{-# LANGUAGE NondecreasingIndentation   #-}

module Agda.TypeChecking.Rules.Record where

import Prelude hiding (null)

import Control.Monad
import Data.Maybe

import Agda.Interaction.Options

import qualified Agda.Syntax.Abstract as A
import Agda.Syntax.Common
import Agda.Syntax.Internal
import Agda.Syntax.Internal.Pattern
import Agda.Syntax.Position
import qualified Agda.Syntax.Info as Info

import Agda.TypeChecking.Monad
import Agda.TypeChecking.Monad.Builtin
import Agda.TypeChecking.Primitive
import Agda.TypeChecking.Rewriting.Confluence
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import Agda.TypeChecking.Reduce
import Agda.TypeChecking.Positivity.Occurrence
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Polarity
import Agda.TypeChecking.Irrelevance
import Agda.TypeChecking.CompiledClause (hasProjectionPatterns)
import Agda.TypeChecking.CompiledClause.Compile

import Agda.TypeChecking.Rules.Data ( getGeneralizedParameters, bindGeneralizedParameters, bindParameters, fitsIn, forceSort,
                                      defineCompData, defineTranspOrHCompForFields )
import Agda.TypeChecking.Rules.Term ( isType_ )
import {-# SOURCE #-} Agda.TypeChecking.Rules.Decl (checkDecl)

import Agda.Utils.Maybe
import Agda.Utils.Monad
import Agda.Utils.Null
import Agda.Utils.Permutation
import Agda.Utils.POMonoid
import qualified Agda.Utils.Pretty as P
import Agda.Utils.Size

import Agda.Utils.Impossible

---------------------------------------------------------------------------
-- * Records
---------------------------------------------------------------------------

-- | @checkRecDef i name con ps contel fields@
--
--     [@name@]    Record type identifier.
--
--     [@con@]     Maybe constructor name and info.
--
--     [@ps@]      Record parameters.
--
--     [@contel@]  Approximate type of constructor (@fields@ -> Set).
--                 Does not include record parameters.
--
--     [@fields@]  List of field signatures.
--
checkRecDef
  :: A.DefInfo                 -- ^ Position and other info.
  -> QName                     -- ^ Record type identifier.
  -> UniverseCheck             -- ^ Check universes?
  -> Maybe (Ranged Induction)  -- ^ Optional: (co)inductive declaration.
  -> Maybe HasEta              -- ^ Optional: user specified eta/no-eta
  -> Maybe QName               -- ^ Optional: constructor name.
  -> A.DataDefParams           -- ^ Record parameters.
  -> A.Expr                    -- ^ Approximate type of constructor (@fields@ -> Set).
                               --   Does not include record parameters.
  -> [A.Field]                 -- ^ Field signatures.
  -> TCM ()
checkRecDef i name uc ind eta con (A.DataDefParams gpars ps) contel fields =
  traceCall (CheckRecDef (getRange name) name ps fields) $ do
    reportSDoc "tc.rec" 10 $ vcat
      [ "checking record def" <+> prettyTCM name
      , nest 2 $ "ps ="     <+> prettyList (map prettyA ps)
      , nest 2 $ "contel =" <+> prettyA contel
      , nest 2 $ "fields =" <+> prettyA (map Constr fields)
      ]
    -- get type of record
    def <- instantiateDef =<< getConstInfo name
    t   <- instantiateFull $ defType def
    let npars =
          case theDef def of
            DataOrRecSig n -> n
            _              -> __IMPOSSIBLE__

    parNames <- getGeneralizedParameters gpars name

    bindGeneralizedParameters parNames t $ \ gtel t0 ->
     bindParameters (npars - length parNames) ps t0 $ \ ptel t0 -> do

      let tel = abstract gtel ptel

      -- Generate type of constructor from field telescope @contel@,
      -- which is the approximate constructor type (target missing).

      -- Check and evaluate field types.
      reportSDoc "tc.rec" 15 $ "checking fields"
      contype <- workOnTypes $ instantiateFull =<< isType_ contel
      reportSDoc "tc.rec" 20 $ vcat
        [ "contype = " <+> prettyTCM contype ]

      -- compute the field telescope (does not include record parameters)
      let TelV ftel _ = telView' contype

      -- Compute correct type of constructor

      -- t = tel -> t0 where t0 must be a sort s
      TelV idxTel s <- telView t0
      unless (null idxTel) $ typeError $ ShouldBeASort t0
      s <- forceSort s

      -- needed for impredicative Prop (not implemented yet)
      -- ftel <- return $
      --   if s == Prop
      --   then telFromList $ map (setRelevance Irrelevant) $ telToList ftel
      --   else ftel

      reportSDoc "tc.rec" 20 $ do
        gamma <- getContextTelescope  -- the record params (incl. module params)
        "gamma = " <+> inTopContext (prettyTCM gamma)

      -- record type (name applied to parameters)
      rect <- El s . Def name . map Apply <$> getContextArgs

      -- Put in @rect@ as correct target of constructor type.
      -- Andreas, 2011-05-10 use telePi_ instead of telePi to preserve
      -- even names of non-dependent fields in constructor type (Issue 322).
      let contype = telePi_ ftel (raise (size ftel) rect)
        -- NB: contype does not contain the parameter telescope

      -- Obtain name of constructor (if present).
      (hasNamedCon, conName, conInfo) <- case con of
        Just c  -> return (True, c, i)
        Nothing -> do
          m <- killRange <$> currentModule
          c <- qualify m <$> freshName_ ("recCon-NOT-PRINTED" :: String)
          return (False, c, i)

      -- Add record type to signature.
      reportSDoc "tc.rec" 15 $ "adding record type to signature"

      etaenabled <- etaEnabled

      let getName :: A.Declaration -> [Dom QName]
          getName (A.Field _ x arg)    = [x <$ domFromArg arg]
          getName (A.ScopedDecl _ [f]) = getName f
          getName _                    = []

          setTactic dom f = f { domTactic = domTactic dom }

          fs = zipWith setTactic (telToList ftel) $ concatMap getName fields

          -- indCo is what the user wrote: inductive/coinductive/Nothing.
          -- We drop the Range.
          indCo = rangedThing <$> ind
          -- A constructor is inductive unless declared coinductive.
          conInduction = fromMaybe Inductive indCo
          -- Andreas, 2016-09-20, issue #2197.
          -- Eta is inferred by the positivity checker.
          -- We should turn it off until it is proven to be safe.
          haveEta      = maybe (Inferred NoEta) Specified eta
          -- haveEta      = maybe (Inferred $ conInduction == Inductive && etaenabled) Specified eta
          con = ConHead conName conInduction $ map argFromDom fs

          -- A record is irrelevant if all of its fields are.
          -- In this case, the associated module parameter will be irrelevant.
          -- See issue 392.
          -- Unless it's been declared coinductive or no-eta-equality (#2607).
          recordRelevance
            | eta          == Just NoEta  = Relevant
            | conInduction == CoInductive = Relevant
            | otherwise                   = minimum $ Irrelevant : (map getRelevance $ telToList ftel)

      -- Andreas, 2017-01-26, issue #2436
      -- Disallow coinductive records with eta-equality
      when (conInduction == CoInductive && theEtaEquality haveEta == YesEta) $ do
        typeError . GenericDocError =<< do
          sep [ "Agda doesn't like coinductive records with eta-equality."
              , "If you must, use pragma"
              , "{-# ETA" <+> prettyTCM name <+> "#-}"
              ]
      reportSDoc "tc.rec" 30 $ "record constructor is " <+> prettyTCM con

      -- Add the record definition.

      -- Andreas, 2016-06-17, Issue #2018:
      -- Do not rely on @addConstant@ to put in the record parameters,
      -- as they might be renamed in the context.
      -- By putting them ourselves (e.g. by using the original type @t@)
      -- we make sure we get the original names!
      let npars = size tel
          telh  = fmap hideAndRelParams tel
      escapeContext __IMPOSSIBLE__ npars $ do
        addConstant name $
          defaultDefn defaultArgInfo name t $
            Record
              { recPars           = npars
              , recClause         = Nothing
              , recConHead        = con
              , recNamedCon       = hasNamedCon
              , recFields         = fs
              , recTel            = telh `abstract` ftel
              , recAbstr          = Info.defAbstract i
              , recEtaEquality'   = haveEta
              , recInduction      = indCo
                  -- We retain the original user declaration [(co)inductive]
                  -- in case the record turns out to be recursive.
              -- Determined by positivity checker:
              , recMutual         = Nothing
              , recComp           = emptyCompKit -- filled in later
              }

        -- Add record constructor to signature
        addConstant conName $
          defaultDefn defaultArgInfo conName (telh `abstract` contype) $
            Constructor
              { conPars   = npars
              , conArity  = size fs
              , conSrcCon = con
              , conData   = name
              , conAbstr  = Info.defAbstract conInfo
              , conInd    = conInduction
              , conComp   = emptyCompKit  -- filled in later
              , conProj   = Nothing       -- filled in later
              , conForced = []
              , conErased = Nothing
              }

      -- Declare the constructor as eligible for instance search
      case Info.defInstance i of
        InstanceDef r -> setCurrentRange r $ do
          -- Andreas, 2020-01-28, issue #4360:
          -- Use addTypedInstance instead of addNamedInstance
          -- to detect unusable instances.
          addTypedInstance conName contype
          -- addNamedInstance conName name
        NotInstanceDef -> pure ()

      -- Check that the fields fit inside the sort
      _ <- fitsIn uc [] contype s

      {- Andreas, 2011-04-27 WRONG because field types are checked again
         and then non-stricts should not yet be irrelevant

      -- make record parameters hidden and non-stricts irrelevant
      -- ctx <- (reverse . map hideAndRelParams . take (size tel)) <$> getContext
      -}

{- Andreas, 2013-09-13 DEBUGGING the debug printout
      reportSDoc "tc.rec" 80 $ sep
        [ "current module record telescope"
        , nest 2 $ (prettyTCM =<< getContextTelescope)
        ]
      reportSDoc "tc.rec" 80 $ sep
        [ "current module record telescope"
        , nest 2 $ (text . show =<< getContextTelescope)
        ]
      reportSDoc "tc.rec" 80 $ sep
        [ "current module record telescope"
        , nest 2 $ (inTopContext . prettyTCM =<< getContextTelescope)
        ]
      reportSDoc "tc.rec" 80 $ sep
        [ "current module record telescope"
        , nest 2 $ do
           tel <- getContextTelescope
           text (show tel) $+$ do
           inTopContext $ do
             prettyTCM tel $+$ do
               telA <- reify tel
               text (show telA) $+$ do
               ctx <- getContextTelescope
               "should be empty:" <+> prettyTCM ctx
        ]
-}

      let info = setRelevance recordRelevance defaultArgInfo
          addRecordVar =
            addRecordNameContext (setArgInfo info $ defaultDom rect)

      let m = qnameToMName name  -- Name of record module.

      -- Andreas, 2016-02-09 setting all parameters hidden in the record
      -- section telescope changes the semantics, see e.g.
      -- test/Succeed/RecordInParModule.
      -- Ulf, 2016-03-02 but it's the right thing to do (#1759)
      modifyContextInfo hideOrKeepInstance $ addRecordVar $ do

        -- Add the record section.

        reportSDoc "tc.rec.def" 10 $ sep
          [ "record section:"
          , nest 2 $ sep
            [ prettyTCM m <+> (inTopContext . prettyTCM =<< getContextTelescope)
            , fsep $ punctuate comma $ map (return . P.pretty . map argFromDom . getName) fields
            ]
          ]
        reportSDoc "tc.rec.def" 15 $ nest 2 $ vcat
          [ "field tel =" <+> escapeContext __IMPOSSIBLE__ 1 (prettyTCM ftel)
          ]
        addSection m

      -- Andreas, 2016-02-09, Issue 1815 (see also issue 1759).
      -- For checking the record declarations, hide the record parameters
      -- and the parameters of the parent modules.
      modifyContextInfo hideOrKeepInstance $ addRecordVar $ do

        -- Check the types of the fields and the other record declarations.
        withCurrentModule m $ do

          -- Andreas, 2013-09-13, 2016-01-06.
          -- Argument telescope for the projections: all parameters are hidden.
          -- This means parameters of the parent modules and of the current
          -- record type.
          -- See test/Succeed/ProjectionsTakeModuleTelAsParameters.agda.
          tel' <- getContextTelescope
          setModuleCheckpoint m
          checkRecordProjections m name hasNamedCon con tel' (raise 1 ftel) fields


      -- we define composition here so that the projections are already in the signature.
      escapeContext __IMPOSSIBLE__ npars $ do
        addCompositionForRecord name con tel (map argFromDom fs) ftel rect

      -- Jesper, 2019-06-07: Check confluence of projection clauses
      whenM (optConfluenceCheck <$> pragmaOptions) $ forM_ fs $ \f -> do
        cls <- defClauses <$> getConstInfo (unDom f)
        forM (zip cls [0..]) $ \(cl,i) ->
          checkConfluenceOfClause (unDom f) i cl

      return ()


addCompositionForRecord
  :: QName       -- ^ Datatype name.
  -> ConHead
  -> Telescope   -- ^ @Γ@ parameters.
  -> [Arg QName] -- ^ Projection names.
  -> Telescope   -- ^ @Γ ⊢ Φ@ field types.
  -> Type        -- ^ @Γ ⊢ T@ target type.
  -> TCM ()
addCompositionForRecord name con tel fs ftel rect = do
  cxt <- getContextTelescope
  inTopContext $ do

    -- Record has no fields: attach composition data to record constructor
    if null fs then do
      kit <- defineCompData name con (abstract cxt tel) [] ftel rect []
      modifySignature $ updateDefinition (conName con) $ updateTheDef $ \case
        r@Constructor{} -> r { conComp = kit, conProj = Just [] }  -- no projections
        _ -> __IMPOSSIBLE__

    -- Record has fields: attach composition data to record type
    else do
      -- If record has irrelevant fields but irrelevant projections are disabled,
      -- we cannot generate composition data.
      kit <- ifM (return (any isIrrelevant fs)
                  `and2M` do not . optIrrelevantProjections <$> pragmaOptions)
        {-then-} (return emptyCompKit)
        {-else-} (defineCompKitR name (abstract cxt tel) ftel fs rect)
      modifySignature $ updateDefinition name $ updateTheDef $ \case
        r@Record{} -> r { recComp = kit }
        _          -> __IMPOSSIBLE__

defineCompKitR ::
    QName          -- ^ some name, e.g. record name
  -> Telescope   -- ^ param types Δ
  -> Telescope   -- ^ fields' types Δ ⊢ Φ
  -> [Arg QName] -- ^ fields' names
  -> Type        -- ^ record type Δ ⊢ T
  -> TCM CompKit
defineCompKitR name params fsT fns rect = do
  required <- mapM getTerm'
        [ builtinInterval
        , builtinIZero
        , builtinIOne
        , builtinIMin
        , builtinIMax
        , builtinINeg
        , builtinPOr
        , builtinItIsOne
        ]
  reportSDoc "tc.rec.cxt" 30 $ prettyTCM params
  reportSDoc "tc.rec.cxt" 30 $ prettyTCM fsT
  reportSDoc "tc.rec.cxt" 30 $ pretty rect
  if not $ all isJust required then return $ emptyCompKit else do
    transp <- whenDefined [builtinTrans]              (defineTranspOrHCompR DoTransp name params fsT fns rect)
    hcomp  <- whenDefined [builtinTrans,builtinHComp] (defineTranspOrHCompR DoHComp name params fsT fns rect)
    return $ CompKit
      { nameOfTransp = transp
      , nameOfHComp  = hcomp
      }
  where
    whenDefined xs m = do
      xs <- mapM getTerm' xs
      if all isJust xs then m else return Nothing


defineTranspOrHCompR ::
  TranspOrHComp
  -> QName       -- ^ some name, e.g. record name
  -> Telescope   -- ^ param types Δ
  -> Telescope   -- ^ fields' types Δ ⊢ Φ
  -> [Arg QName] -- ^ fields' names
  -> Type        -- ^ record type Δ ⊢ T
  -> TCM (Maybe QName)
defineTranspOrHCompR cmd name params fsT fns rect = do
  let project = (\ t fn -> t `applyE` [Proj ProjSystem fn])
  stuff <- fmap fst <$> defineTranspOrHCompForFields cmd Nothing project name params fsT fns rect

  caseMaybe stuff (return Nothing) $ \ (theName, gamma, rtype, clause_types, bodies) -> do
  -- phi = 1 clause
  c' <- do
           io <- primIOne
           Just io_name <- getBuiltinName' builtinIOne
           one <- primItIsOne
           tInterval <- elInf primInterval
           let
              (ix,rhs) =
                case cmd of
                  -- TranspRArgs = phi : I, a0 : ..
                  -- Γ = Δ^I , CompRArgs
                  -- pats = ... | phi = i1
                  -- body = a0
                  DoTransp -> (1,Var 0 [])
                  -- HCompRArgs = phi : I, u : .., a0 : ..
                  -- Γ = Δ, CompRArgs
                  -- pats = ... | phi = i1
                  -- body = u i1 itIsOne
                  DoHComp  -> (2,Var 1 [] `apply` [argN io, setRelevance Irrelevant $ argN one])

              p = ConP (ConHead io_name Inductive [])
                       (noConPatternInfo { conPType = Just (Arg defaultArgInfo tInterval)
                                         , conPFallThrough = True })
                         []

              -- gamma, rtype

              s = singletonS ix p

              pats :: [NamedArg DeBruijnPattern]
              pats = s `applySubst` teleNamedArgs gamma

              t :: Type
              t = s `applyPatSubst` rtype

              gamma' :: Telescope
              gamma' = unflattenTel (ns0 ++ ns1) $ s `applyPatSubst` (g0 ++ g1)
               where
                (g0,_:g1) = splitAt (size gamma - 1 - ix) $ flattenTel gamma
                (ns0,_:ns1) = splitAt (size gamma - 1 - ix) $ teleNames gamma

              c = Clause { clauseTel       = gamma'
                         , clauseType      = Just $ argN t
                         , namedClausePats = pats
                         , clauseFullRange = noRange
                         , clauseLHSRange  = noRange
                         , clauseCatchall  = False
                         , clauseBody      = Just $ rhs
                         , clauseRecursive   = Just False  -- definitely non-recursive!
                         , clauseUnreachable = Just False
                         , clauseEllipsis  = NoEllipsis
                         }
           reportSDoc "trans.rec.face" 17 $ text $ show c
           return c
  cs <- flip mapM (zip3 fns clause_types bodies) $ \ (fname, clause_ty, body) -> do
          let
              pats = teleNamedArgs gamma ++ [defaultNamedArg $ ProjP ProjSystem $ unArg fname]
              c = Clause { clauseTel       = gamma
                         , clauseType      = Just $ argN (unDom clause_ty)
                         , namedClausePats = pats
                         , clauseFullRange = noRange
                         , clauseLHSRange  = noRange
                         , clauseCatchall  = False
                         , clauseBody      = Just body
                         , clauseRecursive   = Nothing
                             -- Andreas 2020-02-06 TODO
                             -- Or: Just False;  is it known to be non-recursive?
                         , clauseUnreachable = Just False
                         , clauseEllipsis  = NoEllipsis
                         }
          reportSDoc "trans.rec" 17 $ text $ show c
          reportSDoc "trans.rec" 16 $ text "type =" <+> text (show (clauseType c))
          reportSDoc "trans.rec" 15 $ prettyTCM $ abstract gamma (unDom clause_ty)
          reportSDoc "trans.rec" 10 $ text "body =" <+> prettyTCM (abstract gamma body)
          return c
  addClauses theName $ c' : cs
  reportSDoc "trans.rec" 15 $ text $ "compiling clauses for " ++ show theName
  (mst, _, cc) <- inTopContext (compileClauses Nothing cs)
  whenJust mst $ setSplitTree theName
  setCompiledClauses theName cc
  reportSDoc "trans.rec" 15 $ text $ "compiled"
  return $ Just theName


{-| @checkRecordProjections m r q tel ftel fs@.

    [@m@    ]  name of the generated module

    [@r@    ]  name of the record type

    [@con@  ]  name of the record constructor

    [@tel@  ]  parameters and record variable r ("self")

    [@ftel@ ]  telescope of fields

    [@fs@   ]  the fields to be checked
-}
checkRecordProjections ::
  ModuleName -> QName -> Bool -> ConHead -> Telescope -> Telescope ->
  [A.Declaration] -> TCM ()
checkRecordProjections m r hasNamedCon con tel ftel fs = do
    checkProjs EmptyTel ftel fs
  where

    checkProjs :: Telescope -> Telescope -> [A.Declaration] -> TCM ()

    checkProjs _ _ [] = return ()

    checkProjs ftel1 ftel2 (A.ScopedDecl scope fs' : fs) =
      setScope scope >> checkProjs ftel1 ftel2 (fs' ++ fs)

    -- Case: projection.
    checkProjs ftel1 (ExtendTel (dom@Dom{domInfo = ai,unDom = t}) ftel2) (A.Field info x _ : fs) =
      traceCall (CheckProjection (getRange info) x t) $ do
      -- Andreas, 2012-06-07:
      -- Issue 387: It is wrong to just type check field types again
      -- because then meta variables are created again.
      -- Instead, we take the field type t from the field telescope.
      reportSDoc "tc.rec.proj" 5 $ sep
        [ "checking projection" <+> prettyTCM x
        , nest 2 $ vcat
          [ "top   =" <+> (inTopContext . prettyTCM =<< getContextTelescope)
          , "tel   =" <+> (inTopContext . prettyTCM $ tel)
          , "ftel1 =" <+> prettyTCM ftel1
          , "t     =" <+> prettyTCM t
          , "ftel2 =" <+> addContext ftel1 (underAbstraction_ ftel2 prettyTCM)
          , "abstr =" <+> (text . show) (Info.defAbstract info)
          , "quant =" <+> (text . show) (getQuantity ai)
          , "coh   =" <+> (text . show) (getCohesion ai)
          ]
        ]

      -- Cohesion check:
      -- For a field `@c π : A` we would create a projection `π : .., (@(c^-1) r : R as) -> A`
      -- So we want to check that `@.., (c^-1 . c) x : A |- x : A` is allowed by the modalities.
      --
      -- Alternatively we could create a projection `.. |- π r :c A`
      -- but that would require support for a `t :c A` judgment.
      if hasLeftAdjoint (getCohesion ai)
        then unless (getCohesion ai == Continuous)
                    -- Andrea TODO: properly update the context/type of the projection when we add Sharp
                    __IMPOSSIBLE__
        else genericError $ "Cannot have record fields with modality " ++ show (getCohesion ai)

      -- Andreas, 2010-09-09 The following comments are misleading, TODO: update
      -- in fact, tel includes the variable of record type as last one
      -- e.g. for cartesion product it is
      --
      --   tel = {A' : Set} {B' : Set} (r : Prod A' B')

      -- create the projection functions (instantiate the type with the values
      -- of the previous fields)

      {- what are the contexts?

          Γ, tel            ⊢ t
          Γ, tel, r         ⊢ vs
          Γ, tel, r, ftel₁  ⊢ raiseFrom (size ftel₁) 1 t
      -}

      -- The type of the projection function should be
      --  {tel} -> (r : R Δ) -> t
      -- where Δ = Γ, tel is the current context
      let finalt   = telePi (replaceEmptyName "r" tel) t
          projname = qualify m $ qnameName x
          projcall o = Var 0 [Proj o projname]
          rel      = getRelevance ai
          -- the recursive call
          recurse  = checkProjs (abstract ftel1 $ ExtendTel dom
                                 $ Abs (nameToArgName $ qnameName projname) EmptyTel)
                                (ftel2 `absApp` projcall ProjSystem) fs

      reportSDoc "tc.rec.proj" 25 $ nest 2 $ "finalt=" <+> do
        inTopContext $ prettyTCM finalt

      -- -- Andreas, 2012-02-20 do not add irrelevant projections if
      -- -- disabled by --no-irrelevant-projections
      -- ifM (return (rel == Irrelevant) `and2M` do not . optIrrelevantProjections <$> pragmaOptions) recurse $ do
      -- Andreas, 2018-06-09 issue #2170
      -- Always create irrelevant projections (because the scope checker accepts irrelevant fields).
      -- If --no-irrelevant-projections, then their use should be disallowed by the type checker for expressions.
      do
        reportSDoc "tc.rec.proj" 10 $ sep
          [ "adding projection"
          , nest 2 $ prettyTCM projname <+> ":" <+> inTopContext (prettyTCM finalt)
          ]

        -- The body should be
        --  P.xi {tel} (r _ .. x .. _) = x
        -- Ulf, 2011-08-22: actually we're dropping the parameters from the
        -- projection functions so the body is now
        --  P.xi (r _ .. x .. _) = x
        -- Andreas, 2012-01-12: irrelevant projections get translated to
        --  P.xi (r _ .. x .. _) = irrAxiom {level of t} {t} x
        -- PROBLEM: because of dropped parameters, cannot refer to t
        -- 2012-04-02: DontCare instead of irrAxiom

        -- compute body modification for irrelevant projections
        let bodyMod = case rel of
              Relevant   -> id
              NonStrict  -> id
              Irrelevant -> dontCare

        let -- Andreas, 2010-09-09: comment for existing code
            -- split the telescope into parameters (ptel) and the type or the record
            -- (rt) which should be  R ptel
            telList = telToList tel
            (ptelList,[rt]) = splitAt (size tel - 1) telList
            ptel   = telFromList ptelList
            cpo    = if hasNamedCon then PatOCon else PatORec
            cpi    = ConPatternInfo { conPInfo   = PatternInfo cpo []
                                    , conPRecord = True
                                    , conPFallThrough = False
                                    , conPType   = Just $ argFromDom $ fmap snd rt
                                    , conPLazy   = True }
            conp   = defaultArg $ ConP con cpi $
                     [ Arg ai' $ unnamed $ varP ("x" :: String)
                     | Dom{domInfo = ai'} <- telToList ftel
                     ]
            body   = Just $ bodyMod $ var (size ftel2)
            cltel  = ptel `abstract` ftel
            clause = Clause { clauseLHSRange  = getRange info
                            , clauseFullRange = getRange info
                            , clauseTel       = killRange cltel
                            , namedClausePats = [Named Nothing <$> numberPatVars __IMPOSSIBLE__ (idP $ size ftel) conp]
                            , clauseBody      = body
                            , clauseType      = Just $ Arg ai t
                            , clauseCatchall  = False
                            , clauseRecursive   = Just False
                            , clauseUnreachable = Just False
                            , clauseEllipsis  = NoEllipsis
                            }

        let projection = Projection
              { projProper   = Just r
              , projOrig     = projname
              -- name of the record type:
              , projFromType = defaultArg r
              -- index of the record argument (in the type),
              -- start counting with 1:
              , projIndex    = size tel -- which is @size ptel + 1@
              , projLams     = ProjLams $ map (argFromDom . fmap fst) telList
              }

        reportSDoc "tc.rec.proj" 80 $ sep
          [ "adding projection"
          , nest 2 $ prettyTCM projname <+> text (show clause)
          ]
        reportSDoc "tc.rec.proj" 70 $ sep
          [ "adding projection"
          , nest 2 $ prettyTCM projname <+> text (show (clausePats clause)) <+> "=" <+>
                       inTopContext (addContext ftel (maybe "_|_" prettyTCM (clauseBody clause)))
          ]
        reportSDoc "tc.rec.proj" 10 $ sep
          [ "adding projection"
          , nest 2 $ prettyTCM (QNamed projname clause)
          ]

              -- Record patterns should /not/ be translated when the
              -- projection functions are defined. Record pattern
              -- translation is defined in terms of projection
              -- functions.
        (mst, _, cc) <- compileClauses Nothing [clause]

        reportSDoc "tc.cc" 60 $ do
          sep [ "compiled clauses of " <+> prettyTCM projname
              , nest 2 $ text (show cc)
              ]

        escapeContext __IMPOSSIBLE__ (size tel) $ do
          addConstant projname $
            (defaultDefn ai projname (killRange finalt)
              emptyFunction
                { funClauses        = [clause]
                , funCompiled       = Just cc
                , funSplitTree      = mst
                , funProjection     = Just projection
                , funMutual         = Just []  -- Projections are not mutually recursive with anything
                , funTerminates     = Just True
                })
              { defArgOccurrences = [StrictPos]
              , defCopatternLHS   = hasProjectionPatterns cc
              }
          computePolarity [projname]

        case Info.defInstance info of
          -- fields do not have an @instance@ keyword!?
          InstanceDef _r -> addTypedInstance projname t
          NotInstanceDef -> pure ()

        recurse

    -- Case: definition.
    checkProjs ftel1 ftel2 (d : fs) = do
      checkDecl d
      checkProjs ftel1 ftel2 fs