Agda-2.8.0.2: src/full/Agda/TypeChecking/Positivity.hs
{-# LANGUAGE NondecreasingIndentation #-}
-- | Check that a datatype is strictly positive.
module Agda.TypeChecking.Positivity where
import Prelude hiding ( null, (!!) )
import Control.Applicative hiding (empty)
import Control.DeepSeq
import Control.Monad.Reader ( MonadReader(..), asks, ReaderT, runReaderT )
import Data.Either
import qualified Data.Foldable as Fold
import Data.Function (on)
import Data.Graph (SCC(..))
import Data.IntMap (IntMap)
import qualified Data.IntMap as IntMap
import qualified Data.List as List
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Sequence (Seq)
import qualified Data.Sequence as DS
import Data.Set (Set)
import qualified Data.Set as Set
import Data.Strict.These
import Debug.Trace
import Agda.Interaction.Options.Base ( optPolarity )
import Agda.Syntax.Common
import qualified Agda.Syntax.Info as Info
import Agda.Syntax.Internal
import Agda.Syntax.Internal.Pattern
import Agda.Syntax.Position (HasRange(..), noRange)
import Agda.TypeChecking.Datatypes ( isDataOrRecordType )
import Agda.TypeChecking.Functions
import Agda.TypeChecking.Monad
import Agda.TypeChecking.Patterns.Match ( properlyMatching )
import Agda.TypeChecking.Positivity.Occurrence
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Records
import Agda.TypeChecking.Reduce
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import Agda.TypeChecking.Warnings
import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
import Agda.Utils.Function (applyUnless)
import Agda.Utils.Functor
import Agda.Utils.List
import qualified Agda.Utils.List1 as List1
import Agda.Utils.Maybe
import Agda.Utils.Monad
import Agda.Utils.Null
import qualified Agda.Syntax.Common.Pretty as P
import Agda.Syntax.Common.Pretty (Pretty, prettyShow)
import Agda.Utils.SemiRing
import Agda.Utils.Singleton
import Agda.Utils.Size
import Agda.Utils.Impossible
type Graph n e = Graph.Graph n e
-- | Check that the datatypes in the mutual block containing the given
-- declarations are strictly positive.
--
-- Find polarity of datatypes parameters and indices.
--
-- Also add information about positivity and recursivity of records
-- to the signature.
--
checkStrictlyPositive :: Info.MutualInfo -> Set QName -> TCM ()
checkStrictlyPositive mi qset = do
-- compute the occurrence graph for qs
let qs = Set.toList qset
reportSDoc "tc.pos.tick" 100 $ "positivity of" <+> prettyTCM qs
g <- buildOccurrenceGraph qset
let (gstar, sccs) =
Graph.gaussJordanFloydWarshallMcNaughtonYamada $ fmap occ g
reportSDoc "tc.pos.tick" 100 $ "constructed graph"
reportSLn "tc.pos.graph" 5 $ "Positivity graph: N=" ++ show (size $ Graph.nodes g) ++
" E=" ++ show (length $ Graph.edges g)
reportSDoc "tc.pos.graph" 10 $ vcat
[ "positivity graph for" <+> fsep (map prettyTCM qs)
, nest 2 $ prettyTCM g
]
reportSLn "tc.pos.graph" 5 $
"Positivity graph (completed): E=" ++ show (length $ Graph.edges gstar)
reportSDoc "tc.pos.graph" 50 $ vcat
[ "transitive closure of positivity graph for" <+>
prettyTCM qs
, nest 2 $ prettyTCM gstar
]
-- remember argument occurrences for qs in the signature
setArgOccs qset qs gstar
reportSDoc "tc.pos.tick" 100 $ "set args"
-- check positivity for all strongly connected components of the graph for qs
reportSDoc "tc.pos.graph.sccs" 10 $ do
let (triv, others) = partitionEithers $ for sccs $ \case
AcyclicSCC v -> Left v
CyclicSCC vs -> Right vs
sep [ text $ show (length triv) ++ " trivial sccs"
, text $ show (length others) ++ " non-trivial sccs with lengths " ++
show (map length others)
]
reportSLn "tc.pos.graph.sccs" 15 $
" sccs = " ++ prettyShow [ scc | CyclicSCC scc <- sccs ]
-- #7133: Note that the graph doesn't necessarily contain all of qs in the case where there are no
-- occurrences of a name, but we still need to setMutual for them.
let sccMap = Map.unions [ case scc of
AcyclicSCC (DefNode q) -> Map.singleton q []
AcyclicSCC ArgNode{} -> mempty
CyclicSCC scc -> Map.fromList [ (q, qs) | q <- qs ]
where qs = [ q | DefNode q <- scc ]
| scc <- sccs ]
inAbstractMode $ forM_ qs $ \ q ->
whenM (isNothing <$> getMutual q) $ do
let qs = fromMaybe [] $ Map.lookup q sccMap
reportSLn "tc.pos.mutual" 10 $ "setting " ++ prettyShow q ++ " to " ++
if | null qs -> "non-recursive"
| length qs == 1 -> "recursive"
| otherwise -> "mutually recursive"
setMutual q qs
mapM_ (checkPos g gstar) qs
reportSDoc "tc.pos.tick" 100 $ "checked positivity"
where
checkPos :: Graph Node (Edge OccursWhere) ->
Graph Node Occurrence ->
QName -> TCM ()
checkPos g gstar q = inConcreteOrAbstractMode q $ \ def -> do
-- we check positivity only for data or record definitions
whenJust (isDatatype def) $ \ dr -> do
reportSDoc "tc.pos.check" 10 $ "Checking positivity of" <+> prettyTCM q
let loop :: Maybe Occurrence
loop = Graph.lookup (DefNode q) (DefNode q) gstar
g' :: Graph Node (Edge (Seq OccursWhere))
g' = fmap (fmap DS.singleton) g
-- Note the property
-- Internal.Utils.Graph.AdjacencyMap.Unidirectional.prop_productOfEdgesInBoundedWalk,
-- which relates productOfEdgesInBoundedWalk to
-- gaussJordanFloydWarshallMcNaughtonYamada.
reason bound =
case productOfEdgesInBoundedWalk
occ g' (DefNode q) (DefNode q) bound of
Just (Edge _ how) -> how
Nothing -> __IMPOSSIBLE__
how :: String -> Occurrence -> TCM Doc
how msg bound = fsep $
[prettyTCM q] ++ pwords "is" ++
pwords (msg ++ ", because it occurs") ++
[prettyTCM (reason bound)]
-- if we have a negative loop, raise error
-- ASR (23 December 2015). We don't raise a strictly positive
-- error if the NO_POSITIVITY_CHECK pragma was set on in the
-- mutual block. See Issue 1614.
when (Info.mutualPositivityCheck mi == YesPositivityCheck) $
whenM positivityCheckEnabled $
case loop of
Just o | o <= JustPos ->
warning $ NotStrictlyPositive q (reason JustPos)
_ -> return ()
-- if we find an unguarded record, mark it as such
case dr of
IsData -> return ()
IsRecord pat -> case loop of
Just o | o <= StrictPos -> do
reportSDoc "tc.pos.record" 5 $ how "not guarded" StrictPos
unguardedRecord q pat
checkInduction q
-- otherwise, if the record is recursive, mark it as well
Just o | o <= GuardPos -> do
reportSDoc "tc.pos.record" 5 $ how "recursive" GuardPos
recursiveRecord q
checkInduction q
-- If the record is not recursive, switch on eta
-- unless it is coinductive or a no-eta-equality record.
Nothing -> do
reportSDoc "tc.pos.record" 10 $
"record type " <+> prettyTCM q <+>
"is not recursive"
nonRecursiveRecord q
_ -> return ()
checkInduction :: QName -> TCM ()
checkInduction q =
-- ASR (01 January 2016). We don't raise this error if the
-- NO_POSITIVITY_CHECK pragma was set on in the record. See
-- Issue 1760.
when (Info.mutualPositivityCheck mi == YesPositivityCheck) $
whenM positivityCheckEnabled $ do
-- Check whether the recursive record has been declared as
-- 'Inductive' or 'Coinductive'. Otherwise, error.
unlessM (isJust . recInduction . theDef <$> getConstInfo q) $
setCurrentRange (nameBindingSite $ qnameName q) $
typeError $ RecursiveRecordNeedsInductivity q
occ (Edge o _) = o
isDatatype :: Definition -> Maybe DataOrRecord
isDatatype def = do
case theDef def of
Datatype{dataClause = Nothing} -> Just IsData
Record {recClause = Nothing, recPatternMatching } -> Just $ IsRecord recPatternMatching
_ -> Nothing
-- Set the polarity of the arguments to a couple of definitions
setArgOccs :: Set QName -> [QName] -> Graph Node Occurrence -> TCM ()
setArgOccs qset qs g = do
-- Andreas, 2018-05-11, issue #3049: we need to be pessimistic about
-- argument polarity beyond the formal arity of the function.
--
-- -- Compute a map from each name in q to the maximal argument index
-- let maxs = Map.fromListWith max
-- [ (q, i) | ArgNode q i <- Set.toList $ Graph.nodes g, q `Set.member` qset ]
forM_ qs $ \ q -> inConcreteOrAbstractMode q $ \ def -> when (hasDefinition $ theDef def) $ do
reportSDoc "tc.pos.args" 10 $ "checking args of" <+> prettyTCM q
n <- getDefArity def
-- If there is no outgoing edge @ArgNode q i@, all @n@ arguments are @Unused@.
-- Otherwise, we obtain the occurrences from the Graph.
let findOcc i = fromMaybe Unused $ Graph.lookup (ArgNode q i) (DefNode q) g
args = -- caseMaybe (Map.lookup q maxs) (replicate n Unused) $ \ m ->
map findOcc [0 .. n-1] -- [0 .. max m (n - 1)] -- triggers issue #3049
reportSDoc "tc.pos.args" 10 $ sep
[ "args of" <+> prettyTCM q <+> "="
, nest 2 $ prettyList $ map prettyTCM args
]
-- The list args can take a long time to compute, but contains
-- small elements, and is stored in the interface (right?), so
-- it is computed deep-strictly.
modifyArgOccurrences q (mergeOccs $!! args)
where
mergeOccs :: [Occurrence] -> [Occurrence] -> [Occurrence]
mergeOccs poccs toccs =
-- Lucas, 2022-12-01:
-- `poccs` are the occurences computed by the positivity-checker
-- `toccs` are the occurences/polarities explicitely given by the user
-- (and enforced through type-checking)
-- We consider the polarities explicitely given (toccs) to take priority over the ones
-- found out by the positivity checker.
-- Note: Alas, this is hard to enforce given that non-annotated variables are
-- always annotated with Mixed polarity. If the annotated polarity is Mixed,
-- for now we always rely on the result from the positivity analysis.
align poccs toccs <&> mergeThese (\a b -> if b == Mixed then a else b)
-- Andreas, 2018-11-23, issue #3404
-- Only assign argument occurrences to things which have a definition.
-- Things without a definition would be judged "constant" in all arguments,
-- since no occurrence could possibly be found, naturally.
hasDefinition :: Defn -> Bool
hasDefinition = \case
Axiom{} -> False
DataOrRecSig{} -> False
GeneralizableVar{} -> False
AbstractDefn{} -> False
Primitive{} -> False
PrimitiveSort{} -> False
Constructor{} -> False
Function{} -> True
Datatype{} -> True
Record{} -> True
getDefArity :: Definition -> TCM Int
getDefArity def = do
TelV tel _ <- telView (defType def)
return $ size tel - projectionArgs def
-- Computing occurrences --------------------------------------------------
data Item = AnArg Nat [Occurrence]
| ADef QName
deriving (Eq, Ord, Show)
instance HasRange Item where
getRange (AnArg _ _) = noRange
getRange (ADef qn) = getRange qn
instance Pretty Item where
prettyPrec p (AnArg i t) = P.mparens (p > 9) $ "AnArg" P.<+> P.pretty i P.<+> P.pretty t
prettyPrec p (ADef qn) = P.mparens (p > 9) $ "ADef" P.<+> P.pretty qn
type Occurrences = Map Item [OccursWhere]
-- | Used to build 'Occurrences' and occurrence graphs.
data OccurrencesBuilder
= Concat [OccurrencesBuilder]
| OccursAs Where OccurrencesBuilder
| OccursHere Item
| OnlyVarsUpTo Nat OccurrencesBuilder
-- ^ @OnlyVarsUpTo n occs@ discards occurrences of de Bruijn index
-- @>= n@.
-- | Used to build 'Occurrences' and occurrence graphs.
data OccurrencesBuilder'
= Concat' [OccurrencesBuilder']
| OccursAs' Where OccurrencesBuilder'
| OccursHere' Item
-- | The semigroup laws only hold up to flattening of 'Concat'.
instance Semigroup OccurrencesBuilder where
occs1 <> occs2 = Concat [occs1, occs2]
-- | The monoid laws only hold up to flattening of 'Concat'.
instance Monoid OccurrencesBuilder where
mempty = Concat []
mappend = (<>)
mconcat = Concat
-- | Removes 'OnlyVarsUpTo' entries.
preprocess :: OccurrencesBuilder -> OccurrencesBuilder'
preprocess ob = case pp Nothing ob of
Nothing -> Concat' []
Just ob -> ob
where
pp :: Maybe Nat -- Variables larger than or equal to this number, if any,
-- are not retained.
-> OccurrencesBuilder
-> Maybe OccurrencesBuilder'
pp !m = \case
Concat obs -> case mapMaybe (pp m) obs of
[] -> Nothing
obs -> return (Concat' obs)
OccursAs w ob -> OccursAs' w <$> pp m ob
OnlyVarsUpTo n ob -> pp (Just $! maybe n (min n) m) ob
OccursHere i -> do
guard keep
return (OccursHere' i)
where
keep = case (m, i) of
(Nothing, _) -> True
(_, ADef _) -> True
(Just m, AnArg i _) -> i < m
-- | An interpreter for 'OccurrencesBuilder'.
--
-- WARNING: There can be lots of sharing between the generated
-- 'OccursWhere' entries. Traversing all of these entries could be
-- expensive. (See 'computeEdges' for an example.)
flatten :: OccurrencesBuilder -> Map Item Integer
flatten =
Map.fromListWith (+) .
flip flatten' [] .
preprocess
where
flatten'
:: OccurrencesBuilder'
-> [(Item, Integer)]
-> [(Item, Integer)]
flatten' (Concat' obs) = foldr (\occs f -> flatten' occs . f) id obs
flatten' (OccursAs' _ ob) = flatten' ob
flatten' (OccursHere' i) = ((i, 1) :)
-- | Context for computing occurrences.
data OccEnv = OccEnv
{ vars :: [Maybe Item]
-- ^ Items corresponding to the free variables.
--
-- Potential invariant: It seems as if the list has the form
-- @'genericReplicate' n 'Nothing' ++ 'map' ('Just' . 'AnArg') is@,
-- for some @n@ and @is@, where @is@ is decreasing
-- (non-strictly).
, inf :: Maybe QName
-- ^ Name for ∞ builtin.
}
-- | Monad for computing occurrences.
type OccM = ReaderT OccEnv ReduceM
instance (Semigroup a, Monoid a) => Monoid (OccM a) where
mempty = return mempty
mappend = (<>)
mconcat = mconcat <.> sequence
withExtendedOccEnv :: Maybe Item -> OccM a -> OccM a
withExtendedOccEnv i = withExtendedOccEnv' [i]
withExtendedOccEnv' :: [Maybe Item] -> OccM a -> OccM a
withExtendedOccEnv' is = local $ \ e -> e { vars = is ++ vars e }
-- | Running the monad
getOccurrences
:: (Show a, PrettyTCM a, ComputeOccurrences a)
=> [Maybe Item] -- ^ Extension of the 'OccEnv', usually a local variable context.
-> a
-> TCM OccurrencesBuilder
getOccurrences vars a = do
reportSDoc "tc.pos.occ" 70 $ "computing occurrences in " <+> text (show a)
reportSDoc "tc.pos.occ" 20 $ "computing occurrences in " <+> prettyTCM a
reportSDoc "tc.pos.var" 20 $ "variables in context: " <+> pretty vars
env <- OccEnv vars . fmap nameOfInf <$> coinductionKit
runReduceM $ runReaderT (occurrences a) env
class ComputeOccurrences a where
occurrences :: a -> OccM OccurrencesBuilder
default occurrences :: (Foldable t, ComputeOccurrences b, t b ~ a) => a -> OccM OccurrencesBuilder
occurrences = foldMap occurrences
instance ComputeOccurrences Clause where
occurrences cl = do
let ps = namedClausePats cl
items = IntMap.elems $ patItems ps -- sorted from low to high DBI
-- TODO #3733: handle hcomp/transp clauses properly
if hasDefP ps then return mempty else do
argOccs <- mapMaybeM matching $ zip [0..] ps
(Concat argOccs <>) <$> do
withExtendedOccEnv' items $
occurrences $ clauseBody cl
where
matching :: (Int, NamedArg (Pattern' a)) -> OccM (Maybe OccurrencesBuilder)
matching (i, p) = do
properlyMatching (namedThing $ unArg p) >>= \case
True -> return $ Just $ OccursAs Matched $ OccursHere $ AnArg i []
False -> return Nothing
-- @patItems ps@ creates a map from the pattern variables of @ps@
-- to the index of the argument they are bound in.
patItems ps = mconcat $ zipWith patItem [0..] ps
-- @patItem i p@ assigns index @i@ to each pattern variable in @p@
patItem :: Int -> NamedArg DeBruijnPattern -> IntMap (Maybe Item)
patItem i p = Fold.foldMap makeEntry ixs
where
ixs = map dbPatVarIndex $ lefts $ map unArg $ patternVars $ namedThing <$> p
makeEntry x = singleton (x, Just $ AnArg i [])
instance ComputeOccurrences Term where
occurrences v = case unSpine v of
Var i args ->
asks (occI . vars) <> do
occs <- mapM occurrences args
-- Lucas, 2022-12-01: Now, variables may have the polarities of their arguments
-- stored in the context (say, if the variable refers to a datatype parameter)
item <- reader ((!! i) . vars)
let getPol i = fromMaybe Mixed $ do
AnArg _ aoccs <- item
aoccs !!! i
return $ Concat $ zipWith (\i -> OccursAs (VarArg (getPol i) i)) [0..] occs
where
occI vars = maybe mempty OccursHere $ indexWithDefault unbound vars i
unbound = flip trace __IMPOSSIBLE__ $
"impossible: occurrence of de Bruijn index " ++ show i ++
" in vars " ++ show vars ++ " is unbound"
Def d args -> do
inf <- asks inf
let occsAs = if Just d /= inf then OccursAs . DefArg d else \ n ->
-- the principal argument of builtin INF (∞) is the second (n==1)
-- the first is a level argument (n==0, counting from 0!)
if n == 1 then OccursAs UnderInf else OccursAs (DefArg d n)
occs <- mapM occurrences args
return . Concat $ OccursHere (ADef d) : zipWith occsAs [0..] occs
Con _ _ args -> occurrences args
MetaV _ args -> OccursAs MetaArg <$> occurrences args
Pi a b -> (OccursAs LeftOfArrow <$> occurrences a) <> occurrences b
Lam _ b -> occurrences b
Level l -> occurrences l
Lit{} -> mempty
Sort{} -> mempty
-- Jesper, 2020-01-12: this information is also used for the
-- occurs check, so we need to look under DontCare (see #4371)
DontCare v -> occurrences v
Dummy{} -> mempty
instance ComputeOccurrences Level where
occurrences (Max _ as) = occurrences as
instance ComputeOccurrences PlusLevel where
occurrences (Plus _ l) = occurrences l
instance ComputeOccurrences Type where
occurrences (El _ v) = occurrences v
instance ComputeOccurrences a => ComputeOccurrences (Tele a) where
occurrences EmptyTel = mempty
occurrences (ExtendTel a b) = occurrences (a, b)
instance ComputeOccurrences a => ComputeOccurrences (Abs a) where
occurrences (Abs _ b) = withExtendedOccEnv Nothing $ occurrences b
occurrences (NoAbs _ b) = occurrences b
instance ComputeOccurrences a => ComputeOccurrences (Elim' a) where
occurrences Proj{} = __IMPOSSIBLE__ -- unSpine
occurrences (Apply a) = occurrences a
occurrences (IApply x y a) = occurrences (x,(y,a)) -- TODO Andrea: conservative
instance (ComputeOccurrences x, ComputeOccurrences a) => ComputeOccurrences (Boundary' x a) where
occurrences = occurrences . theBoundary
instance ComputeOccurrences a => ComputeOccurrences (Arg a) where
instance ComputeOccurrences a => ComputeOccurrences (Dom a) where
instance ComputeOccurrences a => ComputeOccurrences [a] where
instance ComputeOccurrences a => ComputeOccurrences (Maybe a) where
instance (ComputeOccurrences a, ComputeOccurrences b) => ComputeOccurrences (a, b) where
occurrences (x, y) = occurrences x <> occurrences y
instance ComputeOccurrences Int where
occurrences _ = mempty
-- | Computes the number of occurrences of different 'Item's in the
-- given definition.
--
-- WARNING: There can be lots of sharing between the 'OccursWhere'
-- entries. Traversing all of these entries could be expensive. (See
-- 'computeEdges' for an example.)
computeOccurrences :: QName -> TCM (Map Item Integer)
computeOccurrences q = flatten <$> computeOccurrences' q
-- | Computes the occurrences in the given definition.
computeOccurrences' :: QName -> TCM OccurrencesBuilder
computeOccurrences' q = inConcreteOrAbstractMode q $ \ def -> do
reportSDoc "tc.pos" 25 $ do
let a = defAbstract def
m <- asksTC envAbstractMode
cur <- asksTC envCurrentModule
o <- asksTC envCurrentOpaqueId
"computeOccurrences" <+> prettyTCM q <+> text (show a) <+> text (show o) <+> text (show m)
<+> prettyTCM cur
OccursAs (InDefOf q) <$> case theDef def of
Function{funClauses = cs} -> do
cs <- mapM etaExpandClause =<< instantiateFull cs
Concat . zipWith (OccursAs . InClause) [0..] <$>
mapM (getOccurrences []) cs
Datatype{dataClause = Just c} -> getOccurrences [] =<< instantiateFull c
Datatype{dataPars = np0, dataCons = cs, dataTranspIx = trx} -> do
-- Andreas, 2013-02-27 (later edited by someone else): First,
-- include each index of an inductive family.
TelV telD _ <- telView $ defType def
-- Andreas, 2017-04-26, issue #2554: count first index as parameter if it has type Size.
-- We compute sizeIndex=1 if first first index has type Size, otherwise sizeIndex==0
sizeIndex <- caseList (drop np0 $ telToList telD) (return 0) $ \ dom _ -> do
caseMaybeM (isSizeType dom) (return 0) $ \ _ -> return 1
let np = np0 + sizeIndex
let xs = [np .. size telD - 1] -- argument positions corresponding to indices
let ioccs = Concat $ map (\i -> OccursHere $ AnArg i []) [np0 .. np - 1]
++ map (\i -> OccursAs IsIndex $ OccursHere $ AnArg i []) xs
-- Then, we compute the occurrences in the constructor types.
let conOcc c = do
-- Andreas, 2020-02-15, issue #4447:
-- Allow UnconfimedReductions here to make sure we get the constructor type
-- in same way as it was obtained when the data types was checked.
(TelV tel t, bnd) <- putAllowedReductions allReductions $
telViewPathBoundary . defType =<< getConstInfo c
let (tel0,tel1) = splitTelescopeAt np tel
-- Do not collect occurrences in the data parameters.
-- Normalization needed e.g. for test/succeed/Bush.agda.
-- (Actually, for Bush.agda, reducing the parameters should be sufficient.)
tel1' <- addContext tel0 $ normalise $ tel1
-- Make parameters into context items, with polarity info
pvars <- parametersToItems tel0 np
let telvars = replicate (size tel1') Nothing ++ pvars
reportSLn "tc.pos.params" 50 $ "Adding datatypes parameters in context " ++ prettyShow pvars
-- Occurrences in the types of the constructor arguments.
(OccursAs (ConArgType c) <$> getOccurrences pvars tel1') <>
(OccursAs (ConEndpoint c) <$> getOccurrences telvars bnd) <> do
-- Occurrences in the indices of the data type the constructor targets.
-- Andreas, 2020-02-15, issue #4447:
-- WAS: @t@ is not necessarily a data type, but it could be something
-- that reduces to a data type once UnconfirmedReductions are confirmed
-- as safe by the termination checker.
-- In any case, if @t@ is not showing itself as the data type, we need to
-- do something conservative. We will just collect *all* occurrences
-- and flip their sign (variance) using 'LeftOfArrow'.
case unEl t of
Def q' vs
| q == q' -> do
let indices = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ drop np vs
OccursAs (IndArgType c) . OnlyVarsUpTo np <$> getOccurrences telvars indices
| otherwise -> __IMPOSSIBLE__ -- this ought to be impossible now (but wasn't, see #4447)
Pi{} -> __IMPOSSIBLE__ -- eliminated by telView
MetaV{} -> __IMPOSSIBLE__ -- not a constructor target; should have been solved by now
Var{} -> __IMPOSSIBLE__ -- not a constructor target
Sort{} -> __IMPOSSIBLE__ -- not a constructor target
Lam{} -> __IMPOSSIBLE__ -- not a type
Lit{} -> __IMPOSSIBLE__ -- not a type
Con{} -> __IMPOSSIBLE__ -- not a type
Level{} -> __IMPOSSIBLE__ -- not a type
DontCare{} -> __IMPOSSIBLE__ -- not a type
Dummy{} -> __IMPOSSIBLE__
-- If the data type has a transport constructor (i.e. it's an
-- indexed family in cubical mode) we should also consider it for
-- positivity.
mconcat $ pure ioccs : map conOcc (cs ++ maybeToList trx)
Record{recClause = Just c} -> getOccurrences [] =<< instantiateFull c
Record{recPars = np, recTel = tel} -> do
let (tel0,tel1) = splitTelescopeAt np tel
pvars <- parametersToItems tel0 np
getOccurrences pvars =<< addContext tel0 (normalise tel1) -- Andreas, 2017-01-01, issue #1899, treat like data types
-- Arguments to other kinds of definitions are hard-wired.
Constructor{} -> mempty
Axiom{} -> mempty
DataOrRecSig{} -> mempty
Primitive{} -> mempty
PrimitiveSort{} -> mempty
GeneralizableVar{} -> mempty
AbstractDefn{} -> __IMPOSSIBLE__
where
parametersToItems :: Telescope -> Nat -> TCM [Maybe Item]
parametersToItems tel n = reverse <$>
zipWithM (\i -> fmap (Just . AnArg i) . getOccurrencesFromType)
[0 .. n -1]
(snd . unDom <$> telToList tel)
-- Building the occurrence graph ------------------------------------------
data Node = DefNode !QName
| ArgNode !QName !Nat
deriving (Eq, Ord)
-- | Edge labels for the positivity graph.
data Edge a = Edge !Occurrence a
deriving (Eq, Ord, Show, Functor)
-- | Merges two edges between the same source and target.
mergeEdges :: Edge a -> Edge a -> Edge a
mergeEdges _ e@(Edge Mixed _) = e -- dominant
mergeEdges e@(Edge Mixed _) _ = e
mergeEdges (Edge Unused _) e = e -- neutral
mergeEdges e (Edge Unused _) = e
mergeEdges (Edge JustNeg _) e@(Edge JustNeg _) = e
mergeEdges _ e@(Edge JustNeg w) = Edge Mixed w
mergeEdges e@(Edge JustNeg w) _ = Edge Mixed w
mergeEdges _ e@(Edge JustPos _) = e -- dominates strict pos.
mergeEdges e@(Edge JustPos _) _ = e
mergeEdges _ e@(Edge StrictPos _) = e -- dominates 'GuardPos'
mergeEdges e@(Edge StrictPos _) _ = e
mergeEdges (Edge GuardPos _) e@(Edge GuardPos _) = e
-- | These operations form a semiring if we quotient by the relation
-- \"the 'Occurrence' components are equal\".
instance SemiRing (Edge (Seq OccursWhere)) where
ozero = Edge ozero DS.empty
oone = Edge oone DS.empty
oplus = mergeEdges
otimes (Edge o1 w1) (Edge o2 w2) = Edge (otimes o1 o2) (w1 DS.>< w2)
-- | WARNING: There can be lots of sharing between the 'OccursWhere'
-- entries in the edges. Traversing all of these entries could be
-- expensive. (See 'computeEdges' for an example.)
buildOccurrenceGraph :: Set QName -> TCM (Graph Node (Edge OccursWhere))
buildOccurrenceGraph qs =
Graph.fromEdgesWith mergeEdges . concat <$>
mapM defGraph (Set.toList qs)
where
defGraph :: QName -> TCM [Graph.Edge Node (Edge OccursWhere)]
defGraph q = inConcreteOrAbstractMode q $ \ _def -> do
occs <- computeOccurrences' q
reportSDoc "tc.pos.occs" 40 $
(("Occurrences in" <+> prettyTCM q) <> ":")
$+$
nest 2 (vcat $
map (\(i, n) ->
(pretty i <> ":") <+> text (show n) <+>
"occurrences") $
List.sortBy (compare `on` snd) $
Map.toList (flatten occs))
-- Placing this line before the reportSDoc lines above creates a
-- space leak: occs is retained for too long.
es <- computeEdges qs q occs
reportSDoc "tc.pos.occs.edges" 60 $
"Edges:"
$+$
nest 2 (vcat $
map (\e ->
let Edge o w = Graph.label e in
prettyTCM (Graph.source e) <+>
"-[" <+> (return (P.pretty o) <> ",") <+>
return (P.pretty w) <+> "]->" <+>
prettyTCM (Graph.target e))
es)
return es
-- | Computes all non-'ozero' occurrence graph edges represented by
-- the given 'OccurrencesBuilder'.
--
-- WARNING: There can be lots of sharing between the 'OccursWhere'
-- entries in the edges. Traversing all of these entries could be
-- expensive. For instance, for the function @F@ in
-- @benchmark/misc/SlowOccurrences.agda@ a large number of edges from
-- the argument @X@ to the function @F@ are computed. These edges have
-- polarity 'StrictPos', 'JustNeg' or 'JustPos', and contain the
-- following 'OccursWhere' elements:
--
-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0])@,
--
-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow'])@,
--
-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow', 'LeftOfArrow'])@,
--
-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow', 'LeftOfArrow', 'LeftOfArrow'])@,
--
-- * and so on.
computeEdges
:: Set QName
-- ^ The names in the current mutual block.
-> QName
-- ^ The current name.
-> OccurrencesBuilder
-> TCM [Graph.Edge Node (Edge OccursWhere)]
computeEdges muts q ob =
($ []) <$> mkEdge StrictPos (preprocess ob)
__IMPOSSIBLE__ DS.empty DS.empty
where
mkEdge
:: Occurrence
-> OccurrencesBuilder'
-> Node -- The current target node.
-> DS.Seq Where -- 'Where' information encountered before the current target
-- node was (re)selected.
-> DS.Seq Where -- 'Where' information encountered after the current target
-- node was (re)selected.
-> TCM ([Graph.Edge Node (Edge OccursWhere)] ->
[Graph.Edge Node (Edge OccursWhere)])
mkEdge !pol ob to cs os = case ob of
Concat' obs ->
foldr (liftM2 (.)) (return id)
[ mkEdge pol ob to cs os | ob <- obs ]
OccursAs' w ob -> do
(to', pol) <- mkEdge' to pol w
let mk = mkEdge pol ob
case to' of
Nothing -> mk to cs (os DS.|> w)
Just to -> mk to (cs DS.>< os) (DS.singleton w)
OccursHere' i ->
let o = OccursWhere (getRange i) cs os in
case i of
AnArg i t ->
return $ applyUnless (null pol) (Graph.Edge
{ Graph.source = ArgNode q i
, Graph.target = to
, Graph.label = Edge pol o
} :)
ADef q' ->
-- Andreas, 2017-04-26, issue #2555
-- Skip nodes pointing outside the mutual block.
return $ applyUnless (null pol || Set.notMember q' muts)
(Graph.Edge
{ Graph.source = DefNode q'
, Graph.target = to
, Graph.label = Edge pol o
} :)
-- This function might return a new target node.
mkEdge'
:: Node -- The current target node.
-> Occurrence
-> Where
-> TCM (Maybe Node, Occurrence)
mkEdge' to !pol = \case
VarArg p i -> addPol p
MetaArg -> mixed
LeftOfArrow -> negative
DefArg d i -> do
pol' <- isGuarding d
if Set.member d muts
then return (Just (ArgNode d i), pol')
else addPol =<< otimes pol' <$> getArgOccurrence d i
UnderInf -> addPol GuardPos -- Andreas, 2012-06-09: ∞ is guarding
ConArgType _ -> keepGoing
IndArgType _ -> mixed
ConEndpoint _ -> keepGoing
InClause _ -> keepGoing
Matched -> mixed -- consider arguments matched against as used
IsIndex -> mixed -- And similarly for indices.
InDefOf d -> do
pol' <- isGuarding d
return (Just (DefNode d), pol')
where
keepGoing = return (Nothing, pol)
mixed = return (Nothing, Mixed)
negative = return (Nothing, otimes pol JustNeg)
addPol pol' = return (Nothing, otimes pol pol')
isGuarding d = do
isDataOrRecordType d <&> \case
Just IsData -> GuardPos -- a datatype is guarding
_ -> StrictPos
-- Pretty-printing -----------------------------------------------------
instance Pretty Node where
pretty = \case
DefNode q -> P.pretty q
ArgNode q i -> P.pretty q <> P.text ("." ++ show i)
instance PrettyTCM Node where
prettyTCM = return . P.pretty
instance PrettyTCMWithNode (Edge OccursWhere) where
prettyTCMWithNode (WithNode n (Edge o w)) = vcat
[ prettyTCM o <+> prettyTCM n
, nest 2 $ return $ P.pretty w
]
instance PrettyTCM (Seq OccursWhere) where
prettyTCM =
fmap snd . prettyOWs . map adjustLeftOfArrow . uniq . Fold.toList
where
nth 0 = pwords "first"
nth 1 = pwords "second"
nth 2 = pwords "third"
nth n = pwords $ show (n + 1) ++ "th"
-- Removes consecutive duplicates.
uniq :: [OccursWhere] -> [OccursWhere]
uniq = map List1.head . List1.groupBy ((==) `on` snd')
where
snd' (OccursWhere _ _ ws) = ws
prettyOWs :: MonadPretty m => [OccursWhere] -> m (String, Doc)
prettyOWs [] = __IMPOSSIBLE__
prettyOWs [o] = do
(s, d) <- prettyOW o
return (s, d <> ".")
prettyOWs (o:os) = do
(s1, d1) <- prettyOW o
(s2, d2) <- prettyOWs os
return (s1, d1 <> ("," P.<+> "which" P.<+> P.text s2 P.$$ d2))
prettyOW :: MonadPretty m => OccursWhere -> m (String, Doc)
prettyOW (OccursWhere _ cs ws)
| null cs = prettyWs ws
| otherwise = do
(s, d1) <- prettyWs ws
(_, d2) <- prettyWs cs
return (s, d1 P.$$ "(" <> d2 <> ")")
prettyWs :: MonadPretty m => Seq Where -> m (String, Doc)
prettyWs ws = case Fold.toList ws of
[InDefOf d, IsIndex] ->
(,) "is" <$> fsep (pwords "an index of" ++ [prettyTCM d])
_ ->
(,) "occurs" <$>
Fold.foldrM (\w d -> return d $$ fsep (prettyW w)) empty ws
prettyW :: MonadPretty m => Where -> [m Doc]
prettyW = \case
LeftOfArrow -> pwords "to the left of an arrow"
DefArg q i -> pwords "in the" ++ nth i ++ pwords "argument of" ++
[prettyTCM q]
UnderInf -> pwords "under" ++
[do -- this cannot fail if an 'UnderInf' has been generated
inf <- fromMaybe __IMPOSSIBLE__ <$> getBuiltinName' builtinInf
prettyTCM inf]
VarArg p i -> pwords "in an argument of a bound variable at position" ++ [prettyTCM i]
++ pwords "which uses its argument with polarity" ++ [ pretty p ]
MetaArg -> pwords "in an argument of a metavariable"
ConArgType c -> pwords "in the type of the constructor" ++ [prettyTCM c]
IndArgType c -> pwords "in an index of the target type of the constructor" ++ [prettyTCM c]
ConEndpoint c
-> pwords "in an endpoint of the target of the" ++
pwords "higher constructor" ++ [prettyTCM c]
InClause i -> pwords "in the" ++ nth i ++ pwords "clause"
Matched -> pwords "as matched against"
IsIndex -> pwords "as an index"
InDefOf d -> pwords "in the definition of" ++ [prettyTCM d]
adjustLeftOfArrow :: OccursWhere -> OccursWhere
adjustLeftOfArrow (OccursWhere r cs os) =
OccursWhere r (DS.filter (not . isArrow) cs) $
noArrows
DS.><
case DS.viewl startsWithArrow of
DS.EmptyL -> DS.empty
w DS.:< ws -> w DS.<| DS.filter (not . isArrow) ws
where
(noArrows, startsWithArrow) = DS.breakl isArrow os
isArrow LeftOfArrow{} = True
isArrow _ = False