cf. @SizedTypes.oldCanonicalizeSizeConstraint@.
  --
  --   Fixes (the rather artificial) issue 300.
  --   But it is unsound when pruned metas occur and triggers issue 1914.
  --   Thus we deactivate it.
  --   This needs to be properly implemented, possibly using the
  --   metaPermuatation of each meta variable.
  
  canonicalizeSizeConstraint :: SizeConstraint -> Maybe (SizeConstraint)
  canonicalizeSizeConstraint c@(Constraint a cmp b) = Just c
  {-
    case (a,b) of
  
      -- Case flex-flex
      (Flex (SizeMeta m xs) n, Flex (SizeMeta l ys) n')
           -- try to invert xs on ys
         | let len = size xs
         , Just ys' <- mapM (\ y -> (len-1 -) <$> findIndex (==y) xs) ys ->
             return $ Constraint (Flex (SizeMeta m $ downFrom len) n)
                             cmp (Flex (SizeMeta l ys') n')
           -- try to invert ys on xs
         | let len = size ys
         , Just xs' <- mapM (\ x -> (len-1 -) <$> findIndex (==x) ys) xs ->
             return $ Constraint (Flex (SizeMeta m xs') n)
                             cmp (Flex (SizeMeta l $ downFrom len) n')
           -- give up
         | otherwise -> Nothing
  
      -- Case flex-rigid
      (Flex (SizeMeta m xs) n, Rigid (NamedRigid x i) n') -> do
        let len = size xs
        j <- (len-1 -) <$> findIndex (==i) xs
        return $ Constraint (Flex (SizeMeta m $ downFrom len) n)
                        cmp (Rigid (NamedRigid x j) n')
  
      -- Case rigid-flex
      (Rigid (NamedRigid x i) n, Flex (SizeMeta m xs) n') -> do
        let len = size xs
        j <- (len-1 -) <$> findIndex (==i) xs
        return $ Constraint (Rigid (NamedRigid x j) n)
                        cmp (Flex (SizeMeta m $ downFrom len) n')
  
      -- Case flex-const
      (Flex (SizeMeta m xs) n, _)      ->
        return $ Constraint (Flex (SizeMeta m $ downFrom $ size xs) n) cmp b
  
      -- Case const-flex
      (_, Flex (SizeMeta m xs) n') -> do
        return $ Constraint a cmp (Flex (SizeMeta m $ downFrom $ size xs) n')
  
      -- Case no flex
      _ -> return c
  -}
  
  instance Subst SizeMeta where
    type SubstArg SizeMeta = Term
    applySubst sigma (SizeMeta x es) = SizeMeta x (map raise es)
      where
        raise i =
          case lookupS sigma i of
            Var j [] -> j
            _        -> __IMPOSSIBLE__
  
  -- | Only for 'raise'.
  instance Subst (SizeExpr' NamedRigid SizeMeta) where
    type SubstArg (SizeExpr' NamedRigid SizeMeta) = Term
    applySubst sigma a =
      case a of
        Infty   -> a
        Const{} -> a
        Flex  x n -> Flex (applySubst sigma x) n
        Rigid r n ->
          case lookupS sigma $ rigidIndex r of
            Var j [] -> Rigid r{ rigidIndex = j } n
            _        -> __IMPOSSIBLE__
  
  instance Subst SizeConstraint where
    type SubstArg SizeConstraint = Term
    applySubst sigma (Constraint a cmp b) =
      Constraint (applySubst sigma a) cmp (applySubst sigma b)
  
  -- | Turn a constraint over de Bruijn indices into a size constraint.
  computeSizeConstraint :: ProblemConstraint -> TCM (Maybe HypSizeConstraint)
  computeSizeConstraint c = do
    let cxt = envContext $ clEnv $ theConstraint c
    unsafeModifyContext (const cxt) $ do
      case clValue $ theConstraint c of
        ValueCmp CmpLeq _ u v -> do
          reportSDoc "tc.size.solve" 50 $ sep $
            [ "converting size constraint"
            , prettyTCM c
            ]
          ma <- sizeExpr u
          mb <- sizeExpr v
          (hids, hs) <- unzip <$> getSizeHypotheses cxt
          let mk a b = HypSizeConstraint cxt hids hs $ Size.Constraint a Le b
          -- We only create a size constraint if both terms can be
          -- parsed to our format of size expressions.
          return $ mk <$> ma <*> mb
        _ -> __IMPOSSIBLE__
  
  -- | Turn a term into a size expression.
  --
  --   Returns 'Nothing' if the term isn't a proper size expression.
  
  sizeExpr :: Term -> TCM (Maybe DBSizeExpr)
  sizeExpr u = do
    u <- reduce u -- Andreas, 2009-02-09.
                  -- This is necessary to surface the solutions of metavariables.
    reportSDoc "tc.conv.size" 60 $ "sizeExpr:" <+> prettyTCM u
    s <- sizeView u
    case s of
      SizeInf     -> return $ Just Infty
      SizeSuc u   -> fmap (`plus` (1 :: Offset)) <$> sizeExpr u
      OtherSize u -> case u of
        Var i []    -> (\ x -> Just $ Rigid (NamedRigid x i) 0) . prettyShow <$> nameOfBV i
  --      MetaV m es  -> return $ Just $ Flex (SizeMeta m es) 0
        MetaV m es | Just xs <- mapM isVar es, List.fastDistinct xs
                    -> return $ Just $ Flex (SizeMeta m xs) 0
        _           -> return Nothing
    where
      isVar (Proj{})  = Nothing
      isVar (IApply _ _ v) = isVar (Apply (defaultArg v))
      isVar (Apply v) = case unArg v of
        Var i [] -> Just i
        _        -> Nothing
  