{-# LANGUAGE NamedFieldPuns #-} -- | -- Type class entailment -- module Language.PureScript.TypeChecker.Entailment ( InstanceContext , SolverOptions(..) , replaceTypeClassDictionaries , newDictionaries , entails ) where import Prelude.Compat import Protolude (ordNub) import Control.Arrow (second) import Control.Monad.Error.Class (MonadError(..)) import Control.Monad.State import Control.Monad.Supply.Class (MonadSupply(..)) import Control.Monad.Writer import Data.Foldable (for_, fold, toList) import Data.Function (on) import Data.Functor (($>)) import Data.List (minimumBy) import Data.Maybe (fromMaybe, maybeToList, mapMaybe) import qualified Data.Map as M import qualified Data.Set as S import Data.Text (Text) import Language.PureScript.AST import Language.PureScript.Crash import Language.PureScript.Environment import Language.PureScript.Errors import Language.PureScript.Names import Language.PureScript.TypeChecker.Monad import Language.PureScript.TypeChecker.Unify import Language.PureScript.TypeClassDictionaries import Language.PureScript.Types import Language.PureScript.Label (Label(..)) import Language.PureScript.PSString (PSString, mkString) import qualified Language.PureScript.Constants as C -- | Describes what sort of dictionary to generate for type class instances data Evidence = NamedInstance (Qualified Ident) -- ^ An existing named instance | WarnInstance Type -- ^ Computed instance of the Warn type class with a user-defined warning message | IsSymbolInstance PSString -- ^ Computed instance of the IsSymbol type class for a given Symbol literal | CompareSymbolInstance -- ^ Computed instance of CompareSymbol | AppendSymbolInstance -- ^ Computed instance of AppendSymbol | UnionInstance -- ^ Computed instance of RowUnion deriving (Show, Eq) -- | Extract the identifier of a named instance namedInstanceIdentifier :: Evidence -> Maybe (Qualified Ident) namedInstanceIdentifier (NamedInstance i) = Just i namedInstanceIdentifier _ = Nothing -- | Description of a type class dictionary with instance evidence type TypeClassDict = TypeClassDictionaryInScope Evidence -- | The 'InstanceContext' tracks those constraints which can be satisfied. type InstanceContext = M.Map (Maybe ModuleName) (M.Map (Qualified (ProperName 'ClassName)) (M.Map (Qualified Ident) NamedDict)) -- | A type substitution which makes an instance head match a list of types. -- -- Note: we store many types per type variable name. For any name, all types -- should unify if we are going to commit to an instance. type Matching a = M.Map Text a combineContexts :: InstanceContext -> InstanceContext -> InstanceContext combineContexts = M.unionWith (M.unionWith M.union) -- | Replace type class dictionary placeholders with inferred type class dictionaries replaceTypeClassDictionaries :: forall m . (MonadState CheckState m, MonadError MultipleErrors m, MonadWriter MultipleErrors m, MonadSupply m) => Bool -> Expr -> m (Expr, [(Ident, InstanceContext, Constraint)]) replaceTypeClassDictionaries shouldGeneralize expr = flip evalStateT M.empty $ do -- Loop, deferring any unsolved constraints, until there are no more -- constraints which can be solved, then make a generalization pass. let loop e = do (e', solved) <- deferPass e if getAny solved then loop e' else return e' loop expr >>= generalizePass where -- This pass solves constraints where possible, deferring constraints if not. deferPass :: Expr -> StateT InstanceContext m (Expr, Any) deferPass = fmap (second fst) . runWriterT . f where f :: Expr -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr (_, f, _) = everywhereOnValuesTopDownM return (go True) return -- This pass generalizes any remaining constraints generalizePass :: Expr -> StateT InstanceContext m (Expr, [(Ident, InstanceContext, Constraint)]) generalizePass = fmap (second snd) . runWriterT . f where f :: Expr -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr (_, f, _) = everywhereOnValuesTopDownM return (go False) return go :: Bool -> Expr -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr go deferErrors (TypeClassDictionary constraint context hints) = rethrow (addHints hints) $ entails (SolverOptions shouldGeneralize deferErrors) constraint context hints go _ other = return other -- | Three options for how we can handle a constraint, depending on the mode we're in. data EntailsResult a = Solved a TypeClassDict -- ^ We solved this constraint | Unsolved Constraint -- ^ We couldn't solve this constraint right now, it will be generalized | Deferred -- ^ We couldn't solve this constraint right now, so it has been deferred deriving Show -- | Options for the constraint solver data SolverOptions = SolverOptions { solverShouldGeneralize :: Bool -- ^ Should the solver be allowed to generalize over unsolved constraints? , solverDeferErrors :: Bool -- ^ Should the solver be allowed to defer errors by skipping constraints? } -- | Check that the current set of type class dictionaries entail the specified type class goal, and, if so, -- return a type class dictionary reference. entails :: forall m . (MonadState CheckState m, MonadError MultipleErrors m, MonadWriter MultipleErrors m, MonadSupply m) => SolverOptions -- ^ Solver options -> Constraint -- ^ The constraint to solve -> InstanceContext -- ^ The contexts in which to solve the constraint -> [ErrorMessageHint] -- ^ Error message hints to apply to any instance errors -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr entails SolverOptions{..} constraint context hints = solve constraint where forClassName :: InstanceContext -> Qualified (ProperName 'ClassName) -> [Type] -> [TypeClassDict] forClassName _ C.Warn [msg] = [TypeClassDictionaryInScope (WarnInstance msg) [] C.Warn [msg] Nothing] forClassName _ C.IsSymbol [TypeLevelString sym] = [TypeClassDictionaryInScope (IsSymbolInstance sym) [] C.IsSymbol [TypeLevelString sym] Nothing] forClassName _ C.CompareSymbol [arg0@(TypeLevelString lhs), arg1@(TypeLevelString rhs), _] = let ordering = case compare lhs rhs of LT -> C.orderingLT EQ -> C.orderingEQ GT -> C.orderingGT args = [arg0, arg1, TypeConstructor ordering] in [TypeClassDictionaryInScope CompareSymbolInstance [] C.CompareSymbol args Nothing] forClassName _ C.AppendSymbol [arg0@(TypeLevelString lhs), arg1@(TypeLevelString rhs), _] = let args = [arg0, arg1, TypeLevelString (lhs <> rhs)] in [TypeClassDictionaryInScope AppendSymbolInstance [] C.AppendSymbol args Nothing] forClassName _ C.Union [l, r, u] | Just (lOut, rOut, uOut, cst) <- unionRows l r u = [ TypeClassDictionaryInScope UnionInstance [] C.Union [lOut, rOut, uOut] cst ] forClassName ctx cn@(Qualified (Just mn) _) tys = concatMap (findDicts ctx cn) (ordNub (Nothing : Just mn : map Just (mapMaybe ctorModules tys))) forClassName _ _ _ = internalError "forClassName: expected qualified class name" ctorModules :: Type -> Maybe ModuleName ctorModules (TypeConstructor (Qualified (Just mn) _)) = Just mn ctorModules (TypeConstructor (Qualified Nothing _)) = internalError "ctorModules: unqualified type name" ctorModules (TypeApp ty _) = ctorModules ty ctorModules (KindedType ty _) = ctorModules ty ctorModules _ = Nothing findDicts :: InstanceContext -> Qualified (ProperName 'ClassName) -> Maybe ModuleName -> [TypeClassDict] findDicts ctx cn = fmap (fmap NamedInstance) . maybe [] M.elems . (>>= M.lookup cn) . flip M.lookup ctx valUndefined :: Expr valUndefined = Var (Qualified (Just (ModuleName [ProperName C.prim])) (Ident C.undefined)) solve :: Constraint -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr solve con = go 0 con where go :: Int -> Constraint -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) Expr go work (Constraint className' tys' _) | work > 1000 = throwError . errorMessage $ PossiblyInfiniteInstance className' tys' go work con'@(Constraint className' tys' conInfo) = WriterT . StateT . (withErrorMessageHint (ErrorSolvingConstraint con') .) . runStateT . runWriterT $ do -- We might have unified types by solving other constraints, so we need to -- apply the latest substitution. latestSubst <- lift . lift $ gets checkSubstitution let tys'' = map (substituteType latestSubst) tys' -- Get the inferred constraint context so far, and merge it with the global context inferred <- lift get -- We need information about functional dependencies, so we have to look up the class -- name in the environment: classesInScope <- lift . lift $ gets (typeClasses . checkEnv) TypeClassData{ typeClassDependencies } <- case M.lookup className' classesInScope of Nothing -> throwError . errorMessage $ UnknownClass className' Just tcd -> pure tcd let instances = [ (substs, tcd) | tcd <- forClassName (combineContexts context inferred) className' tys'' -- Make sure the type unifies with the type in the type instance definition , substs <- maybeToList (matches typeClassDependencies tcd tys'') ] solution <- lift . lift $ unique tys'' instances case solution of Solved substs tcd -> do -- Note that we solved something. tell (Any True, mempty) -- Make sure the substitution is valid: lift . lift . for_ substs $ pairwiseM unifyTypes -- Now enforce any functional dependencies, using unification -- Note: we need to generate fresh types for any unconstrained -- type variables before unifying. let subst = fmap head substs currentSubst <- lift . lift $ gets checkSubstitution subst' <- lift . lift $ withFreshTypes tcd (fmap (substituteType currentSubst) subst) lift . lift $ zipWithM_ (\t1 t2 -> do let inferredType = replaceAllTypeVars (M.toList subst') t1 unifyTypes inferredType t2) (tcdInstanceTypes tcd) tys'' currentSubst' <- lift . lift $ gets checkSubstitution let subst'' = fmap (substituteType currentSubst') subst' -- Solve any necessary subgoals args <- solveSubgoals subst'' (tcdDependencies tcd) initDict <- lift . lift $ mkDictionary (tcdValue tcd) args let match = foldr (\(className, index) dict -> subclassDictionaryValue dict className index) initDict (tcdPath tcd) return match Unsolved unsolved -> do -- Generate a fresh name for the unsolved constraint's new dictionary ident <- freshIdent ("dict" <> runProperName (disqualify (constraintClass unsolved))) let qident = Qualified Nothing ident -- Store the new dictionary in the InstanceContext so that we can solve this goal in -- future. newDicts <- lift . lift $ newDictionaries [] qident unsolved let newContext = mkContext newDicts modify (combineContexts newContext) -- Mark this constraint for generalization tell (mempty, [(ident, context, unsolved)]) return (Var qident) Deferred -> -- Constraint was deferred, just return the dictionary unchanged, -- with no unsolved constraints. Hopefully, we can solve this later. return (TypeClassDictionary (Constraint className' tys'' conInfo) context hints) where -- | When checking functional dependencies, we need to use unification to make -- sure it is safe to use the selected instance. We will unify the solved type with -- the type in the instance head under the substition inferred from its instantiation. -- As an example, when solving MonadState t0 (State Int), we choose the -- MonadState s (State s) instance, and we unify t0 with Int, since the functional -- dependency from MonadState dictates that t0 should unify with s\[s -> Int], which is -- Int. This is fine, but in some cases, the substitution does not remove all TypeVars -- from the type, so we end up with a unification error. So, any type arguments which -- appear in the instance head, but not in the substitution need to be replaced with -- fresh type variables. This function extends a substitution with fresh type variables -- as necessary, based on the types in the instance head. withFreshTypes :: TypeClassDict -> Matching Type -> m (Matching Type) withFreshTypes TypeClassDictionaryInScope{..} subst = do let onType = everythingOnTypes S.union fromTypeVar typeVarsInHead = foldMap onType tcdInstanceTypes <> foldMap (foldMap (foldMap onType . constraintArgs)) tcdDependencies typeVarsInSubst = S.fromList (M.keys subst) uninstantiatedTypeVars = typeVarsInHead S.\\ typeVarsInSubst newSubst <- traverse withFreshType (S.toList uninstantiatedTypeVars) return (subst <> M.fromList newSubst) where fromTypeVar (TypeVar v) = S.singleton v fromTypeVar _ = S.empty withFreshType s = do t <- freshType return (s, t) unique :: [Type] -> [(a, TypeClassDict)] -> m (EntailsResult a) unique tyArgs [] | solverDeferErrors = return Deferred -- We need a special case for nullary type classes, since we want -- to generalize over Partial constraints. | solverShouldGeneralize && (null tyArgs || any canBeGeneralized tyArgs) = return (Unsolved (Constraint className' tyArgs conInfo)) | otherwise = throwError . errorMessage $ NoInstanceFound (Constraint className' tyArgs conInfo) unique _ [(a, dict)] = return $ Solved a dict unique tyArgs tcds | pairwiseAny overlapping (map snd tcds) = do tell . errorMessage $ OverlappingInstances className' tyArgs (tcds >>= (toList . namedInstanceIdentifier . tcdValue . snd)) return $ uncurry Solved (head tcds) | otherwise = return $ uncurry Solved (minimumBy (compare `on` length . tcdPath . snd) tcds) canBeGeneralized :: Type -> Bool canBeGeneralized TUnknown{} = True canBeGeneralized (KindedType t _) = canBeGeneralized t canBeGeneralized _ = False -- | -- Check if two dictionaries are overlapping -- -- Dictionaries which are subclass dictionaries cannot overlap, since otherwise the overlap would have -- been caught when constructing superclass dictionaries. overlapping :: TypeClassDict -> TypeClassDict -> Bool overlapping TypeClassDictionaryInScope{ tcdPath = _ : _ } _ = False overlapping _ TypeClassDictionaryInScope{ tcdPath = _ : _ } = False overlapping TypeClassDictionaryInScope{ tcdDependencies = Nothing } _ = False overlapping _ TypeClassDictionaryInScope{ tcdDependencies = Nothing } = False overlapping tcd1 tcd2 = tcdValue tcd1 /= tcdValue tcd2 -- Create dictionaries for subgoals which still need to be solved by calling go recursively -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively. solveSubgoals :: Matching Type -> Maybe [Constraint] -> WriterT (Any, [(Ident, InstanceContext, Constraint)]) (StateT InstanceContext m) (Maybe [Expr]) solveSubgoals _ Nothing = return Nothing solveSubgoals subst (Just subgoals) = Just <$> traverse (go (work + 1) . mapConstraintArgs (map (replaceAllTypeVars (M.toList subst)))) subgoals -- Make a dictionary from subgoal dictionaries by applying the correct function mkDictionary :: Evidence -> Maybe [Expr] -> m Expr mkDictionary (NamedInstance n) args = return $ foldl App (Var n) (fold args) mkDictionary UnionInstance (Just [e]) = -- We need the subgoal dictionary to appear in the term somewhere return $ App (Abs (VarBinder (Ident C.__unused)) valUndefined) e mkDictionary UnionInstance _ = return valUndefined mkDictionary (WarnInstance msg) _ = do tell . errorMessage $ UserDefinedWarning msg -- We cannot call the type class constructor here because Warn is declared in Prim. -- This means that it doesn't have a definition that we can import. -- So pass an empty placeholder (undefined) instead. return valUndefined mkDictionary (IsSymbolInstance sym) _ = let fields = [ ("reflectSymbol", Abs (VarBinder (Ident C.__unused)) (Literal (StringLiteral sym))) ] in return $ TypeClassDictionaryConstructorApp C.IsSymbol (Literal (ObjectLiteral fields)) mkDictionary CompareSymbolInstance _ = return $ TypeClassDictionaryConstructorApp C.CompareSymbol (Literal (ObjectLiteral [])) mkDictionary AppendSymbolInstance _ = return $ TypeClassDictionaryConstructorApp C.AppendSymbol (Literal (ObjectLiteral [])) -- Turn a DictionaryValue into a Expr subclassDictionaryValue :: Expr -> Qualified (ProperName 'ClassName) -> Integer -> Expr subclassDictionaryValue dict className index = App (Accessor (mkString (superclassName className index)) dict) valUndefined -- | Left biased union of two row types unionRows :: Type -> Type -> Type -> Maybe (Type, Type, Type, Maybe [Constraint]) unionRows l r _ = guard canMakeProgress $> (l, r, rowFromList out, cons) where (fixed, rest) = rowToList l rowVar = TypeVar "r" (canMakeProgress, out, cons) = case rest of -- If the left hand side is a closed row, then we can merge -- its labels into the right hand side. REmpty -> (True, (fixed, r), Nothing) -- If the left hand side is not definitely closed, then the only way we -- can safely make progress is to move any known labels from the left -- input into the output, and add a constraint for any remaining labels. -- Otherwise, the left hand tail might contain the same labels as on -- the right hand side, and we can't be certain we won't reorder the -- types for such labels. _ -> (not (null fixed), (fixed, rowVar), Just [ Constraint C.Union [rest, r, rowVar] Nothing ]) -- Check if an instance matches our list of types, allowing for types -- to be solved via functional dependencies. If the types match, we return a -- substitution which makes them match. If not, we return 'Nothing'. matches :: [FunctionalDependency] -> TypeClassDict -> [Type] -> Maybe (Matching [Type]) matches deps TypeClassDictionaryInScope{..} tys = do -- First, find those types which match exactly let matched = zipWith typeHeadsAreEqual tys tcdInstanceTypes -- Now, use any functional dependencies to infer any remaining types guard $ covers matched -- Verify that any repeated type variables are unifiable let determinedSet = foldMap (S.fromList . fdDetermined) deps solved = map snd . filter ((`S.notMember` determinedSet) . fst) $ zipWith (\(_, ts) i -> (i, ts)) matched [0..] verifySubstitution (M.unionsWith (++) solved) where -- | Find the closure of a set of functional dependencies. covers :: [(Bool, subst)] -> Bool covers ms = finalSet == S.fromList [0..length ms - 1] where initialSet :: S.Set Int initialSet = S.fromList . map snd . filter (fst . fst) $ zip ms [0..] finalSet :: S.Set Int finalSet = untilFixedPoint applyAll initialSet untilFixedPoint :: Eq a => (a -> a) -> a -> a untilFixedPoint f = go where go a | a' == a = a' | otherwise = go a' where a' = f a applyAll :: S.Set Int -> S.Set Int applyAll s = foldr applyDependency s deps applyDependency :: FunctionalDependency -> S.Set Int -> S.Set Int applyDependency FunctionalDependency{..} xs | S.fromList fdDeterminers `S.isSubsetOf` xs = xs <> S.fromList fdDetermined | otherwise = xs -- -- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup), -- and return a substitution from type variables to types which makes the type heads unify. -- typeHeadsAreEqual :: Type -> Type -> (Bool, Matching [Type]) typeHeadsAreEqual (KindedType t1 _) t2 = typeHeadsAreEqual t1 t2 typeHeadsAreEqual t1 (KindedType t2 _) = typeHeadsAreEqual t1 t2 typeHeadsAreEqual (TUnknown u1) (TUnknown u2) | u1 == u2 = (True, M.empty) typeHeadsAreEqual (Skolem _ s1 _ _) (Skolem _ s2 _ _) | s1 == s2 = (True, M.empty) typeHeadsAreEqual t (TypeVar v) = (True, M.singleton v [t]) typeHeadsAreEqual (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = (True, M.empty) typeHeadsAreEqual (TypeLevelString s1) (TypeLevelString s2) | s1 == s2 = (True, M.empty) typeHeadsAreEqual (TypeApp h1 t1) (TypeApp h2 t2) = both (typeHeadsAreEqual h1 h2) (typeHeadsAreEqual t1 t2) typeHeadsAreEqual REmpty REmpty = (True, M.empty) typeHeadsAreEqual r1@RCons{} r2@RCons{} = foldr both (uncurry go rest) common where (common, rest) = alignRowsWith typeHeadsAreEqual r1 r2 go :: ([(Label, Type)], Type) -> ([(Label, Type)], Type) -> (Bool, Matching [Type]) go (l, KindedType t1 _) (r, t2) = go (l, t1) (r, t2) go (l, t1) (r, KindedType t2 _) = go (l, t1) (r, t2) go ([], REmpty) ([], REmpty) = (True, M.empty) go ([], TUnknown u1) ([], TUnknown u2) | u1 == u2 = (True, M.empty) go ([], TypeVar v1) ([], TypeVar v2) | v1 == v2 = (True, M.empty) go ([], Skolem _ sk1 _ _) ([], Skolem _ sk2 _ _) | sk1 == sk2 = (True, M.empty) go (sd, r) ([], TypeVar v) = (True, M.singleton v [rowFromList (sd, r)]) go _ _ = (False, M.empty) typeHeadsAreEqual _ _ = (False, M.empty) both :: (Bool, Matching [Type]) -> (Bool, Matching [Type]) -> (Bool, Matching [Type]) both (b1, m1) (b2, m2) = (b1 && b2, M.unionWith (++) m1 m2) -- Ensure that a substitution is valid verifySubstitution :: Matching [Type] -> Maybe (Matching [Type]) verifySubstitution = traverse meet where meet ts | pairwiseAll typesAreEqual ts = Just ts | otherwise = Nothing -- Note that unknowns are only allowed to unify if they came from a type -- which was _not_ solved, i.e. one which was inferred by a functional -- dependency. typesAreEqual :: Type -> Type -> Bool typesAreEqual (KindedType t1 _) t2 = typesAreEqual t1 t2 typesAreEqual t1 (KindedType t2 _) = typesAreEqual t1 t2 typesAreEqual (TUnknown u1) (TUnknown u2) | u1 == u2 = True typesAreEqual (Skolem _ s1 _ _) (Skolem _ s2 _ _) = s1 == s2 typesAreEqual (TypeVar v1) (TypeVar v2) = v1 == v2 typesAreEqual (TypeLevelString s1) (TypeLevelString s2) = s1 == s2 typesAreEqual (TypeConstructor c1) (TypeConstructor c2) = c1 == c2 typesAreEqual (TypeApp h1 t1) (TypeApp h2 t2) = typesAreEqual h1 h2 && typesAreEqual t1 t2 typesAreEqual REmpty REmpty = True typesAreEqual r1 r2 | isRCons r1 || isRCons r2 = let (common, rest) = alignRowsWith typesAreEqual r1 r2 in and common && uncurry go rest where go :: ([(Label, Type)], Type) -> ([(Label, Type)], Type) -> Bool go (l, KindedType t1 _) (r, t2) = go (l, t1) (r, t2) go (l, t1) (r, KindedType t2 _) = go (l, t1) (r, t2) go ([], TUnknown u1) ([], TUnknown u2) | u1 == u2 = True go ([], Skolem _ s1 _ _) ([], Skolem _ s2 _ _) = s1 == s2 go ([], REmpty) ([], REmpty) = True go ([], TypeVar v1) ([], TypeVar v2) = v1 == v2 go _ _ = False typesAreEqual _ _ = False isRCons :: Type -> Bool isRCons RCons{} = True isRCons _ = False -- | Add a dictionary for the constraint to the scope, and dictionaries -- for all implied superclass instances. newDictionaries :: MonadState CheckState m => [(Qualified (ProperName 'ClassName), Integer)] -> Qualified Ident -> Constraint -> m [NamedDict] newDictionaries path name (Constraint className instanceTy _) = do tcs <- gets (typeClasses . checkEnv) let TypeClassData{..} = fromMaybe (internalError "newDictionaries: type class lookup failed") $ M.lookup className tcs supDicts <- join <$> zipWithM (\(Constraint supName supArgs _) index -> newDictionaries ((supName, index) : path) name (Constraint supName (instantiateSuperclass (map fst typeClassArguments) supArgs instanceTy) Nothing) ) typeClassSuperclasses [0..] return (TypeClassDictionaryInScope name path className instanceTy Nothing : supDicts) where instantiateSuperclass :: [Text] -> [Type] -> [Type] -> [Type] instantiateSuperclass args supArgs tys = map (replaceAllTypeVars (zip args tys)) supArgs mkContext :: [NamedDict] -> InstanceContext mkContext = foldr combineContexts M.empty . map fromDict where fromDict d = M.singleton Nothing (M.singleton (tcdClassName d) (M.singleton (tcdValue d) d)) -- | Check all pairs of values in a list match a predicate pairwiseAll :: (a -> a -> Bool) -> [a] -> Bool pairwiseAll _ [] = True pairwiseAll _ [_] = True pairwiseAll p (x : xs) = all (p x) xs && pairwiseAll p xs -- | Check any pair of values in a list match a predicate pairwiseAny :: (a -> a -> Bool) -> [a] -> Bool pairwiseAny _ [] = False pairwiseAny _ [_] = False pairwiseAny p (x : xs) = any (p x) xs || pairwiseAny p xs pairwiseM :: Applicative m => (a -> a -> m ()) -> [a] -> m () pairwiseM _ [] = pure () pairwiseM _ [_] = pure () pairwiseM p (x : xs) = traverse (p x) xs *> pairwiseM p xs