{-# LANGUAGE CPP #-} {-# LANGUAGE NondecreasingIndentation #-} {-| Coverage checking, case splitting, and splitting for refine tactics. -} module Agda.TypeChecking.Coverage ( SplitClause(..), clauseToSplitClause, fixTarget , Covering(..), splitClauses , coverageCheck , isCovered , splitClauseWithAbsurd , splitLast , splitResult , normaliseProjP ) where import Prelude hiding (null, (!!)) -- do not use partial functions like !! import Control.Arrow (second) import Control.Monad import Control.Monad.Reader import Control.Monad.Trans ( lift ) import Data.Either (lefts) import Data.Foldable (for_) import qualified Data.List as List import Data.Monoid (Any(..)) import Data.Map (Map) import qualified Data.Map as Map import Data.Set (Set) import qualified Data.Set as Set import qualified Data.Traversable as Trav import Agda.Syntax.Common import Agda.Syntax.Position import Agda.Syntax.Literal import Agda.Syntax.Internal import Agda.Syntax.Internal.Pattern import Agda.TypeChecking.Names import Agda.TypeChecking.Primitive hiding (Nat) import Agda.TypeChecking.Primitive.Cubical import Agda.TypeChecking.Monad import Agda.TypeChecking.Monad.Builtin import Agda.TypeChecking.Rules.LHS (checkSortOfSplitVar) import Agda.TypeChecking.Rules.LHS.Problem (allFlexVars) import Agda.TypeChecking.Rules.LHS.Unify import Agda.TypeChecking.Coverage.Match import Agda.TypeChecking.Coverage.SplitTree import Agda.TypeChecking.Conversion (tryConversion, equalType, equalTermOnFace) import Agda.TypeChecking.Datatypes (getConForm) import {-# SOURCE #-} Agda.TypeChecking.Empty ( checkEmptyTel, isEmptyTel, isEmptyType ) import Agda.TypeChecking.Free import Agda.TypeChecking.Irrelevance import Agda.TypeChecking.Patterns.Internal (dotPatternsToPatterns) import Agda.TypeChecking.Pretty import Agda.TypeChecking.Substitute import Agda.TypeChecking.Reduce import Agda.TypeChecking.Records import Agda.TypeChecking.Telescope import Agda.TypeChecking.Telescope.Path import Agda.TypeChecking.MetaVars import Agda.TypeChecking.Warnings import Agda.Interaction.Options import Agda.Utils.Either import Agda.Utils.Except ( ExceptT , MonadError(catchError, throwError) , runExceptT ) import Agda.Utils.Function import Agda.Utils.Functor import Agda.Utils.List import Agda.Utils.Maybe import Agda.Utils.Monad import Agda.Utils.Null import Agda.Utils.Permutation import Agda.Utils.Pretty (prettyShow) import Agda.Utils.Size import Agda.Utils.Tuple import Agda.Utils.Lens #include "undefined.h" import Agda.Utils.Impossible data SplitClause = SClause { scTel :: Telescope -- ^ Type of variables in @scPats@. , scPats :: [NamedArg SplitPattern] -- ^ The patterns leading to the currently considered branch of -- the split tree. , scSubst :: Substitution' SplitPattern -- ^ Substitution from 'scTel' to old context. -- Only needed directly after split on variable: -- * To update 'scTarget' -- * To rename other split variables when splitting on -- multiple variables. -- @scSubst@ is not ``transitive'', i.e., does not record -- the substitution from the original context to 'scTel' -- over a series of splits. It is freshly computed -- after each split by 'computeNeighborhood'; also -- 'splitResult', which does not split on a variable, -- should reset it to the identity 'idS', lest it be -- applied to 'scTarget' again, leading to Issue 1294. , scCheckpoints :: Map CheckpointId Substitution -- ^ We need to keep track of the module parameter checkpoints for the -- clause for the purpose of inferring missing instance clauses. , scTarget :: Maybe (Arg Type) -- ^ The type of the rhs, living in context 'scTel'. -- This invariant is broken before calls to 'fixTarget'; -- there, 'scTarget' lives in the old context. -- 'fixTarget' moves 'scTarget' to the new context by applying -- substitution 'scSubst'. } -- | A @Covering@ is the result of splitting a 'SplitClause'. data Covering = Covering { covSplitArg :: Arg Nat -- ^ De Bruijn level (counting dot patterns) of argument we split on. , covSplitClauses :: [(SplitTag, SplitClause)] -- ^ Covering clauses, indexed by constructor/literal these clauses share. } -- | Project the split clauses out of a covering. splitClauses :: Covering -> [SplitClause] splitClauses (Covering _ qcs) = map snd qcs -- | Create a split clause from a clause in internal syntax. Used by make-case. clauseToSplitClause :: Clause -> SplitClause clauseToSplitClause cl = SClause { scTel = clauseTel cl , scPats = toSplitPatterns $ namedClausePats cl , scSubst = idS -- Andreas, 2014-07-15 TODO: Is this ok? , scCheckpoints = Map.empty -- #2996: not __IMPOSSIBLE__ for debug printing , scTarget = clauseType cl } type CoverM = ExceptT SplitError TCM -- | Top-level function for checking pattern coverage. -- -- Effects: -- -- - Marks unreachable clauses as such in the signature. -- -- - Adds missing instances clauses to the signature. -- coverageCheck :: QName -- ^ Name @f@ of definition. -> Type -- ^ Absolute type (including the full parameter telescope). -> [Clause] -- ^ Clauses of @f@. These are the very clauses of @f@ in the signature. -> TCM SplitTree coverageCheck f t cs = do reportSLn "tc.cover.top" 30 $ "entering coverageCheck for " ++ show f reportSDoc "tc.cover.top" 75 $ " of type (raw): " <+> (text . prettyShow) t reportSDoc "tc.cover.top" 45 $ " of type: " <+> prettyTCM t TelV gamma a <- telViewUpTo (-1) t reportSLn "tc.cover.top" 30 $ "coverageCheck: computed telView" let -- n = arity -- xs = variable patterns fitting lgamma n = size gamma xs = map (setOrigin Inserted) $ teleNamedArgs gamma reportSLn "tc.cover.top" 30 $ "coverageCheck: getDefFreeVars" -- The initial module parameter substitutions need to be weakened by the -- number of arguments that aren't module parameters. fv <- getDefFreeVars f reportSLn "tc.cover.top" 30 $ "coverageCheck: getting checkpoints" -- TODO: does this make sense? Why are we weakening by n - fv? checkpoints <- applySubst (raiseS (n - fv)) <$> viewTC eCheckpoints -- construct the initial split clause let sc = SClause gamma xs idS checkpoints $ Just $ defaultArg a reportSDoc "tc.cover.top" 10 $ do let prCl cl = addContext (clauseTel cl) $ prettyTCMPatternList $ namedClausePats cl vcat [ text $ "Coverage checking " ++ prettyShow f ++ " with patterns:" , nest 2 $ vcat $ map prCl cs ] -- used = actually used clauses for cover -- pss = uncovered cases CoverResult splitTree used pss qss noex <- cover f cs sc -- Andreas, 2018-11-12, issue #378: -- some indices in @used@ and @noex@ point outside of @cs@, -- since missing hcomp clauses have been added during the course of @cover@. -- We simply delete theses indices from @noex@. noex <- return $ List.filter (< length cs) $ Set.toList noex reportSDoc "tc.cover.top" 10 $ vcat [ "cover computed!" , text $ "used clauses: " ++ show used , text $ "non-exact clauses: " ++ show noex ] reportSDoc "tc.cover.splittree" 10 $ vcat [ "generated split tree for" <+> prettyTCM f , text $ prettyShow splitTree ] reportSDoc "tc.cover.covering" 10 $ vcat [ text $ "covering patterns for " ++ prettyShow f , nest 2 $ vcat $ map (\cl -> enterClosure cl $ \ cl -> addContext (clauseTel cl) $ prettyTCMPatternList $ namedClausePats cl) qss ] -- Storing the covering clauses so that checkIApplyConfluence_ can -- find them later. -- Andreas, 2019-03-27, only needed when --cubical whenM (optCubical <$> pragmaOptions) $ do modifySignature $ updateDefinition f $ updateTheDef $ updateCovering $ const qss -- filter out the missing clauses that are absurd. pss <- flip filterM pss $ \(tel,ps) -> -- Andreas, 2019-04-13, issue #3692: when adding missing absurd -- clauses, also put the absurd pattern in. caseEitherM (checkEmptyTel noRange tel) (\ _ -> return True) $ \ l -> do -- Now, @l@ is the first type in @tel@ (counting from 0=leftmost) -- which is empty. Turn it into a de Bruijn index @i@. let i = size tel - 1 - l -- Build a substitution mapping this pattern variable to the absurd pattern. let sub = inplaceS i $ absurdP i -- ifNotM (isEmptyTel tel) (return True) $ do -- Jesper, 2018-11-28, Issue #3407: if the clause is absurd, -- add the appropriate absurd clause to the definition. let cl = Clause { clauseLHSRange = noRange , clauseFullRange = noRange , clauseTel = tel , namedClausePats = applySubst sub ps , clauseBody = Nothing , clauseType = Nothing , clauseCatchall = False , clauseUnreachable = Just False } reportSDoc "tc.cover.missing" 20 $ inTopContext $ do sep [ "adding missing absurd clause" , nest 2 $ prettyTCM $ QNamed f cl ] reportSDoc "tc.cover.missing" 80 $ inTopContext $ vcat [ "l = " <+> pretty l , "i = " <+> pretty i , "cl = " <+> pretty (QNamed f cl) ] addClauses f [cl] return False -- report a warning if there are uncovered cases, -- generate a catch-all clause with a metavariable as its body to avoid -- internal errors in the reduction machinery. unless (null pss) $ setCurrentRange cs $ warning $ CoverageIssue f pss -- Andreas, 2017-08-28, issue #2723: -- Mark clauses as reachable or unreachable in the signature. let (is0, cs1) = unzip $ for (zip [0..] cs) $ \ (i, cl) -> let unreachable = i `Set.notMember` used in (boolToMaybe unreachable i, cl { clauseUnreachable = Just unreachable }) -- is = indices of unreachable clauses let is = catMaybes is0 reportSDoc "tc.cover.top" 10 $ vcat [ text $ "unreachable clauses: " ++ if null is then "(none)" else show is ] -- Replace the first clauses by @cs1@. There might be more -- added by @inferMissingClause@. modifyFunClauses f $ \ cs0 -> cs1 ++ drop (length cs1) cs0 -- Warn if there are unreachable clauses and mark them as unreachable. unless (null is) $ do -- Warn about unreachable clauses. let unreached = filter ((Just True ==) . clauseUnreachable) cs1 setCurrentRange (map clauseFullRange unreached) $ warning $ UnreachableClauses f $ map namedClausePats unreached -- report a warning if there are clauses that are not preserved as -- definitional equalities and --exact-split is enabled unless (null noex) $ do let noexclauses = map (indexWithDefault __IMPOSSIBLE__ cs1) noex setCurrentRange (map clauseLHSRange noexclauses) $ warning $ CoverageNoExactSplit f $ noexclauses return splitTree -- | Top-level function for eliminating redundant clauses in the interactive -- case splitter isCovered :: QName -> [Clause] -> SplitClause -> TCM Bool isCovered f cs sc = do CoverResult { coverMissingClauses = missing } <- cover f cs sc return $ null missing data CoverResult = CoverResult { coverSplitTree :: SplitTree , coverUsedClauses :: Set Nat , coverMissingClauses :: [(Telescope, [NamedArg DeBruijnPattern])] , coverPatterns :: [Closure Clause] -- ^ The set of patterns used as cover. -- Entering the closure puts you directly in the right context (and cps) for the RHS. , coverNoExactClauses :: Set Nat } -- | @cover f cs (SClause _ _ ps _) = return (splitTree, used, pss)@. -- checks that the list of clauses @cs@ covers the given split clause. -- Returns the @splitTree@, the @used@ clauses, and missing cases @pss@. -- -- Effect: adds missing instance clauses for @f@ to signature. -- cover :: QName -> [Clause] -> SplitClause -> TCM CoverResult cover f cs sc@(SClause tel ps _ _ target) = updateRelevance $ do reportSDoc "tc.cover.cover" 10 $ inTopContext $ vcat [ "checking coverage of pattern:" , nest 2 $ "tel =" <+> prettyTCM tel , nest 2 $ "ps =" <+> do addContext tel $ prettyTCMPatternList $ fromSplitPatterns ps , nest 2 $ "target =" <+> do addContext tel $ maybe (text "") prettyTCM target , nest 2 $ "target sort =" <+> do addContext tel $ maybe (text "") (prettyTCM . getSort . unArg) target ] match cs ps >>= \case Yes (i,mps) -> do exact <- allM (map snd mps) isTrivialPattern let cl0 = indexWithDefault __IMPOSSIBLE__ cs i let noExactClause = if exact || clauseCatchall (indexWithDefault __IMPOSSIBLE__ cs i) then Set.empty else Set.singleton i reportSLn "tc.cover.cover" 10 $ "pattern covered by clause " ++ show i reportSDoc "tc.cover.cover" 20 $ text "with mps = " <+> do addContext tel $ pretty $ mps cl <- applyCl sc cl0 mps return $ CoverResult (SplittingDone (size tel)) (Set.singleton i) [] [cl] noExactClause No -> do reportSLn "tc.cover" 20 $ "pattern is not covered" -- TODO Andrea: add hcomp clause! case fmap getHiding target of Just h | isInstance h -> do -- Ulf, 2016-10-31: For now we only infer instance clauses. It would -- make sense to do it also for hidden, but since the value of a -- hidden clause is expected to be forced by later clauses, it's too -- late to add it now. If it was inferrable we would have gotten a -- type error before getting to this point. cl <- inferMissingClause f sc return $ CoverResult (SplittingDone (size tel)) Set.empty [] [cl] Set.empty _ -> do let ps' = fromSplitPatterns ps return $ CoverResult (SplittingDone (size tel)) Set.empty [(tel, ps')] [] Set.empty -- We need to split! -- If all clauses have an unsplit copattern, we try that first. Block res bs -> trySplitRes res (null bs) $ do when (null bs) __IMPOSSIBLE__ -- Otherwise, if there are variables to split, we try them -- in the order determined by a split strategy. reportSLn "tc.cover.strategy" 20 $ "blocking vars = " ++ prettyShow bs -- xs is a non-empty lists of blocking variables -- try splitting on one of them xs <- splitStrategy bs tel -- Andreas, 2017-10-08, issue #2594 -- First, try to find split order for complete coverage. -- If this fails, try to at least carry out the splitting to the end. continue xs NoAllowPartialCover $ \ _err -> do continue xs YesAllowPartialCover $ \ err -> do typeError $ SplitError err where applyCl :: SplitClause -> Clause -> [(Nat, SplitPattern)] -> TCM (Closure Clause) applyCl SClause{scTel = tel, scCheckpoints = cps} cl mps = addContext tel $ locallyTC eCheckpoints (const cps) $ checkpoint IdS $ do reportSDoc "tc.cover.applyCl" 40 $ "applyCl" reportSDoc "tc.cover.applyCl" 40 $ "tel =" <+> prettyTCM tel reportSDoc "tc.cover.applyCl" 40 $ "ps =" <+> pretty (namedClausePats cl) reportSDoc "tc.cover.applyCl" 40 $ "mps =" <+> pretty mps reportSDoc "tc.cover.applyCl" 40 $ "s =" <+> pretty s reportSDoc "tc.cover.applyCl" 40 $ "new ps =" <+> pretty (s `applySubst` namedClausePats cl) buildClosure $ Clause { clauseLHSRange = clauseLHSRange cl , clauseFullRange = clauseFullRange cl , clauseTel = tel , namedClausePats = s `applySubst` namedClausePats cl , clauseBody = (s `applyPatSubst`) <$> clauseBody cl , clauseType = (s `applyPatSubst`) <$> clauseType cl , clauseCatchall = clauseCatchall cl , clauseUnreachable = clauseUnreachable cl } where (vs,qs) = unzip mps mps' = zip vs $ map namedArg $ fromSplitPatterns $ map defaultNamedArg qs s = parallelS (for [0..maximum (-1:vs)] $ (\ i -> fromMaybe (deBruijnVar i) (List.lookup i mps'))) updateRelevance :: TCM a -> TCM a updateRelevance cont = -- Don't do anything if there is no target type info. caseMaybe target cont $ \ b -> do -- TODO (2018-10-16): if proofs get erased in the compiler, also wake erased vars! let m = getModality b applyModalityToContext m cont continue :: [BlockingVar] -> AllowPartialCover -> (SplitError -> TCM CoverResult) -> TCM CoverResult continue xs allowPartialCover handle = do r <- altM1 (\ x -> fmap (,x) <$> split Inductive allowPartialCover sc x) xs case r of Left err -> handle err -- If we get the empty covering, we have reached an impossible case -- and are done. Right (Covering n [], _) -> do -- TODO Andrea: I guess an empty pattern is not part of the cover? let qs = [] return $ CoverResult (SplittingDone (size tel)) Set.empty [] qs Set.empty Right (Covering n scs, x) -> do cs <- do let fallback = return cs caseMaybeM (getPrimitiveName' builtinHComp) fallback $ \ comp -> do let isComp = \case SplitCon c -> comp == c _ -> False caseMaybe (List.find (isComp . fst) scs) fallback $ \ (_, newSc) -> do snoc cs <$> createMissingHCompClause f n x sc newSc results <- mapM (cover f cs) (map snd scs) let trees = map coverSplitTree results useds = map coverUsedClauses results psss = map coverMissingClauses results qsss = map coverPatterns results noex = map coverNoExactClauses results -- Jesper, 2016-03-10 We need to remember which variables were -- eta-expanded by the unifier in order to generate a correct split -- tree (see Issue 1872). reportSDoc "tc.cover.split.eta" 60 $ vcat [ "etaRecordSplits" , nest 2 $ vcat [ "n = " <+> text (show n) , "scs = " <+> prettyTCM scs , "ps = " <+> prettyTCMPatternList (fromSplitPatterns ps) ] ] -- TODO Andrea: do something with etaRecordSplits and qsss? let trees' = zipWith (etaRecordSplits (unArg n) ps) scs trees tree = SplitAt n trees' return $ CoverResult tree (Set.unions useds) (concat psss) (concat qsss) (Set.unions noex) -- Try to split result trySplitRes :: BlockedOnResult -- ^ Are we blocked on the result? -> Bool -- ^ Is this the last thing we try? -> TCM CoverResult -- ^ Continuation -> TCM CoverResult -- not blocked on result: try regular splits trySplitRes NotBlockedOnResult finalSplit cont | finalSplit = __IMPOSSIBLE__ -- there must be *some* reason we are blocked | otherwise = cont -- blocked on arguments that are not yet introduced: -- we must split on a variable so that the target type becomes a pi type trySplitRes (BlockedOnApply IsApply) finalSplit cont | finalSplit = __IMPOSSIBLE__ -- already ruled out by lhs checker | otherwise = cont -- ...or it was an IApply pattern, so we might just need to introduce the variable now. trySplitRes (BlockedOnApply IsIApply) finalSplit cont = do caseMaybeM (splitResultPath f sc) fallback $ \ sc -> cover f cs . snd =<< fixTarget sc where fallback | finalSplit = __IMPOSSIBLE__ -- already ruled out by lhs checker? | otherwise = cont -- blocked on result but there are catchalls: -- try regular splits if there are any, or else throw an error, -- this is nicer than continuing and reporting unreachable clauses -- (see issue #2833) trySplitRes (BlockedOnProj True) finalSplit cont | finalSplit = typeError $ SplitError CosplitCatchall | otherwise = cont -- all clauses have an unsplit copattern: try to split trySplitRes (BlockedOnProj False) finalSplit cont = do reportSLn "tc.cover" 20 $ "blocked by projection pattern" -- forM is a monadic map over a Maybe here mcov <- splitResultRecord f sc case mcov of Left err | finalSplit -> typeError $ SplitError err | otherwise -> cont Right (Covering n scs) -> do -- If result splitting was successful, continue coverage checking. (projs, results) <- unzip <$> do mapM (traverseF $ cover f cs <=< (snd <.> fixTarget)) scs -- OR: -- forM scs $ \ (proj, sc') -> (proj,) <$> do -- cover f cs =<< do -- snd <$> fixTarget sc' let trees = map coverSplitTree results useds = map coverUsedClauses results psss = map coverMissingClauses results qsss = map coverPatterns results noex = map coverNoExactClauses results tree = SplitAt n $ zip projs trees return $ CoverResult tree (Set.unions useds) (concat psss) (concat qsss) (Set.unions noex) gatherEtaSplits :: Int -> SplitClause -> [NamedArg SplitPattern] -> [NamedArg SplitPattern] gatherEtaSplits n sc [] | n >= 0 = __IMPOSSIBLE__ -- we should have encountered the main -- split by now already | otherwise = [] gatherEtaSplits n sc (p:ps) = case namedArg p of VarP _ x | n == 0 -> case p' of -- this is the main split VarP _ _ -> p : gatherEtaSplits (-1) sc ps DotP _ _ -> __IMPOSSIBLE__ ConP _ _ qs -> qs ++ gatherEtaSplits (-1) sc ps LitP _ -> gatherEtaSplits (-1) sc ps ProjP{} -> __IMPOSSIBLE__ IApplyP{} -> __IMPOSSIBLE__ DefP _ _ qs -> qs ++ gatherEtaSplits (-1) sc ps -- __IMPOSSIBLE__ -- Andrea: maybe? | otherwise -> updateNamedArg (\ _ -> p') p : gatherEtaSplits (n-1) sc ps where p' = lookupS (scSubst sc) $ splitPatVarIndex x IApplyP{} -> updateNamedArg (applySubst (scSubst sc)) p : gatherEtaSplits (n-1) sc ps DotP _ _ -> p : gatherEtaSplits (n-1) sc ps -- count dot patterns ConP _ _ qs -> gatherEtaSplits n sc (qs ++ ps) DefP _ _ qs -> gatherEtaSplits n sc (qs ++ ps) LitP _ -> gatherEtaSplits n sc ps ProjP{} -> gatherEtaSplits n sc ps addEtaSplits :: Int -> [NamedArg SplitPattern] -> SplitTree -> SplitTree addEtaSplits k [] t = t addEtaSplits k (p:ps) t = case namedArg p of VarP _ _ -> addEtaSplits (k+1) ps t DotP _ _ -> addEtaSplits (k+1) ps t ConP c cpi qs -> SplitAt (p $> k) [(SplitCon (conName c) , addEtaSplits k (qs ++ ps) t)] LitP _ -> __IMPOSSIBLE__ ProjP{} -> __IMPOSSIBLE__ DefP{} -> __IMPOSSIBLE__ -- Andrea: maybe? IApplyP{} -> addEtaSplits (k+1) ps t etaRecordSplits :: Int -> [NamedArg SplitPattern] -> (SplitTag,SplitClause) -> SplitTree -> (SplitTag,SplitTree) etaRecordSplits n ps (q , sc) t = (q , addEtaSplits 0 (gatherEtaSplits n sc ps) t) -- | Append an hcomp clause to the clauses of a function. createMissingHCompClause :: QName -- ^ Function name. -> Arg Nat -- ^ index of hcomp pattern -> BlockingVar -- ^ Blocking var that lead to hcomp split. -> SplitClause -- ^ Clause before the hcomp split -> SplitClause -- ^ Clause to add. -> TCM Clause createMissingHCompClause f n x old_sc (SClause tel ps _sigma' cps (Just t)) = setCurrentRange f $ do reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "Trying to create right-hand side of type" <+> prettyTCM t reportSDoc "tc.cover.hcomp" 30 $ addContext tel $ text "ps = " <+> prettyTCMPatternList (fromSplitPatterns ps) reportSDoc "tc.cover.hcomp" 30 $ text "tel = " <+> prettyTCM tel io <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIOne iz <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIZero let cannotCreate doc t = do typeError . SplitError $ CannotCreateMissingClause f (tel,fromSplitPatterns ps) doc t let old_ps = patternsToElims $ fromSplitPatterns $ scPats old_sc old_t = fromJust $ scTarget old_sc old_tel = scTel old_sc -- old_tel = Γ(x:H)Δ -- Γ(x:H)Δ ⊢ old_t -- vs = iApplyVars old_ps -- [ α ⇒ b ] = [(i,f old_ps (i=0),f old_ps (i=1)) | i <- vs] -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ] -- Γ(x:H)Δ ⊢ f old_ps : old_t [ α ⇒ b ] -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢ rhs_we_define : (old_t[ α ⇒ b ])(x = hcomp φ u u0) -- Extra assumption: -- tel = Γ,φ,u,u0,Δ(x = hcomp φ u u0),Δ' -- ps = old_ps[x = hcomp φ u u0],ps' -- with Δ' and ps' introduced by fixTarget. -- So final clause will be: -- tel ⊢ ps ↦ rhs_we_define{wkS ..} ps' getLevel t = do s <- reduce $ getSort t case s of Type l -> pure (Level l) s -> do reportSDoc "tc.cover.hcomp" 20 $ text "getLevel, s = " <+> prettyTCM s typeError . GenericDocError =<< (text "The sort of" <+> prettyTCM t <+> text "should be of the form \"Set l\"") -- Γ ⊢ hdelta = (x : H)(δ : Δ) (gamma,hdelta@(ExtendTel hdom delta)) = splitTelescopeAt (size old_tel - (blockingVarNo x + 1)) old_tel -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢ (working_tel,_deltaEx) = splitTelescopeAt (size gamma + 3 + size delta) tel -- Γ,φ,u,u0,(x:H)(δ : Δ) ⊢ rhoS : Γ(x:H)(δ : Δ) rhoS = liftS (size hdelta) $ raiseS 3 vs = iApplyVars (scPats old_sc) -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ] = [(i,f old_ps (i=0),f old_ps (i=1)) | i <- vs] alphab <- forM vs $ \ i -> do let -- Γ(x:H)(δ : Δ) ⊢ tm = Def f old_ps -- TODO only reduce IApply _ _ (0/1), as to avoid termination problems (l,r) <- reduce (inplaceS i iz `applySubst` tm, inplaceS i io `applySubst` tm) return $ (var i, (l, r)) cl <- do (ty,rhs) <- addContext working_tel $ do -- Γ(x:H)Δ ⊢ g = f old_ps : old_t [ α ⇒ b ] -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ] -- Γ,φ,u,u0 ⊢ Δf = i.Δ[x = hfill φ u u0 i] -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ δ_fill = i.tFillTel (i. Δf[~i]) δ (~ i) : i.Δf[i] -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ old_t_fill = i.old_t[x = hfill φ u u0 i, δ_fill[i]] -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ comp (\ i. old_t_fill[i]) -- (\ i. [ φ ↦ g[x = hfill φ u u0 i,δ_fill[i]] = g[u i,δ_fill[i]] -- α ↦ b[x = hfill φ u u0 i,δ_fill[i]] -- ]) -- (g[x = u0,δ_fill[0]]) : old_t[x = hcomp φ u u0,δ] runNamesT [] $ do tPOr <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPOr tIMax <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIMax tIMin <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIMin tINeg <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinINeg tHComp <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinHComp tTrans <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinTrans extra_ps <- open $ patternsToElims $ fromSplitPatterns $ drop (length old_ps) ps let ineg j = pure tINeg <@> j imax i j = pure tIMax <@> i <@> j imin i j = pure tIMin <@> i <@> j trFillTel' a b c d = do m <- trFillTel <$> a <*> b <*> c <*> d x <- lift $ runExceptT m case x of Left bad_t -> cannotCreate "Cannot transport with type family:" bad_t Right args -> return args comp <- do let forward la bA r u = pure tTrans <#> (lam "i" $ \ i -> la <@> (i `imax` r)) <@> (lam "i" $ \ i -> bA <@> (i `imax` r)) <@> r <@> u return $ \ la bA phi u u0 -> pure tHComp <#> (la <@> pure io) <#> (bA <@> pure io) <#> phi <@> (lam "i" $ \ i -> ilam "o" $ \ o -> forward la bA i (u <@> i <..> o)) <@> forward la bA (pure iz) u0 let hcomp la bA phi u u0 = pure tHComp <#> la <#> bA <#> phi <@> u <@> u0 hfill la bA phi u u0 i = hcomp la bA (pure tIMax <@> phi <@> (pure tINeg <@> i)) (lam "j" $ \ j -> pure tPOr <#> la <@> phi <@> (pure tINeg <@> i) <#> (ilam "o" $ \ _ -> bA) <@> (ilam "o" $ \ o -> u <@> (pure tIMin <@> i <@> j) <..> o) <@> (ilam "o" $ \ _ -> u0) ) u0 -- Γ,φ,u,u0,(δ : Δ(x = hcomp φ u u0)) ⊢ hcompS : Γ(x:H)(δ : Δ) hcompS <- lift $ do hdom <- pure $ raise 3 hdom let [phi,u,u0] = map (pure . var) [2,1,0] htype = pure $ unEl . unDom $ hdom lvl = getLevel $ unDom hdom hc <- pure tHComp <#> lvl <#> htype <#> phi <@> u <@> u0 return $ liftS (size delta) $ hc `consS` raiseS 3 -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ raise 3+|Δ| hdom hdom <- pure $ raise (3+size delta) hdom htype <- open $ unEl . unDom $ hdom lvl <- open =<< (lift . getLevel $ unDom hdom) -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ [phi,u,u0] <- mapM (open . raise (size delta) . var) [2,1,0] -- Γ,x,Δ ⊢ f old_ps -- Γ ⊢ abstract hdelta (f old_ps) g <- open $ raise (3+size delta) $ abstract hdelta (Def f old_ps) old_t <- open $ raise (3+size delta) $ abstract hdelta (unArg old_t) let bapp a x = lazyAbsApp <$> a <*> x (delta_fill :: NamesT TCM (Abs Args)) <- (open =<<) $ do -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ x.Δ delta <- open $ raise (3+size delta) delta -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ i.Δ(x = hfill phi u u0 (~ i)) deltaf <- open =<< bind "i" (\ i -> (delta `bapp` hfill lvl htype phi u u0 (ineg i))) -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ Δ(x = hcomp phi u u0) = Δf[0] args <- (open =<<) $ teleArgs <$> (lazyAbsApp <$> deltaf <*> pure iz) bind "i" $ \ i -> addContext ("i" :: String) $ do -- for error messages. -- Γ,φ,u,u0,Δ(x = hcomp phi u u0),(i:I) ⊢ ... : Δ(x = hfill phi u u0 i) trFillTel' deltaf (pure iz) args (ineg i) let apply_delta_fill i f = apply <$> f <*> (delta_fill `bapp` i) call v i = apply_delta_fill i $ g <@> v ty <- do return $ \ i -> do v <- hfill lvl htype phi u u0 i hd <- old_t args <- delta_fill `bapp` i lift $ piApplyM hd $ [Arg (domInfo hdom) v] ++ args ty_level <- do t <- bind "i" ty s <- reduce $ getSort (absBody t) reportSDoc "tc.cover.hcomp" 20 $ text "ty_level, s = " <+> prettyTCM s case s of Type l -> open =<< (lam "i" $ \ _ -> pure $ Level l) _ -> cannotCreate "Cannot compose with type family:" =<< (liftTCM $ buildClosure t) let pOr_ty i phi psi u0 u1 = pure tPOr <#> (ty_level <@> i) <@> phi <@> psi <#> (ilam "o" $ \ _ -> unEl <$> ty i) <@> u0 <@> u1 alpha <- do vars <- mapM (open . applySubst hcompS . fst) alphab return $ foldr imax (pure iz) $ map (\ v -> v `imax` ineg v) vars -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢ b : (i : I) → [α] -> old_t[x = hfill φ u u0 i,δ_fill[i]] b <- do sides <- forM alphab $ \ (psi,(side0,side1)) -> do psi <- open $ hcompS `applySubst` psi [side0,side1] <- mapM (open . raise (3+size delta) . abstract hdelta) [side0,side1] return $ (ineg psi `imax` psi, \ i -> pOr_ty i (ineg psi) psi (ilam "o" $ \ _ -> apply_delta_fill i $ side0 <@> hfill lvl htype phi u u0 i) (ilam "o" $ \ _ -> apply_delta_fill i $ side1 <@> hfill lvl htype phi u u0 i)) let recurse [] i = __IMPOSSIBLE__ recurse [(psi,u)] i = u i recurse ((psi,u):xs) i = pOr_ty i psi (foldr imax (pure iz) (map fst xs)) (u i) (recurse xs i) return $ recurse sides ((,) <$> ty (pure io) <*>) $ do comp ty_level (lam "i" $ \ i -> unEl <$> ty i) (phi `imax` alpha) (lam "i" $ \ i -> let rhs = (ilam "o" $ \ o -> call (u <@> i <..> o) i) in if null alphab then rhs else pOr_ty i phi alpha rhs (b i) ) (call u0 (pure iz)) reportSDoc "tc.cover.hcomp" 20 $ text "old_tel =" <+> prettyTCM tel let n = size tel - (size gamma + 3 + size delta) reportSDoc "tc.cover.hcomp" 20 $ text "n =" <+> text (show n) (TelV deltaEx t,bs) <- telViewUpToPathBoundary' n ty rhs <- pure $ raise n rhs `applyE` teleElims deltaEx bs cxt <- getContextTelescope reportSDoc "tc.cover.hcomp" 30 $ text "cxt = " <+> prettyTCM cxt reportSDoc "tc.cover.hcomp" 30 $ text "tel = " <+> prettyTCM tel reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "t = " <+> prettyTCM t reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "rhs = " <+> prettyTCM rhs return $ Clause { clauseLHSRange = noRange , clauseFullRange = noRange , clauseTel = tel , namedClausePats = fromSplitPatterns ps , clauseBody = Just $ rhs , clauseType = Just $ defaultArg t , clauseCatchall = False , clauseUnreachable = Just False -- missing, thus, not unreachable } addClauses f [cl] -- Important: add at the end. return cl createMissingHCompClause _ _ _ _ (SClause _ _ _ _ Nothing) = __IMPOSSIBLE__ -- | Append a instance clause to the clauses of a function. inferMissingClause :: QName -- ^ Function name. -> SplitClause -- ^ Clause to add. Clause hiding (in 'clauseType') must be 'Instance'. -> TCM (Closure Clause) inferMissingClause f (SClause tel ps _ cps (Just t)) = setCurrentRange f $ do reportSDoc "tc.cover.infer" 20 $ addContext tel $ "Trying to infer right-hand side of type" <+> prettyTCM t cl <- addContext tel $ locallyTC eCheckpoints (const cps) $ checkpoint IdS $ do -- introduce a fresh checkpoint (_x, rhs) <- case getHiding t of Instance{} -> newInstanceMeta "" (unArg t) Hidden -> __IMPOSSIBLE__ NotHidden -> __IMPOSSIBLE__ buildClosure $ Clause { clauseLHSRange = noRange , clauseFullRange = noRange , clauseTel = tel , namedClausePats = fromSplitPatterns ps , clauseBody = Just rhs , clauseType = Just t , clauseCatchall = False , clauseUnreachable = Just False -- missing, thus, not unreachable } addClauses f [clValue cl] -- Important: add at the end. return cl inferMissingClause _ (SClause _ _ _ _ Nothing) = __IMPOSSIBLE__ splitStrategy :: BlockingVars -> Telescope -> TCM BlockingVars splitStrategy bs tel = return $ updateLast setBlockingVarOverlap xs -- Make sure we do not insists on precomputed coverage when -- we make our last try to split. -- Otherwise, we will not get a nice error message. where xs = bs {- KEEP! -- Andreas, 2012-10-13 -- The following split strategy which prefers all-constructor columns -- fails on test/fail/CoverStrategy xs = ys ++ zs (ys, zs) = partition allConstructors bs allConstructors :: BlockingVar -> Bool allConstructors = isJust . snd -} -- | Check that a type is a non-irrelevant datatype or a record with -- named constructor. Unless the 'Induction' argument is 'CoInductive' -- the data type must be inductive. isDatatype :: (MonadTCM tcm, MonadError SplitError tcm) => Induction -> Dom Type -> tcm (DataOrRecord, QName, [Arg Term], [Arg Term], [QName], Bool) isDatatype ind at = do let t = unDom at throw f = throwError . f =<< do liftTCM $ buildClosure t t' <- liftTCM $ reduce t mInterval <- liftTCM $ getBuiltinName' builtinInterval mIsOne <- liftTCM $ getBuiltinName' builtinIsOne case unEl t' of Def d [] | Just d == mInterval -> throw NotADatatype Def d [Apply phi] | Just d == mIsOne -> do xs <- liftTCM $ decomposeInterval =<< reduce (unArg phi) if null xs then return $ (IsData, d, [phi], [], [], False) else throw NotADatatype Def d es -> do let ~(Just args) = allApplyElims es def <- liftTCM $ theDef <$> getConstInfo d case def of Datatype{dataPars = np, dataCons = cs, dataInduction = i} | i == CoInductive && ind /= CoInductive -> throw CoinductiveDatatype | otherwise -> do let (ps, is) = splitAt np args return (IsData, d, ps, is, cs, not $ null (dataPathCons def)) Record{recPars = np, recConHead = con, recInduction = i} | i == Just CoInductive && ind /= CoInductive -> throw CoinductiveDatatype | otherwise -> return (IsRecord, d, args, [], [conName con], False) _ -> throw NotADatatype _ -> throw NotADatatype -- | Update the target type, add more patterns to split clause -- if target becomes a function type. -- Returns the domains of the function type (if any). fixTarget :: SplitClause -> TCM (Telescope, SplitClause) fixTarget sc@SClause{ scTel = sctel, scPats = ps, scSubst = sigma, scCheckpoints = cps, scTarget = target } = caseMaybe target (return (empty, sc)) $ \ a -> do reportSDoc "tc.cover.target" 20 $ sep [ "split clause telescope: " <+> prettyTCM sctel , "old patterns : " <+> do addContext sctel $ prettyTCMPatternList $ fromSplitPatterns ps ] reportSDoc "tc.cover.target" 60 $ sep [ "substitution : " <+> prettyTCM sigma ] reportSDoc "tc.cover.target" 30 $ sep [ "target type before substitution (variables may be wrong): " <+> do addContext sctel $ prettyTCM a ] (TelV tel b) <- telViewUpTo (-1) $ applySplitPSubst sigma $ unArg a reportSDoc "tc.cover.target" 15 $ sep [ "target type telescope (after substitution): " <+> do addContext sctel $ prettyTCM tel , "target type core (after substitution): " <+> do addContext sctel $ addContext tel $ prettyTCM b ] let n = size tel -- Andreas, 2016-10-04 issue #2236 -- Need to set origin to "Inserted" to avoid printing of hidden patterns. xs = map (mapArgInfo hiddenInserted) $ teleNamedArgs tel -- Compute new split clause sctel' = telFromList $ telToList (raise n sctel) ++ telToList tel -- Dot patterns in @ps@ need to be raised! (Issue 1298) ps' = applySubst (raiseS n) ps ++ xs newTarget = Just $ a $> b sc' = SClause { scTel = sctel' , scPats = ps' , scSubst = wkS n $ sigma -- Should be wkS instead of liftS since -- variables are only added to new tel. , scCheckpoints = applySubst (raiseS n) cps , scTarget = newTarget } -- Separate debug printing to find cause of crash (Issue 1374) reportSDoc "tc.cover.target" 30 $ sep [ "new split clause telescope : " <+> prettyTCM sctel' ] reportSDoc "tc.cover.target" 30 $ sep [ "new split clause patterns : " <+> do addContext sctel' $ prettyTCMPatternList $ fromSplitPatterns ps' ] reportSDoc "tc.cover.target" 60 $ sep [ "new split clause substitution: " <+> prettyTCM (scSubst sc') ] reportSDoc "tc.cover.target" 30 $ sep [ "new split clause target : " <+> do addContext sctel' $ prettyTCM $ fromJust newTarget ] reportSDoc "tc.cover.target" 20 $ sep [ "new split clause" , prettyTCM sc' ] return $ if n == 0 then (empty, sc { scTarget = newTarget }) else (tel, sc') -- Andreas, 2017-01-18, issue #819, set visible arguments to UserWritten. -- Otherwise, they will be printed as _. hiddenInserted :: ArgInfo -> ArgInfo hiddenInserted ai | visible ai = setOrigin UserWritten ai | otherwise = setOrigin Inserted ai computeHCompSplit :: Telescope -- ^ Telescope before split point. -> PatVarName -- ^ Name of pattern variable at split point. -> Telescope -- ^ Telescope after split point. -> QName -- ^ Name of datatype to split at. -> Args -- ^ Data type parameters. -> Args -- ^ Data type indices. -> Nat -- ^ Index of split variable. -> Telescope -- ^ Telescope for the patterns. -> [NamedArg SplitPattern] -- ^ Patterns before doing the split. -> Map CheckpointId Substitution -- ^ Current checkpoints -- -> QName -- ^ Constructor to fit into hole. -> CoverM (Maybe (SplitTag,SplitClause)) -- ^ New split clause if successful. computeHCompSplit delta1 n delta2 d pars ixs hix tel ps cps = do -- Get the type of the datatype -- Δ1 ⊢ dtype dsort <- liftTCM $ (parallelS (reverse $ map unArg pars) `applySubst`) . dataSort . theDef <$> getConstInfo d hCompName <- fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinHComp theHCompT <- defType <$> getConstInfo hCompName let dlvl = Level . (\ (Type s) -> s) $ dsort dterm = Def d [] `apply` (pars ++ ixs) -- Δ1 ⊢ gamma TelV gamma _ <- lift $ telView (theHCompT `piApply` [setHiding Hidden $ defaultArg $ dlvl , defaultArg $ dterm]) case (delta1 `abstract` gamma,IdS) of (delta1',rho0) -> do -- debugSubst "rho0" rho0 -- We have Δ₁' ⊢ ρ₀ : Δ₁Γ, so split it into the part for Δ₁ and the part for Γ let (rho1,rho2) = splitS (size gamma) $ toSplitPSubst rho0 -- Andreas, 2015-05-01 I guess it is fine to use no @conPType@ -- as the result of splitting is never used further down the pipeline. -- After splitting, Agda reloads the file. -- Andreas, 2017-09-03, issue #2729: remember that pattern was generated by case split. let -- cpi = noConPatternInfo{ conPRecord = Just PatOSplit } -- conp = ConP con cpi $ applySubst rho2 $ -- map (mapArgInfo hiddenInserted) $ tele2NamedArgs gamma0 gamma -- -- Andreas, 2016-09-08, issue #2166: use gamma0 for correct argument names defp = DefP PatOSystem hCompName . map (setOrigin Inserted) $ map (fmap unnamed) [setHiding Hidden $ defaultArg $ applySubst rho1 $ DotP PatOSystem $ dlvl ,setHiding Hidden $ defaultArg $ applySubst rho1 $ DotP PatOSystem $ dterm] ++ applySubst rho2 (teleNamedArgs gamma) -- rho0? -- Compute final context and substitution let rho3 = consS defp rho1 -- Δ₁' ⊢ ρ₃ : Δ₁(x:D) delta2' = applySplitPSubst rho3 delta2 -- Δ₂' = Δ₂ρ₃ delta' = delta1' `abstract` delta2' -- Δ' = Δ₁'Δ₂' rho = liftS (size delta2) rho3 -- Δ' ⊢ ρ : Δ₁(x:D)Δ₂ -- debugTel "delta'" delta' -- debugSubst "rho" rho -- debugPs tel ps -- Apply the substitution let ps' = applySubst rho ps -- debugPlugged delta' ps' let cps' = applySplitPSubst rho cps return $ Just . (SplitCon hCompName,) $ SClause delta' ps' rho cps' Nothing -- target fixed later -- | @computeNeighbourhood delta1 delta2 d pars ixs hix tel ps con@ -- -- @ -- delta1 Telescope before split point -- n Name of pattern variable at split point -- delta2 Telescope after split point -- d Name of datatype to split at -- pars Data type parameters -- ixs Data type indices -- hix Index of split variable -- tel Telescope for patterns ps -- ps Patterns before doing the split -- cps Current module parameter checkpoints -- con Constructor to fit into hole -- @ -- @dtype == d pars ixs@ computeNeighbourhood :: Telescope -- ^ Telescope before split point. -> PatVarName -- ^ Name of pattern variable at split point. -> Telescope -- ^ Telescope after split point. -> QName -- ^ Name of datatype to split at. -> Args -- ^ Data type parameters. -> Args -- ^ Data type indices. -> Nat -- ^ Index of split variable. -> Telescope -- ^ Telescope for the patterns. -> [NamedArg SplitPattern] -- ^ Patterns before doing the split. -> Map CheckpointId Substitution -- ^ Current checkpoints -> QName -- ^ Constructor to fit into hole. -> CoverM (Maybe SplitClause) -- ^ New split clause if successful. computeNeighbourhood delta1 n delta2 d pars ixs hix tel ps cps c = do -- Get the type of the datatype dtype <- liftTCM $ (`piApply` pars) . defType <$> getConstInfo d -- Get the real constructor name con <- liftTCM $ fromRight __IMPOSSIBLE__ <$> getConForm c con <- return $ con { conName = c } -- What if we restore the current name? -- Andreas, 2013-11-29 changes nothing! -- Get the type of the constructor ctype <- liftTCM $ defType <$> getConInfo con -- Lookup the type of the constructor at the given parameters (gamma0, cixs, boundary) <- do (TelV gamma0 (El _ d), boundary) <- liftTCM $ telViewPathBoundaryP (ctype `piApply` pars) let Def _ es = d Just cixs = allApplyElims es return (gamma0, cixs, boundary) -- Andreas, 2012-02-25 preserve name suggestion for recursive arguments -- of constructor let preserve (x, t@(El _ (Def d' _))) | d == d' = (n, t) preserve (x, t) = (x, t) gammal = map (fmap preserve) . telToList $ gamma0 gamma = telFromList gammal delta1Gamma = delta1 `abstract` gamma debugInit con ctype d pars ixs cixs delta1 delta2 gamma tel ps hix -- All variables are flexible let flex = allFlexVars delta1Gamma -- Unify constructor target and given type (in Δ₁Γ) let conIxs = drop (size pars) cixs givenIxs = raise (size gamma) ixs r <- unifyIndices delta1Gamma flex (raise (size gamma) dtype) conIxs givenIxs case r of NoUnify {} -> debugNoUnify $> Nothing DontKnow errs -> do debugCantSplit throwError $ UnificationStuck (conName con) (delta1 `abstract` gamma) conIxs givenIxs errs Unifies (delta1',rho0,_) -> do debugSubst "rho0" rho0 let rho0' = toSplitPSubst rho0 -- We have Δ₁' ⊢ ρ₀ : Δ₁Γ, so split it into the part for Δ₁ and the part for Γ let (rho1,rho2) = splitS (size gamma) $ rho0' -- Andreas, 2015-05-01 I guess it is fine to use no @conPType@ -- as the result of splitting is never used further down the pipeline. -- After splitting, Agda reloads the file. -- Andreas, 2017-09-03, issue #2729: remember that pattern was generated by case split. let cpi = noConPatternInfo{ conPRecord = Just PatOSplit } conp = ConP con cpi $ applySubst rho0' $ map (mapArgInfo hiddenInserted) $ telePatterns' (tele2NamedArgs gamma0) gamma boundary -- Andreas, 2016-09-08, issue #2166: use gamma0 for correct argument names -- Compute final context and substitution let rho3 = consS conp rho1 -- Δ₁' ⊢ ρ₃ : Δ₁(x:D) delta2' = applySplitPSubst rho3 delta2 -- Δ₂' = Δ₂ρ₃ delta' = delta1' `abstract` delta2' -- Δ' = Δ₁'Δ₂' rho = liftS (size delta2) rho3 -- Δ' ⊢ ρ : Δ₁(x:D)Δ₂ debugTel "delta'" delta' debugSubst "rho" rho debugPs tel ps -- Apply the substitution let ps' = applySubst rho ps debugPlugged delta' ps' let cps' = applySplitPSubst rho cps return $ Just $ SClause delta' ps' rho cps' Nothing -- target fixed later where debugInit con ctype d pars ixs cixs delta1 delta2 gamma tel ps hix = liftTCM $ reportSDoc "tc.cover.split.con" 20 $ vcat [ "computeNeighbourhood" , nest 2 $ vcat [ "context=" <+> (inTopContext . prettyTCM =<< getContextTelescope) , "con =" <+> prettyTCM con , "ctype =" <+> prettyTCM ctype , "ps =" <+> do inTopContext $ addContext tel $ prettyTCMPatternList $ fromSplitPatterns ps , "d =" <+> prettyTCM d , "pars =" <+> do prettyList $ map prettyTCM pars , "ixs =" <+> do addContext delta1 $ prettyList $ map prettyTCM ixs , "cixs =" <+> do addContext gamma $ prettyList $ map prettyTCM cixs , "delta1 =" <+> do inTopContext $ prettyTCM delta1 , "delta2 =" <+> do inTopContext $ addContext delta1 $ addContext gamma $ prettyTCM delta2 , "gamma =" <+> do inTopContext $ addContext delta1 $ prettyTCM gamma , "hix =" <+> text (show hix) ] ] debugNoUnify = liftTCM $ reportSLn "tc.cover.split.con" 20 " Constructor impossible!" debugCantSplit = liftTCM $ reportSLn "tc.cover.split.con" 20 " Bad split!" debugSubst s sub = liftTCM $ reportSDoc "tc.cover.split.con" 20 $ nest 2 $ vcat [ text (s ++ " =") <+> prettyTCM sub ] debugTel s tel = liftTCM $ reportSDoc "tc.cover.split.con" 20 $ nest 2 $ vcat [ text (s ++ " =") <+> prettyTCM tel ] debugPs tel ps = liftTCM $ reportSDoc "tc.cover.split.con" 20 $ inTopContext $ addContext tel $ nest 2 $ vcat [ "ps =" <+> prettyTCMPatternList (fromSplitPatterns ps) ] debugPlugged delta' ps' = do liftTCM $ reportSDoc "tc.cover.split.con" 20 $ inTopContext $ addContext delta' $ nest 2 $ vcat [ "ps' =" <+> do prettyTCMPatternList $ fromSplitPatterns ps' ] -- | Introduce trailing pattern variables via 'fixTarget'? data FixTarget = YesFixTarget | NoFixTarget deriving (Show) -- | Allow partial covering for split? data AllowPartialCover = YesAllowPartialCover -- To try to coverage-check incomplete splits. | NoAllowPartialCover -- Default. deriving (Eq, Show) -- | Entry point from @Interaction.MakeCase@. splitClauseWithAbsurd :: SplitClause -> Nat -> TCM (Either SplitError (Either SplitClause Covering)) splitClauseWithAbsurd c x = split' CheckEmpty Inductive NoAllowPartialCover NoFixTarget c (BlockingVar x [] [] True) -- Andreas, 2016-05-03, issue 1950: -- Do not introduce trailing pattern vars after split, -- because this does not work for with-clauses. -- | Entry point from @TypeChecking.Empty@ and @Interaction.BasicOps@. -- @splitLast CoInductive@ is used in the @refine@ tactics. splitLast :: Induction -> Telescope -> [NamedArg DeBruijnPattern] -> TCM (Either SplitError Covering) splitLast ind tel ps = split ind NoAllowPartialCover sc (BlockingVar 0 [] [] True) where sc = SClause tel (toSplitPatterns ps) empty empty Nothing -- | @split ind splitClause x = return res@ -- splits @splitClause@ at pattern var @x@ (de Bruijn index). -- -- Possible results @res@ are: -- -- 1. @Left err@: -- Splitting failed. -- -- 2. @Right covering@: -- A covering set of split clauses, one for each valid constructor. -- This could be the empty set (denoting an absurd clause). split :: Induction -- ^ Coinductive constructors are allowed if this argument is -- 'CoInductive'. -> AllowPartialCover -- ^ Don't fail if computed 'Covering' does not cover all constructors. -> SplitClause -> BlockingVar -> TCM (Either SplitError Covering) split ind allowPartialCover sc x = fmap blendInAbsurdClause <$> split' NoCheckEmpty ind allowPartialCover YesFixTarget sc x where n = lookupPatternVar sc $ blockingVarNo x blendInAbsurdClause :: Either SplitClause Covering -> Covering blendInAbsurdClause = fromRight (const $ Covering n []) -- | Convert a de Bruijn index relative to the clause telescope to a de Bruijn -- level. The result should be the argument position (counted from left, -- starting with 0) to split at (dot patterns included!). lookupPatternVar :: SplitClause -> Int -> Arg Nat lookupPatternVar SClause{ scTel = tel, scPats = pats } x = arg $> if n < 0 then __IMPOSSIBLE__ else n where n = if k < 0 then __IMPOSSIBLE__ else fromMaybe __IMPOSSIBLE__ $ permPicks perm !!! k perm = fromMaybe __IMPOSSIBLE__ $ dbPatPerm $ fromSplitPatterns pats k = size tel - x - 1 arg = indexWithDefault __IMPOSSIBLE__ (telVars (size tel) tel) k data CheckEmpty = CheckEmpty | NoCheckEmpty -- | @split' ind pc ft splitClause x = return res@ -- splits @splitClause@ at pattern var @x@ (de Bruijn index). -- -- Possible results @res@ are: -- -- 1. @Left err@: -- Splitting failed. -- -- 2. @Right (Left splitClause')@: -- Absurd clause (type of @x@ has 0 valid constructors). -- -- 3. @Right (Right covering)@: -- A covering set of split clauses, one for each valid constructor. split' :: CheckEmpty -- ^ Use isEmptyType to check whether the type of the variable to -- split on is empty. This switch is necessary to break the cycle -- between split' and isEmptyType. -> Induction -- ^ Coinductive constructors are allowed if this argument is -- 'CoInductive'. -> AllowPartialCover -- ^ Don't fail if computed 'Covering' does not cover all constructors. -> FixTarget -- ^ If 'YesFixTarget', introduce new trailing variable patterns via -- 'fixTarget'. -> SplitClause -> BlockingVar -> TCM (Either SplitError (Either SplitClause Covering)) split' checkEmpty ind allowPartialCover fixtarget sc@(SClause tel ps _ cps target) (BlockingVar x pcons' plits overlap) = liftTCM $ runExceptT $ do debugInit tel x ps cps -- Split the telescope at the variable -- t = type of the variable, Δ₁ ⊢ t (n, t, delta1, delta2) <- do let (tel1, dom : tel2) = splitAt (size tel - x - 1) $ telToList tel return (fst $ unDom dom, snd <$> dom, telFromList tel1, telFromList tel2) -- Compute the neighbourhoods for the constructors let computeNeighborhoods = do -- Check that t is a datatype or a record -- Andreas, 2010-09-21, isDatatype now directly throws an exception if it fails -- cons = constructors of this datatype (dr, d, pars, ixs, cons', isHIT) <- inContextOfT $ isDatatype ind t cons <- case checkEmpty of CheckEmpty -> ifM (liftTCM $ inContextOfT $ isEmptyType $ unDom t) (pure []) (pure cons') NoCheckEmpty -> pure cons' mns <- forM cons $ \ con -> fmap (SplitCon con,) <$> computeNeighbourhood delta1 n delta2 d pars ixs x tel ps cps con hcompsc <- if isHIT then case fixtarget of YesFixTarget -> computeHCompSplit delta1 n delta2 d pars ixs x tel ps cps; _ -> return Nothing else return Nothing return $ (dr, catMaybes (mns ++ [hcompsc])) computeLitNeighborhoods = do typeOk <- liftTCM $ do t' <- litType $ headWithDefault {-'-} __IMPOSSIBLE__ plits liftTCM $ dontAssignMetas $ tryConversion $ equalType (unDom t) t' unless typeOk $ throwError . NotADatatype =<< do liftTCM $ buildClosure (unDom t) ns <- forM plits $ \lit -> do let delta2' = subst 0 (Lit lit) delta2 delta' = delta1 `abstract` delta2' rho = liftS x $ consS (LitP lit) idS ps' = applySubst rho ps cps' = applySplitPSubst rho cps return (SplitLit lit , SClause delta' ps' rho cps' Nothing) ca <- do let delta' = tel -- telescope is unchanged for catchall branch varp = VarP PatOSplit $ SplitPatVar { splitPatVarName = underscore , splitPatVarIndex = 0 , splitExcludedLits = plits } rho = liftS x $ consS varp $ raiseS 1 ps' = applySubst rho ps return (SplitCatchall , SClause delta' ps' rho cps Nothing) return (IsData , ns ++ [ ca ]) (dr, ns) <- if null pcons' && not (null plits) then computeLitNeighborhoods else computeNeighborhoods ns <- case fixtarget of NoFixTarget -> return ns YesFixTarget -> lift $ forM ns $ \(con,sc) -> (con,) . snd <$> fixTarget sc{ scTarget = target } -- Andreas, 2018-10-27, issue #3324; use isPropM. -- Need to reduce sort to decide on Prop. -- Cannot split if domain is a Prop but target is relevant. propArrowRel <- isPropM t `and2M` maybe (return True) (not <.> isPropM) target mHCompName <- getPrimitiveName' builtinHComp case ns of [] -> do let absurdp = VarP PatOAbsurd $ SplitPatVar underscore 0 [] rho = liftS x $ consS absurdp $ raiseS 1 ps' = applySubst rho ps return $ Left $ SClause { scTel = tel , scPats = ps' , scSubst = __IMPOSSIBLE__ -- not used , scCheckpoints = __IMPOSSIBLE__ -- not used , scTarget = Nothing } -- Jesper, 2018-05-24: If the datatype is in Prop we can -- only do empty splits, unless the target is in Prop too. (_ : _) | dr == IsData && propArrowRel -> throwError . IrrelevantDatatype =<< do liftTCM $ inContextOfT $ buildClosure (unDom t) -- Andreas, 2018-10-17: If more than one constructor matches, we cannot erase. (_ : _ : _) | not (usableQuantity t) -> throwError . ErasedDatatype =<< do liftTCM $ inContextOfT $ buildClosure (unDom t) _ -> do -- Andreas, 2012-10-10 fail if precomputed constructor set does not cover -- all the data type constructors -- Andreas, 2017-10-08 ... unless partial covering is explicitly allowed. let ptags = map (SplitCon . conName) pcons' ++ map SplitLit plits -- clauses for hcomp will be automatically generated. let inferred_tags = maybe Set.empty (Set.singleton . SplitCon) mHCompName let all_tags = Set.fromList ptags `Set.union` inferred_tags when (allowPartialCover == NoAllowPartialCover && overlap == False) $ for_ ns $ \(tag, sc) -> do when (not $ tag `Set.member` all_tags) $ do isImpossibleClause <- liftTCM $ isEmptyTel $ scTel sc unless isImpossibleClause $ do liftTCM $ reportSDoc "tc.cover" 10 $ vcat [ text "Missing case for" <+> prettyTCM tag , nest 2 $ prettyTCM sc ] throwError (GenericSplitError "precomputed set of constructors does not cover all cases") liftTCM $ checkSortOfSplitVar dr (unDom t) target return $ Right $ Covering (lookupPatternVar sc x) ns where inContextOfT, inContextOfDelta2 :: (MonadTCM tcm, MonadDebug tcm) => tcm a -> tcm a inContextOfT = addContext tel . escapeContext (x + 1) inContextOfDelta2 = addContext tel . escapeContext x -- Debug printing debugInit tel x ps cps = liftTCM $ inTopContext $ do reportSDoc "tc.cover.top" 10 $ vcat [ "TypeChecking.Coverage.split': split" , nest 2 $ vcat [ "tel =" <+> prettyTCM tel , "x =" <+> prettyTCM x , "ps =" <+> do addContext tel $ prettyTCMPatternList $ fromSplitPatterns ps , "cps =" <+> prettyTCM cps ] ] debugHoleAndType delta1 delta2 s ps t = liftTCM $ reportSDoc "tc.cover.top" 10 $ nest 2 $ vcat $ [ "p =" <+> text (patVarNameToString s) , "ps =" <+> prettyTCMPatternList ps , "delta1 =" <+> prettyTCM delta1 , "delta2 =" <+> inContextOfDelta2 (prettyTCM delta2) , "t =" <+> inContextOfT (prettyTCM t) ] -- | splitResult for MakeCase, tries to introduce IApply or ProjP copatterns splitResult :: QName -> SplitClause -> TCM (Either SplitError [SplitClause]) splitResult f sc = do caseMaybeM (splitResultPath f sc) ((fmap . fmap) splitClauses $ splitResultRecord f sc) (return . Right . (:[])) -- | Tries to split the result to introduce an IApply pattern. splitResultPath :: QName -> SplitClause -> TCM (Maybe SplitClause) splitResultPath f sc@(SClause tel ps _ _ target) = do caseMaybe target (return Nothing) $ \ t -> do caseMaybeM (isPath (unArg t)) (return Nothing) $ \ _ -> do (TelV i b, boundary) <- telViewUpToPathBoundary' 1 (unArg t) let tel' = abstract tel i rho = raiseS 1 ps' = applySubst rho (scPats sc) ++ telePatterns i boundary cps' = applySubst rho (scCheckpoints sc) target' = Just $ b <$ t return . Just $ SClause tel' ps' idS cps' target' -- | @splitResultRecord f sc = return res@ -- -- If the target type of @sc@ is a record type, a covering set of -- split clauses is returned (@sc@ extended by all valid projection patterns), -- otherwise @res == Left _@. -- Note that the empty set of split clauses is returned if the record has no fields. splitResultRecord :: QName -> SplitClause -> TCM (Either SplitError Covering) splitResultRecord f sc@(SClause tel ps _ _ target) = do reportSDoc "tc.cover.split" 10 $ vcat [ "splitting result:" , nest 2 $ "f =" <+> prettyTCM f , nest 2 $ "target =" <+> (addContext tel $ maybe empty prettyTCM target) ] -- if we want to split projections, but have no target type, we give up let failure = return . Left caseMaybe target (failure CosplitNoTarget) $ \ t -> do isR <- addContext tel $ isRecordType $ unArg t case isR of Just (_r, vs, Record{ recFields = fs }) -> do reportSDoc "tc.cover" 20 $ sep [ text $ "we are of record type _r = " ++ prettyShow _r , text "applied to parameters vs = " <+> (addContext tel $ prettyTCM vs) , text $ "and have fields fs = " ++ prettyShow fs ] -- Andreas, 2018-06-09, issue #2170, we always have irrelevant projections -- available on the lhs. -- -- Andreas, 2018-03-19, issue #2971, check that we have a "strong" record type, -- -- i.e., with all the projections. Otherwise, we may not split. -- ifNotM (strongRecord fs) (failure CosplitIrrelevantProjections) $ {-else-} do let es = patternsToElims $ fromSplitPatterns ps -- Note: module parameters are part of ps let self = defaultArg $ Def f [] `applyE` es pargs = vs ++ [self] reportSDoc "tc.cover" 20 $ sep [ text "we are self = " <+> (addContext tel $ prettyTCM $ unArg self) ] let n = defaultArg $ permRange $ fromMaybe __IMPOSSIBLE__ $ dbPatPerm $ fromSplitPatterns ps -- Andreas & James, 2013-11-19 includes the dot patterns! -- See test/succeed/CopatternsAndDotPatterns.agda for a case with dot patterns -- and copatterns which fails for @n = size tel@ with a broken case tree. -- Andreas, 2016-07-22 read the style of projections from the user's lips projOrigin <- ifM (optPostfixProjections <$> pragmaOptions) (return ProjPostfix) (return ProjPrefix) Right . Covering n <$> do forM fs $ \ proj -> do -- compute the new target dType <- defType <$> do getConstInfo $ unArg proj -- WRONG: typeOfConst $ unArg proj let -- type of projection instantiated at self target' = Just $ proj $> dType `piApply` pargs -- Always visible (#2287) projArg = fmap (Named Nothing . ProjP projOrigin) $ setHiding NotHidden proj sc' = sc { scPats = scPats sc ++ [projArg] , scSubst = idS , scTarget = target' } return (SplitCon (unArg proj), sc') _ -> addContext tel $ do buildClosure (unArg t) >>= failure . CosplitNoRecordType -- Andreas, 2018-06-09, issue #2170: splitting with irrelevant fields is always fine! -- where -- -- A record type is strong if it has all the projections. -- -- This is the case if --irrelevant-projections or no field is irrelevant. -- -- TODO: what about shape irrelevance? -- strongRecord :: [Arg QName] -> TCM Bool -- strongRecord fs = (optIrrelevantProjections <$> pragmaOptions) `or2M` -- (return $ not $ any isIrrelevant fs) -- * Boring instances -- | For debugging only. instance PrettyTCM SplitClause where prettyTCM (SClause tel pats sigma cps target) = sep [ "SplitClause" , nest 2 $ vcat [ "tel =" <+> prettyTCM tel , "pats =" <+> sep (map (prettyTCM . namedArg) pats) , "subst =" <+> prettyTCM sigma , "checkpoints =" <+> prettyTCM cps , "target =" <+> do caseMaybe target empty $ \ t -> do addContext tel $ prettyTCM t -- Triggers crash (see Issue 1374). -- , "subst target = " <+> do -- caseMaybe target empty $ \ t -> do -- addContext tel $ prettyTCM $ applySubst sigma t ] ]