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1−-----------------------------------------------------------------------------
2−--
3−-- Module : Language.PureScript.TypeChecker.Types
4−-- Copyright : (c) Phil Freeman 2013
5−-- License : MIT
6−--
7−-- Maintainer : Phil Freeman <paf31@cantab.net>
8−-- Stability : experimental
9−-- Portability :
10−--
11−-- |
12−-- This module implements the type checker
13−--
14−-----------------------------------------------------------------------------
15−
16−{-# OPTIONS_GHC -fno-warn-orphans #-}
17−{-# LANGUAGE FlexibleInstances #-}
18−{-# LANGUAGE FlexibleContexts #-}
19−{-# LANGUAGE MultiParamTypeClasses #-}
20−
21−module Language.PureScript.TypeChecker.Types (
22− typesOf
23−) where
24−
25−{-
26− The following functions represent the corresponding type checking judgements:
27−
28− infer
29− Synthesize a type for a value
30−
31− check
32− Check a value has a given type
33−
34− checkProperties
35− Check an object with a given type contains specified properties
36−
37− checkFunctionApplication
38− Check a function of a given type returns a value of another type when applied to its arguments
39−
40− subsumes
41− Check a type subsumes another type
42−-}
43−
44−import Data.List
45−import Data.Maybe (maybeToList, fromMaybe)
46−import Data.Function (on)
47−import Data.Ord (comparing)
48−import Data.Monoid
49−import Data.Either (lefts, rights)
50−
51−import Language.PureScript.Declarations
52−import Language.PureScript.Types
53−import Language.PureScript.Kinds
54−import Language.PureScript.Names
55−import Language.PureScript.TypeClassDictionaries
56−import Language.PureScript.TypeChecker.Monad
57−import Language.PureScript.TypeChecker.Kinds
58−import Language.PureScript.TypeChecker.Synonyms
59−import Language.PureScript.Pretty
60−import Language.PureScript.Environment
61−import Language.PureScript.Errors
62−import qualified Language.PureScript.Constants as C
63−
64−import Control.Monad.State
65−import Control.Monad.Error
66−import Control.Monad.Unify
67−
68−import Control.Applicative
69−import Control.Arrow (Arrow(..))
70−
71−import qualified Data.Map as M
72−import qualified Data.HashMap.Strict as H
73−
74−instance Partial Type where
75− unknown = TUnknown
76− isUnknown (TUnknown u) = Just u
77− isUnknown _ = Nothing
78− unknowns = everythingOnTypes (++) go
79− where
80− go (TUnknown u) = [u]
81− go _ = []
82− ($?) sub = everywhereOnTypes go
83− where
84− go t@(TUnknown u) = case H.lookup u (runSubstitution sub) of
85− Nothing -> t
86− Just t' -> t'
87− go other = other
88−
89−instance Unifiable Check Type where
90− (=?=) = unifyTypes
91−
92−-- |
93−-- Unify two types, updating the current substitution
94−--
95−unifyTypes :: Type -> Type -> UnifyT Type Check ()
96−unifyTypes t1 t2 = rethrow (mkErrorStack ("Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2) Nothing <>) $
97− unifyTypes' t1 t2
98− where
99− unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
100− unifyTypes' (TUnknown u) t = u =:= t
101− unifyTypes' t (TUnknown u) = u =:= t
102− unifyTypes' (SaturatedTypeSynonym name args) ty = do
103− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ args
104− ty1 `unifyTypes` ty
105− unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
106− unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
107− case (sc1, sc2) of
108− (Just sc1', Just sc2') -> do
109− sko <- newSkolemConstant
110− let sk1 = skolemize ident1 sko sc1' ty1
111− let sk2 = skolemize ident2 sko sc2' ty2
112− sk1 `unifyTypes` sk2
113− _ -> error "Skolemized type variable was not given a scope"
114− unifyTypes' (ForAll ident ty1 (Just sc)) ty2 = do
115− sko <- newSkolemConstant
116− let sk = skolemize ident sko sc ty1
117− sk `unifyTypes` ty2
118− unifyTypes' ForAll{} _ = throwError . strMsg $ "Skolem variable scope is unspecified"
119− unifyTypes' ty f@ForAll{} = f `unifyTypes` ty
120− unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
121− unifyTypes' (TypeConstructor c1) (TypeConstructor c2) =
122− guardWith (strMsg ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".")) (c1 == c2)
123− unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
124− t3 `unifyTypes` t5
125− t4 `unifyTypes` t6
126− unifyTypes' (Skolem _ s1 _) (Skolem _ s2 _) | s1 == s2 = return ()
127− unifyTypes' (KindedType ty1 _) ty2 = ty1 `unifyTypes` ty2
128− unifyTypes' ty1 (KindedType ty2 _) = ty1 `unifyTypes` ty2
129− unifyTypes' r1@RCons{} r2 = unifyRows r1 r2
130− unifyTypes' r1 r2@RCons{} = unifyRows r1 r2
131− unifyTypes' r1@REmpty r2 = unifyRows r1 r2
132− unifyTypes' r1 r2@REmpty = unifyRows r1 r2
133− unifyTypes' t@(ConstrainedType _ _) _ = throwError . strMsg $ "Attempted to unify a constrained type " ++ prettyPrintType t ++ " with another type."
134− unifyTypes' t3 t4@(ConstrainedType _ _) = unifyTypes' t4 t3
135− unifyTypes' t3 t4 = throwError . strMsg $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
136−
137−-- |
138−-- Unify two rows, updating the current substitution
139−--
140−-- Common labels are first identified, and unified. Remaining labels and types are unified with a
141−-- trailing row unification variable, if appropriate, otherwise leftover labels result in a unification
142−-- error.
143−--
144−unifyRows :: Type -> Type -> UnifyT Type Check ()
145−unifyRows r1 r2 =
146− let
147− (s1, r1') = rowToList r1
148− (s2, r2') = rowToList r2
149− int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
150− sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
151− sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
152− in do
153− forM_ int (uncurry (=?=))
154− unifyRows' sd1 r1' sd2 r2'
155− where
156− unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> UnifyT Type Check ()
157− unifyRows' [] (TUnknown u) sd r = u =:= rowFromList (sd, r)
158− unifyRows' sd r [] (TUnknown u) = u =:= rowFromList (sd, r)
159− unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
160− occursCheck un ty
161− forM_ row $ \(_, t) -> occursCheck un t
162− u' <- fresh
163− u =?= RCons name ty u'
164− unifyRows' row r others u'
165− unifyRows' [] REmpty [] REmpty = return ()
166− unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
167− unifyRows' [] (Skolem _ s1 _) [] (Skolem _ s2 _) | s1 == s2 = return ()
168− unifyRows' sd3 r3 sd4 r4 = throwError . strMsg $ "Cannot unify (" ++ prettyPrintRow (rowFromList (sd3, r3)) ++ ") with (" ++ prettyPrintRow (rowFromList (sd4, r4)) ++ ")"
169−
170−-- |
171−-- Infer the types of multiple mutually-recursive values, and return elaborated values including
172−-- type class dictionaries and type annotations.
173−--
174−typesOf :: Maybe ModuleName -> ModuleName -> [(Ident, Expr)] -> Check [(Ident, (Expr, Type))]
175−typesOf mainModuleName moduleName vals = do
176− tys <- fmap tidyUp . liftUnify $ do
177− (untyped, typed, dict, untypedDict) <- typeDictionaryForBindingGroup moduleName vals
178− ds1 <- parU typed $ \e -> do
179− triple@(_, (_, ty)) <- checkTypedBindingGroupElement moduleName e dict
180− checkMain (fst e) ty
181− return triple
182− ds2 <- forM untyped $ \e -> do
183− triple@(_, (_, ty)) <- typeForBindingGroupElement e dict untypedDict
184− checkMain (fst e) ty
185− return triple
186− return $ ds1 ++ ds2
187−
188− forM tys $ \(ident, (val, ty)) -> do
189− -- Replace type class dictionary placeholders with actual dictionaries
190− val' <- replaceTypeClassDictionaries moduleName val
191− -- Check skolem variables did not escape their scope
192− skolemEscapeCheck val'
193− -- Remove type synonyms placeholders, remove duplicate row fields, and replace
194− -- top-level unification variables with named type variables.
195− let val'' = overTypes (desaturateAllTypeSynonyms . setifyAll) val'
196− ty' = varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty
197− return (ident, (val'', ty'))
198− where
199− -- Apply the substitution that was returned from runUnify to both types and (type-annotated) values
200− tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
201− -- If --main is enabled, need to check that `main` has type Eff eff a for some eff, a
202− checkMain nm ty = when (Just moduleName == mainModuleName && nm == Ident C.main) $ do
203− [eff, a] <- replicateM 2 fresh
204− ty =?= TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName [ProperName "Control", ProperName "Monad", ProperName "Eff"])) (ProperName "Eff"))) eff) a
205−
206−type TypeData = M.Map (ModuleName, Ident) (Type, NameKind, NameVisibility)
207−
208−type UntypedData = [(Ident, Type)]
209−
210−typeDictionaryForBindingGroup :: ModuleName -> [(Ident, Expr)] -> UnifyT Type Check ([(Ident, Expr)], [(Ident, (Expr, Type, Bool))], TypeData, UntypedData)
211−typeDictionaryForBindingGroup moduleName vals = do
212− let
213− -- Map each declaration to a name/value pair, with an optional type, if the declaration is typed
214− es = map isTyped vals
215− -- Filter the typed and untyped declarations
216− untyped = lefts es
217− typed = rights es
218− -- Make a map of names to typed declarations
219− typedDict = map (\(ident, (_, ty, _)) -> (ident, ty)) typed
220−
221− -- Create fresh unification variables for the types of untyped declarations
222− untypedNames <- replicateM (length untyped) fresh
223−
224− let
225− -- Make a map of names to the unification variables of untyped declarations
226− untypedDict = zip (map fst untyped) untypedNames
227− -- Create the dictionary of all name/type pairs, which will be added to the environment during type checking
228− dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable, Undefined))) $ typedDict ++ untypedDict)
229− return (untyped, typed, dict, untypedDict)
230−
231−checkTypedBindingGroupElement :: ModuleName -> (Ident, (Expr, Type, Bool)) -> TypeData -> UnifyT Type Check (Ident, (Expr, Type))
232−checkTypedBindingGroupElement moduleName (ident, (val', ty, checkType)) dict = do
233− -- Kind check
234− kind <- liftCheck $ kindOf moduleName ty
235− guardWith (strMsg $ "Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
236− -- Check the type with the new names in scope
237− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
238− val'' <- if checkType
239− then bindNames dict $ TypedValue True <$> check val' ty' <*> pure ty'
240− else return (TypedValue False val' ty')
241− return (ident, (val'', ty'))
242−
243−typeForBindingGroupElement :: (Ident, Expr) -> TypeData -> UntypedData -> UnifyT Type Check (Ident, (Expr, Type))
244−typeForBindingGroupElement (ident, val) dict untypedDict = do
245− -- Infer the type with the new names in scope
246− TypedValue _ val' ty <- bindNames dict $ infer val
247− ty =?= fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
248− return (ident, (TypedValue True val' ty, ty))
249−
250−-- |
251−-- Check if a value contains a type annotation
252−--
253−isTyped :: (Ident, Expr) -> (Either (Ident, Expr) (Ident, (Expr, Type, Bool)))
254−isTyped (name, TypedValue checkType value ty) = Right (name, (value, ty, checkType))
255−isTyped (name, value) = Left (name, value)
256−
257−-- |
258−-- Map a function over type annotations appearing inside a value
259−--
260−overTypes :: (Type -> Type) -> Expr -> Expr
261−overTypes f = let (_, f', _) = everywhereOnValues id g id in f'
262− where
263− g :: Expr -> Expr
264− g (TypedValue checkTy val t) = TypedValue checkTy val (f t)
265− g (TypeClassDictionary b (nm, tys) sco) = TypeClassDictionary b (nm, map f tys) sco
266− g other = other
267−
268−-- |
269−-- Replace type class dictionary placeholders with inferred type class dictionaries
270−--
271−replaceTypeClassDictionaries :: ModuleName -> Expr -> Check Expr
272−replaceTypeClassDictionaries mn =
273− let (_, f, _) = everywhereOnValuesTopDownM return go return
274− in f
275− where
276− go (TypeClassDictionary trySuperclasses constraint dicts) = do
277− env <- getEnv
278− entails env mn dicts constraint trySuperclasses
279− go other = return other
280−
281−-- |
282−-- A simplified representation of expressions which are used to represent type
283−-- class dictionaries at runtime, which can be compared for equality
284−--
285−data DictionaryValue
286− -- |
287− -- A dictionary which is brought into scope by a local constraint
288− --
289− = LocalDictionaryValue (Qualified Ident)
290− -- |
291− -- A dictionary which is brought into scope by an instance declaration
292− --
293− | GlobalDictionaryValue (Qualified Ident)
294− -- |
295− -- A dictionary which depends on other dictionaries
296− --
297− | DependentDictionaryValue (Qualified Ident) [DictionaryValue]
298− -- |
299− -- A subclass dictionary
300− --
301− | SubclassDictionaryValue DictionaryValue (Qualified ProperName) Integer
302− deriving (Show, Ord, Eq)
303−
304−-- |
305−-- Check that the current set of type class dictionaries entail the specified type class goal, and, if so,
306−-- return a type class dictionary reference.
307−--
308−entails :: Environment -> ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, [Type]) -> Bool -> Check Expr
309−entails env moduleName context = solve (sortedNubBy canonicalizeDictionary (filter filterModule context))
310− where
311− sortedNubBy :: (Ord k) => (v -> k) -> [v] -> [v]
312− sortedNubBy f vs = M.elems (M.fromList (map (f &&& id) vs))
313−
314− -- Filter out type dictionaries which are in scope in the current module
315− filterModule :: TypeClassDictionaryInScope -> Bool
316− filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
317− filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
318− filterModule _ = False
319−
320− solve context' (className, tys) trySuperclasses =
321− checkOverlaps $ go trySuperclasses className tys
322− where
323− go trySuperclasses' className' tys' =
324− -- Look for regular type instances
325− [ mkDictionary (canonicalizeDictionary tcd) args
326− | tcd <- context'
327− -- Make sure the type class name matches the one we are trying to satisfy
328− , className' == tcdClassName tcd
329− -- Make sure the type unifies with the type in the type instance definition
330− , subst <- maybeToList . (>>= verifySubstitution) . fmap concat $ zipWithM (typeHeadsAreEqual moduleName env) tys' (tcdInstanceTypes tcd)
331− -- Solve any necessary subgoals
332− , args <- solveSubgoals subst (tcdDependencies tcd) ] ++
333−
334− -- Look for implementations via superclasses
335− [ SubclassDictionaryValue suDict superclass index
336− | trySuperclasses'
337− , (subclassName, (args, _, implies)) <- M.toList (typeClasses env)
338− -- Try each superclass
339− , (index, (superclass, suTyArgs)) <- zip [0..] implies
340− -- Make sure the type class name matches the superclass name
341− , className' == superclass
342− -- Make sure the types unify with the types in the superclass implication
343− , subst <- maybeToList . (>>= verifySubstitution) . fmap concat $ zipWithM (typeHeadsAreEqual moduleName env) tys' suTyArgs
344− -- Finally, satisfy the subclass constraint
345− , args' <- maybeToList $ mapM (flip lookup subst) args
346− , suDict <- go True subclassName args' ]
347−
348− -- Create dictionaries for subgoals which still need to be solved by calling go recursively
349− -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type
350− -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively.
351− solveSubgoals :: [(String, Type)] -> Maybe [(Qualified ProperName, [Type])] -> [Maybe [DictionaryValue]]
352− solveSubgoals _ Nothing = return Nothing
353− solveSubgoals subst (Just subgoals) = do
354− dict <- mapM (uncurry (go True) . second (map (replaceAllTypeVars subst))) subgoals
355− return $ Just dict
356− -- Make a dictionary from subgoal dictionaries by applying the correct function
357− mkDictionary :: Qualified Ident -> Maybe [DictionaryValue] -> DictionaryValue
358− mkDictionary fnName Nothing = LocalDictionaryValue fnName
359− mkDictionary fnName (Just []) = GlobalDictionaryValue fnName
360− mkDictionary fnName (Just dicts) = DependentDictionaryValue fnName dicts
361− -- Turn a DictionaryValue into a Expr
362− dictionaryValueToValue :: DictionaryValue -> Expr
363− dictionaryValueToValue (LocalDictionaryValue fnName) = Var fnName
364− dictionaryValueToValue (GlobalDictionaryValue fnName) = App (Var fnName) valUndefined
365− dictionaryValueToValue (DependentDictionaryValue fnName dicts) = foldl App (Var fnName) (map dictionaryValueToValue dicts)
366− dictionaryValueToValue (SubclassDictionaryValue dict superclassName index) =
367− App (Accessor (C.__superclass_ ++ show superclassName ++ "_" ++ show index)
368− (dictionaryValueToValue dict))
369− valUndefined
370− -- Ensure that a substitution is valid
371− verifySubstitution :: [(String, Type)] -> Maybe [(String, Type)]
372− verifySubstitution subst = do
373− let grps = groupBy ((==) `on` fst) subst
374− guard (all (pairwise (unifiesWith env) . map snd) grps)
375− return $ map head grps
376− -- |
377− -- Check for overlapping instances
378− --
379− checkOverlaps :: [DictionaryValue] -> Check Expr
380− checkOverlaps dicts =
381− case [ (d1, d2) | d1 <- dicts, d2 <- dicts, d1 `overlapping` d2 ] of
382− (d1, d2) : _ -> throwError . strMsg $ unlines
383− [ "Overlapping instances found for " ++ show className ++ " " ++ unwords (map prettyPrintType tys) ++ "."
384− , "For example:"
385− , prettyPrintDictionaryValue d1
386− , "and:"
387− , prettyPrintDictionaryValue d2
388− ]
389− _ -> case chooseSimplestDictionaries dicts of
390− [] -> throwError . strMsg $
391− "No instance found for " ++ show className ++ " " ++ unwords (map prettyPrintTypeAtom tys)
392− d : _ -> return $ dictionaryValueToValue d
393− -- Choose the simplest DictionaryValues from a list of candidates
394− -- The reason for this function is as follows:
395− -- When considering overlapping instances, we don't want to consider the same dictionary
396− -- to be an overlap of itself when obtained as a superclass of another class.
397− -- Observing that we probably don't want to select a superclass instance when an instance
398− -- is available directly, and that there is no way for a superclass instance to actually
399− -- introduce an overlap that wouldn't have been there already, we simply remove dictionaries
400− -- obtained as superclass instances if there are simpler instances available.
401− chooseSimplestDictionaries :: [DictionaryValue] -> [DictionaryValue]
402− chooseSimplestDictionaries ds = case filter isSimpleDictionaryValue ds of
403− [] -> ds
404− simple -> simple
405− isSimpleDictionaryValue SubclassDictionaryValue{} = False
406− isSimpleDictionaryValue (DependentDictionaryValue _ ds) = all isSimpleDictionaryValue ds
407− isSimpleDictionaryValue _ = True
408− -- |
409− -- Check if two dictionaries are overlapping
410− --
411− -- Dictionaries which are subclass dictionaries cannot overlap, since otherwise the overlap would have
412− -- been caught when constructing superclass dictionaries.
413− --
414− overlapping :: DictionaryValue -> DictionaryValue -> Bool
415− overlapping (LocalDictionaryValue nm1) (LocalDictionaryValue nm2) | nm1 == nm2 = False
416− overlapping (GlobalDictionaryValue nm1) (GlobalDictionaryValue nm2) | nm1 == nm2 = False
417− overlapping (DependentDictionaryValue nm1 ds1) (DependentDictionaryValue nm2 ds2)
418− | nm1 == nm2 = any id $ zipWith overlapping ds1 ds2
419− overlapping (SubclassDictionaryValue _ _ _) _ = False
420− overlapping _ (SubclassDictionaryValue _ _ _) = False
421− overlapping _ _ = True
422− -- |
423− -- Render a DictionaryValue fit for human consumption in error messages
424− --
425− prettyPrintDictionaryValue :: DictionaryValue -> String
426− prettyPrintDictionaryValue = unlines . indented 0
427− where
428− indented n (LocalDictionaryValue _) = [spaces n ++ "Dictionary in scope"]
429− indented n (GlobalDictionaryValue nm) = [spaces n ++ show nm]
430− indented n (DependentDictionaryValue nm args) = (spaces n ++ show nm ++ " via") : concatMap (indented (n + 2)) args
431− indented n (SubclassDictionaryValue sup nm _) = (spaces n ++ show nm ++ " via superclass") : indented (n + 2) sup
432−
433− spaces n = replicate n ' ' ++ "- "
434−
435− valUndefined :: Expr
436− valUndefined = Var (Qualified (Just (ModuleName [ProperName C.prim])) (Ident C.undefined))
437−
438−-- |
439−-- Check all values in a list pairwise match a predicate
440−--
441−pairwise :: (a -> a -> Bool) -> [a] -> Bool
442−pairwise _ [] = True
443−pairwise _ [_] = True
444−pairwise p (x : xs) = all (p x) xs && pairwise p xs
445−
446−-- |
447−-- Check that two types unify
448−--
449−unifiesWith :: Environment -> Type -> Type -> Bool
450−unifiesWith _ (TUnknown u1) (TUnknown u2) | u1 == u2 = True
451−unifiesWith _ (Skolem _ s1 _) (Skolem _ s2 _) | s1 == s2 = True
452−unifiesWith _ (TypeVar v1) (TypeVar v2) | v1 == v2 = True
453−unifiesWith _ (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = True
454−unifiesWith e (TypeApp h1 t1) (TypeApp h2 t2) = unifiesWith e h1 h2 && unifiesWith e t1 t2
455−unifiesWith e (SaturatedTypeSynonym name args) t2 =
456− case expandTypeSynonym' e name args of
457− Left _ -> False
458− Right t1 -> unifiesWith e t1 t2
459−unifiesWith e t1 t2@(SaturatedTypeSynonym _ _) = unifiesWith e t2 t1
460−unifiesWith _ _ _ = False
461−
462−-- |
463−-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
464−-- and return a substitution from type variables to types which makes the type heads unify.
465−--
466−typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
467−typeHeadsAreEqual _ _ (Skolem _ s1 _) (Skolem _ s2 _) | s1 == s2 = Just []
468−typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
469−typeHeadsAreEqual _ _ (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = Just []
470−typeHeadsAreEqual m e (TypeApp h1 t1) (TypeApp h2 t2) = (++) <$> typeHeadsAreEqual m e h1 h2 <*> typeHeadsAreEqual m e t1 t2
471−typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e name args of
472− Left _ -> Nothing
473− Right t1 -> typeHeadsAreEqual m e t1 t2
474−typeHeadsAreEqual _ _ _ _ = Nothing
475−
476−-- |
477−-- Ensure skolem variables do not escape their scope
478−--
479−skolemEscapeCheck :: Expr -> Check ()
480−skolemEscapeCheck (TypedValue False _ _) = return ()
481−skolemEscapeCheck root@TypedValue{} =
482− -- Every skolem variable is created when a ForAll type is skolemized.
483− -- This determines the scope of that skolem variable, which is copied from the SkolemScope
484− -- field of the ForAll constructor.
485− -- We traverse the tree top-down, and collect any SkolemScopes introduced by ForAlls.
486− -- If a Skolem is encountered whose SkolemScope is not in the current list, we have found
487− -- an escaped skolem variable.
488− let (_, f, _, _, _) = everythingWithContextOnValues [] [] (++) def go def def def
489− in case f root of
490− [] -> return ()
491− ((binding, val) : _) -> throwError $ mkErrorStack ("Rigid/skolem type variable " ++ maybe "" (("bound by " ++) . prettyPrintValue) binding ++ " has escaped.") (Just (ExprError val))
492− where
493− def s _ = (s, [])
494−
495− go :: [(SkolemScope, Expr)] -> Expr -> ([(SkolemScope, Expr)], [(Maybe Expr, Expr)])
496− go scos val@(TypedValue _ _ (ForAll _ _ (Just sco))) = ((sco, val) : scos, [])
497− go scos val@(TypedValue _ _ ty) = case collectSkolems ty \\ map fst scos of
498− (sco : _) -> (scos, [(findBindingScope sco, val)])
499− _ -> (scos, [])
500− where
501− collectSkolems :: Type -> [SkolemScope]
502− collectSkolems = nub . everythingOnTypes (++) collect
503− where
504− collect (Skolem _ _ scope) = [scope]
505− collect _ = []
506− go scos _ = (scos, [])
507− findBindingScope :: SkolemScope -> Maybe Expr
508− findBindingScope sco =
509− let (_, f, _, _, _) = everythingOnValues mappend (const mempty) go' (const mempty) (const mempty) (const mempty)
510− in getFirst $ f root
511− where
512− go' val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = First (Just val)
513− go' _ = mempty
514−skolemEscapeCheck val = throwError $ mkErrorStack "Untyped value passed to skolemEscapeCheck" (Just (ExprError val))
515−
516−-- |
517−-- Ensure a row contains no duplicate labels
518−--
519−setify :: Type -> Type
520−setify = rowFromList . first (M.toList . M.fromList) . rowToList
521−
522−-- |
523−-- \"Setify\" all rows occuring inside a value
524−--
525−setifyAll :: Type -> Type
526−setifyAll = everywhereOnTypes setify
527−
528−-- |
529−-- Replace outermost unsolved unification variables with named type variables
530−--
531−varIfUnknown :: Type -> Type
532−varIfUnknown ty =
533− let unks = nub $ unknowns ty
534− toName = (:) 't' . show
535− ty' = everywhereOnTypes typeToVar ty
536− typeToVar :: Type -> Type
537− typeToVar (TUnknown u) = TypeVar (toName u)
538− typeToVar t = t
539− in mkForAll (sort . map toName $ unks) ty'
540−
541−-- |
542−-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
543−-- or TypeClassDictionary values.
544−--
545−-- This is necessary during type checking to avoid unifying a polymorphic type with a
546−-- unification variable.
547−--
548−instantiatePolyTypeWithUnknowns :: Expr -> Type -> UnifyT Type Check (Expr, Type)
549−instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
550− ty' <- replaceVarWithUnknown ident ty
551− instantiatePolyTypeWithUnknowns val ty'
552−instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
553− dicts <- getTypeClassDictionaries
554− (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
555− return (foldl App val (map (flip (TypeClassDictionary True) dicts) constraints), ty')
556−instantiatePolyTypeWithUnknowns val ty = return (val, ty)
557−
558−-- |
559−-- Replace a single type variable with a new unification variable
560−--
561−replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
562−replaceVarWithUnknown ident ty = do
563− tu <- fresh
564− return $ replaceTypeVars ident tu ty
565−
566−-- |
567−-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
568−-- better error messages during unification.
569−--
570−replaceAllTypeSynonyms' :: Environment -> Type -> Either String Type
571−replaceAllTypeSynonyms' env d =
572− let
573− syns = map (\(name, (args, _)) -> (name, length args)) . M.toList $ typeSynonyms env
574− in
575− saturateAllTypeSynonyms syns d
576−
577−replaceAllTypeSynonyms :: (Error e, Functor m, Monad m, MonadState CheckState m, MonadError e m) => Type -> m Type
578−replaceAllTypeSynonyms d = do
579− env <- getEnv
580− either (throwError . strMsg) return $ replaceAllTypeSynonyms' env d
581−
582−-- |
583−-- \"Desaturate\" @SaturatedTypeSynonym@s
584−--
585−desaturateAllTypeSynonyms :: Type -> Type
586−desaturateAllTypeSynonyms = everywhereOnTypes replaceSaturatedTypeSynonym
587− where
588− replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
589− replaceSaturatedTypeSynonym t = t
590−
591−-- |
592−-- Replace a type synonym and its arguments with the aliased type
593−--
594−expandTypeSynonym' :: Environment -> Qualified ProperName -> [Type] -> Either String Type
595−expandTypeSynonym' env name args =
596− case M.lookup name (typeSynonyms env) of
597− Just (synArgs, body) -> do
598− let repl = replaceAllTypeVars (zip synArgs args) body
599− replaceAllTypeSynonyms' env repl
600− Nothing -> error "Type synonym was not defined"
601−
602−expandTypeSynonym :: (Error e, Functor m, Monad m, MonadState CheckState m, MonadError e m) => Qualified ProperName -> [Type] -> m Type
603−expandTypeSynonym name args = do
604− env <- getEnv
605− either (throwError . strMsg) return $ expandTypeSynonym' env name args
606−
607−expandAllTypeSynonyms :: (Error e, Functor m, Applicative m, Monad m, MonadState CheckState m, MonadError e m) => Type -> m Type
608−expandAllTypeSynonyms = everywhereOnTypesTopDownM go
609− where
610− go (SaturatedTypeSynonym name args) = expandTypeSynonym name args
611− go other = return other
612−
613−-- |
614−-- Ensure a set of property names and value does not contain duplicate labels
615−--
616−ensureNoDuplicateProperties :: (Error e, MonadError e m) => [(String, Expr)] -> m ()
617−ensureNoDuplicateProperties ps = guardWith (strMsg "Duplicate property names") $ length (nub . map fst $ ps) == length ps
618−
619−-- |
620−-- Infer a type for a value, rethrowing any error to provide a more useful error message
621−--
622−infer :: Expr -> UnifyT Type Check Expr
623−infer val = rethrow (mkErrorStack "Error inferring type of value" (Just (ExprError val)) <>) $ infer' val
624−
625−-- |
626−-- Infer a type for a value
627−--
628−infer' :: Expr -> UnifyT Type Check Expr
629−infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
630−infer' v@(StringLiteral _) = return $ TypedValue True v tyString
631−infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
632−infer' (ArrayLiteral vals) = do
633− ts <- mapM infer vals
634− els <- fresh
635− forM_ ts $ \(TypedValue _ _ t) -> els =?= t
636− return $ TypedValue True (ArrayLiteral ts) (TypeApp tyArray els)
637−infer' (ObjectLiteral ps) = do
638− ensureNoDuplicateProperties ps
639− ts <- mapM (infer . snd) ps
640− let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
641− ty = TypeApp tyObject $ rowFromList (fields, REmpty)
642− return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
643−infer' (ObjectUpdate o ps) = do
644− ensureNoDuplicateProperties ps
645− row <- fresh
646− newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
647− let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
648− oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
649− let oldTy = TypeApp tyObject $ rowFromList (oldTys, row)
650− o' <- TypedValue True <$> check o oldTy <*> pure oldTy
651− return $ TypedValue True (ObjectUpdate o' newVals) $ TypeApp tyObject $ rowFromList (newTys, row)
652−infer' (Accessor prop val) = do
653− typed@(TypedValue _ _ objTy) <- infer val
654− propTy <- inferProperty objTy prop
655− case propTy of
656− Nothing -> do
657− field <- fresh
658− rest <- fresh
659− _ <- subsumes Nothing objTy (TypeApp tyObject (RCons prop field rest))
660− return $ TypedValue True (Accessor prop typed) field
661− Just ty -> return $ TypedValue True (Accessor prop typed) ty
662−infer' (Abs (Left arg) ret) = do
663− ty <- fresh
664− Just moduleName <- checkCurrentModule <$> get
665− makeBindingGroupVisible $ bindLocalVariables moduleName [(arg, ty, Defined)] $ do
666− body@(TypedValue _ _ bodyTy) <- infer' ret
667− return $ TypedValue True (Abs (Left arg) body) $ function ty bodyTy
668−infer' (Abs (Right _) _) = error "Binder was not desugared"
669−infer' (App f arg) = do
670− f'@(TypedValue _ _ ft) <- infer f
671− (ret, app) <- checkFunctionApplication f' ft arg Nothing
672− return $ TypedValue True app ret
673−infer' (Var var) = do
674− Just moduleName <- checkCurrentModule <$> get
675− checkVisibility moduleName var
676− ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
677− case ty of
678− ConstrainedType constraints ty' -> do
679− dicts <- getTypeClassDictionaries
680− return $ TypedValue True (foldl App (Var var) (map (flip (TypeClassDictionary True) dicts) constraints)) ty'
681− _ -> return $ TypedValue True (Var var) ty
682−infer' v@(Constructor c) = do
683− env <- getEnv
684− case M.lookup c (dataConstructors env) of
685− Nothing -> throwError . strMsg $ "Constructor " ++ show c ++ " is undefined"
686− Just (_, _, ty) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
687− return $ TypedValue True v ty'
688−infer' (Case vals binders) = do
689− ts <- mapM infer vals
690− ret <- fresh
691− binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
692− return $ TypedValue True (Case ts binders') ret
693−infer' (IfThenElse cond th el) = do
694− cond' <- check cond tyBoolean
695− v2@(TypedValue _ _ t2) <- infer th
696− v3@(TypedValue _ _ t3) <- infer el
697− (v2', v3', t) <- meet v2 v3 t2 t3
698− return $ TypedValue True (IfThenElse cond' v2' v3') t
699−infer' (Let ds val) = do
700− (ds', val'@(TypedValue _ _ valTy)) <- inferLetBinding [] ds val infer
701− return $ TypedValue True (Let ds' val') valTy
702−infer' (SuperClassDictionary className tys) = do
703− dicts <- getTypeClassDictionaries
704− return $ TypeClassDictionary False (className, tys) dicts
705−infer' (TypedValue checkType val ty) = do
706− Just moduleName <- checkCurrentModule <$> get
707− kind <- liftCheck $ kindOf moduleName ty
708− guardWith (strMsg $ "Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
709− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
710− val' <- if checkType then check val ty' else return val
711− return $ TypedValue True val' ty'
712−infer' (PositionedValue pos val) = rethrowWithPosition pos $ infer' val
713−infer' _ = error "Invalid argument to infer"
714−
715−inferLetBinding :: [Declaration] -> [Declaration] -> Expr -> (Expr -> UnifyT Type Check Expr) -> UnifyT Type Check ([Declaration], Expr)
716−inferLetBinding seen [] ret j = (,) seen <$> makeBindingGroupVisible (j ret)
717−inferLetBinding seen (ValueDeclaration ident nameKind [] Nothing tv@(TypedValue checkType val ty) : rest) ret j = do
718− Just moduleName <- checkCurrentModule <$> get
719− kind <- liftCheck $ kindOf moduleName ty
720− guardWith (strMsg $ "Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
721− let dict = M.singleton (moduleName, ident) (ty, nameKind, Undefined)
722− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
723− TypedValue _ val' ty'' <- if checkType then bindNames dict (check val ty') else return tv
724− bindNames (M.singleton (moduleName, ident) (ty'', nameKind, Defined)) $ inferLetBinding (seen ++ [ValueDeclaration ident nameKind [] Nothing (TypedValue checkType val' ty'')]) rest ret j
725−inferLetBinding seen (ValueDeclaration ident nameKind [] Nothing val : rest) ret j = do
726− valTy <- fresh
727− Just moduleName <- checkCurrentModule <$> get
728− let dict = M.singleton (moduleName, ident) (valTy, nameKind, Undefined)
729− TypedValue _ val' valTy' <- bindNames dict $ infer val
730− valTy =?= valTy'
731− bindNames (M.singleton (moduleName, ident) (valTy', nameKind, Defined)) $ inferLetBinding (seen ++ [ValueDeclaration ident nameKind [] Nothing val']) rest ret j
732−inferLetBinding seen (BindingGroupDeclaration ds : rest) ret j = do
733− Just moduleName <- checkCurrentModule <$> get
734− (untyped, typed, dict, untypedDict) <- typeDictionaryForBindingGroup moduleName (map (\(i, _, v) -> (i, v)) ds)
735− ds1' <- parU typed $ \e -> checkTypedBindingGroupElement moduleName e dict
736− ds2' <- forM untyped $ \e -> typeForBindingGroupElement e dict untypedDict
737− let ds' = [(ident, LocalVariable, val') | (ident, (val', _)) <- ds1' ++ ds2']
738− makeBindingGroupVisible $ bindNames dict $ inferLetBinding (seen ++ [BindingGroupDeclaration ds']) rest ret j
739−inferLetBinding seen (PositionedDeclaration pos d : ds) ret j = rethrowWithPosition pos $ do
740− ((d' : ds'), val') <- inferLetBinding seen (d : ds) ret j
741− return (PositionedDeclaration pos d' : ds', val')
742−inferLetBinding _ _ _ _ = error "Invalid argument to inferLetBinding"
743−
744−-- |
745−-- Infer the type of a property inside a record with a given type
746−--
747−inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
748−inferProperty (TypeApp obj row) prop | obj == tyObject = do
749− let (props, _) = rowToList row
750− return $ lookup prop props
751−inferProperty (SaturatedTypeSynonym name args) prop = do
752− replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
753− inferProperty replaced prop
754−inferProperty (ForAll ident ty _) prop = do
755− replaced <- replaceVarWithUnknown ident ty
756− inferProperty replaced prop
757−inferProperty _ _ = return Nothing
758−
759−-- |
760−-- Infer the types of variables brought into scope by a binder
761−--
762−inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
763−inferBinder _ NullBinder = return M.empty
764−inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
765−inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
766−inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
767−inferBinder val (VarBinder name) = return $ M.singleton name val
768−inferBinder val (ConstructorBinder ctor binders) = do
769− env <- getEnv
770− case M.lookup ctor (dataConstructors env) of
771− Just (_, _, ty) -> do
772− (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contain constraints") ty
773− fn' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ fn
774− go binders fn'
775− where
776− go [] ty' = do
777− _ <- subsumes Nothing val ty'
778− return M.empty
779− go (binder : binders') (TypeApp (TypeApp t obj) ret) | t == tyFunction =
780− M.union <$> inferBinder obj binder <*> go binders' ret
781− go _ _ = throwError . strMsg $ "Wrong number of arguments to constructor " ++ show ctor
782− _ -> throwError . strMsg $ "Constructor " ++ show ctor ++ " is not defined"
783−inferBinder val (ObjectBinder props) = do
784− row <- fresh
785− rest <- fresh
786− m1 <- inferRowProperties row rest props
787− val =?= TypeApp tyObject row
788− return m1
789− where
790− inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
791− inferRowProperties nrow row [] = nrow =?= row >> return M.empty
792− inferRowProperties nrow row ((name, binder):binders) = do
793− propTy <- fresh
794− m1 <- inferBinder propTy binder
795− m2 <- inferRowProperties nrow (RCons name propTy row) binders
796− return $ m1 `M.union` m2
797−inferBinder val (ArrayBinder binders) = do
798− el <- fresh
799− m1 <- M.unions <$> mapM (inferBinder el) binders
800− val =?= TypeApp tyArray el
801− return m1
802−inferBinder val (ConsBinder headBinder tailBinder) = do
803− el <- fresh
804− m1 <- inferBinder el headBinder
805− m2 <- inferBinder val tailBinder
806− val =?= TypeApp tyArray el
807− return $ m1 `M.union` m2
808−inferBinder val (NamedBinder name binder) = do
809− m <- inferBinder val binder
810− return $ M.insert name val m
811−inferBinder val (PositionedBinder pos binder) =
812− rethrowWithPosition pos $ inferBinder val binder
813−
814−-- |
815−-- Check the types of the return values in a set of binders in a case statement
816−--
817−checkBinders :: [Type] -> Type -> [CaseAlternative] -> UnifyT Type Check [CaseAlternative]
818−checkBinders _ _ [] = return []
819−checkBinders nvals ret (CaseAlternative binders grd val : bs) = do
820− guardWith (strMsg "Overlapping binders in case statement") $
821− let ns = concatMap binderNames binders in length (nub ns) == length ns
822− Just moduleName <- checkCurrentModule <$> get
823− m1 <- M.unions <$> zipWithM inferBinder nvals binders
824− r <- bindLocalVariables moduleName [ (name, ty, Defined) | (name, ty) <- M.toList m1 ] $ do
825− val' <- TypedValue True <$> check val ret <*> pure ret
826− case grd of
827− Nothing -> return $ CaseAlternative binders Nothing val'
828− Just g -> do
829− g' <- check g tyBoolean
830− return $ CaseAlternative binders (Just g') val'
831− rs <- checkBinders nvals ret bs
832− return $ r : rs
833−
834−-- |
835−-- Generate a new skolem constant
836−--
837−newSkolemConstant :: UnifyT Type Check Int
838−newSkolemConstant = fresh'
839−
840−-- |
841−-- Generate a new skolem scope
842−--
843−newSkolemScope :: UnifyT Type Check SkolemScope
844−newSkolemScope = SkolemScope <$> fresh'
845−
846−-- |
847−-- Skolemize a type variable by replacing its instances with fresh skolem constants
848−--
849−skolemize :: String -> Int -> SkolemScope -> Type -> Type
850−skolemize ident sko scope = replaceTypeVars ident (Skolem ident sko scope)
851−
852−-- |
853−-- This function has one purpose - to skolemize type variables appearing in a
854−-- SuperClassDictionary placeholder. These type variables are somewhat unique since they are the
855−-- only example of scoped type variables.
856−--
857−skolemizeTypesInValue :: String -> Int -> SkolemScope -> Expr -> Expr
858−skolemizeTypesInValue ident sko scope = let (_, f, _) = everywhereOnValues id go id in f
859− where
860− go (SuperClassDictionary c ts) = SuperClassDictionary c (map (skolemize ident sko scope) ts)
861− go other = other
862−
863−-- |
864−-- Introduce skolem scope at every occurence of a ForAll
865−--
866−introduceSkolemScope :: Type -> UnifyT Type Check Type
867−introduceSkolemScope = everywhereOnTypesM go
868− where
869− go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
870− go other = return other
871−
872−-- |
873−-- Check the type of a value, rethrowing errors to provide a better error message
874−--
875−check :: Expr -> Type -> UnifyT Type Check Expr
876−check val ty = rethrow (mkErrorStack errorMessage (Just (ExprError val)) <>) $ check' val ty
877− where
878− errorMessage =
879− "Error checking type of term " ++
880− prettyPrintValue val ++
881− " against type " ++
882− prettyPrintType ty
883−
884−-- |
885−-- Check the type of a value
886−--
887−check' :: Expr -> Type -> UnifyT Type Check Expr
888−check' val (ForAll ident ty _) = do
889− scope <- newSkolemScope
890− sko <- newSkolemConstant
891− let sk = skolemize ident sko scope ty
892− let skVal = skolemizeTypesInValue ident sko scope val
893− val' <- check skVal sk
894− return $ TypedValue True val' (ForAll ident ty (Just scope))
895−check' val t@(ConstrainedType constraints ty) = do
896− dictNames <- forM constraints $ \(Qualified _ (ProperName className), _) -> do
897− n <- liftCheck freshDictionaryName
898− return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
899− val' <- makeBindingGroupVisible $ withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
900− TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular False) (map (Qualified Nothing) dictNames)
901− constraints) $ check val ty
902− return $ TypedValue True (foldr (Abs . Left) val' dictNames) t
903−check' val (SaturatedTypeSynonym name args) = do
904− ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
905− check val ty
906−check' val u@(TUnknown _) = do
907− val'@(TypedValue _ _ ty) <- infer val
908− -- Don't unify an unknown with an inferred polytype
909− (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
910− ty' =?= u
911− return $ TypedValue True val'' ty'
912−check' v@(NumericLiteral _) t | t == tyNumber =
913− return $ TypedValue True v t
914−check' v@(StringLiteral _) t | t == tyString =
915− return $ TypedValue True v t
916−check' v@(BooleanLiteral _) t | t == tyBoolean =
917− return $ TypedValue True v t
918−check' (ArrayLiteral vals) t@(TypeApp a ty) = do
919− a =?= tyArray
920− array <- ArrayLiteral <$> forM vals (`check` ty)
921− return $ TypedValue True array t
922−check' (Abs (Left arg) ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
923− Just moduleName <- checkCurrentModule <$> get
924− ret' <- makeBindingGroupVisible $ bindLocalVariables moduleName [(arg, argTy, Defined)] $ check ret retTy
925− return $ TypedValue True (Abs (Left arg) ret') ty
926−check' (Abs (Right _) _) _ = error "Binder was not desugared"
927−check' (App f arg) ret = do
928− f'@(TypedValue _ _ ft) <- infer f
929− (_, app) <- checkFunctionApplication f' ft arg (Just ret)
930− return $ TypedValue True app ret
931−check' v@(Var var) ty = do
932− Just moduleName <- checkCurrentModule <$> get
933− checkVisibility moduleName var
934− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
935− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
936− v' <- subsumes (Just v) repl ty'
937− case v' of
938− Nothing -> throwError . strMsg $ "Unable to check type subsumption"
939− Just v'' -> return $ TypedValue True v'' ty'
940−check' (SuperClassDictionary className tys) _ = do
941− {-
942− -- Here, we replace a placeholder for a superclass dictionary with a regular
943− -- TypeClassDictionary placeholder. The reason we do this is that it is necessary to have the
944− -- correct super instance dictionaries in scope, and these are not available when the type class
945− -- declaration gets desugared.
946− --
947− -- Note also that the first argument to TypeClassDictionary is False, meaning we _do not_ want
948− -- to consider superclass instances when searching for this dictionary - doing so might lead
949− -- to traversing a cycle in the instance graph.
950− -}
951− dicts <- getTypeClassDictionaries
952− return $ TypeClassDictionary False (className, tys) dicts
953−check' (TypedValue checkType val ty1) ty2 = do
954− Just moduleName <- checkCurrentModule <$> get
955− kind <- liftCheck $ kindOf moduleName ty1
956− guardWith (strMsg $ "Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
957− ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
958− ty2' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty2
959− val' <- subsumes (Just val) ty1' ty2'
960− case val' of
961− Nothing -> throwError . strMsg $ "Unable to check type subsumption"
962− Just val'' -> do
963− val''' <- if checkType then check val'' ty2' else return val''
964− return $ TypedValue checkType (TypedValue True val''' ty1') ty2'
965−check' (Case vals binders) ret = do
966− vals' <- mapM infer vals
967− let ts = map (\(TypedValue _ _ t) -> t) vals'
968− binders' <- checkBinders ts ret binders
969− return $ TypedValue True (Case vals' binders') ret
970−check' (IfThenElse cond th el) ty = do
971− cond' <- check cond tyBoolean
972− th' <- check th ty
973− el' <- check el ty
974− return $ TypedValue True (IfThenElse cond' th' el') ty
975−check' (ObjectLiteral ps) t@(TypeApp obj row) | obj == tyObject = do
976− ensureNoDuplicateProperties ps
977− ps' <- checkProperties ps row False
978− return $ TypedValue True (ObjectLiteral ps') t
979−check' (TypeClassDictionaryConstructorApp name ps) t = do
980− ps' <- check' ps t
981− return $ TypedValue True (TypeClassDictionaryConstructorApp name ps') t
982−check' (ObjectUpdate obj ps) t@(TypeApp o row) | o == tyObject = do
983− ensureNoDuplicateProperties ps
984− us <- zip (map fst ps) <$> replicateM (length ps) fresh
985− let (propsToCheck, rest) = rowToList row
986− propsToRemove = map fst ps
987− remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
988− obj' <- check obj (TypeApp tyObject (rowFromList (us ++ remainingProps, rest)))
989− ps' <- checkProperties ps row True
990− return $ TypedValue True (ObjectUpdate obj' ps') t
991−check' (Accessor prop val) ty = do
992− rest <- fresh
993− val' <- check val (TypeApp tyObject (RCons prop ty rest))
994− return $ TypedValue True (Accessor prop val') ty
995−check' (Constructor c) ty = do
996− env <- getEnv
997− case M.lookup c (dataConstructors env) of
998− Nothing -> throwError . strMsg $ "Constructor " ++ show c ++ " is undefined"
999− Just (_, _, ty1) -> do
1000− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
1001− _ <- subsumes Nothing repl ty
1002− return $ TypedValue True (Constructor c) ty
1003−check' (Let ds val) ty = do
1004− (ds', val') <- inferLetBinding [] ds val (flip check ty)
1005− return $ TypedValue True (Let ds' val') ty
1006−check' val ty | containsTypeSynonyms ty = do
1007− ty' <- introduceSkolemScope <=< expandAllTypeSynonyms $ ty
1008− check val ty'
1009−check' val kt@(KindedType ty kind) = do
1010− guardWith (strMsg $ "Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
1011− val' <- check' val ty
1012− return $ TypedValue True val' kt
1013−check' (PositionedValue pos val) ty =
1014− rethrowWithPosition pos $ check val ty
1015−check' val ty = throwError $ mkErrorStack ("Expr does not have type " ++ prettyPrintType ty) (Just (ExprError val))
1016−
1017−containsTypeSynonyms :: Type -> Bool
1018−containsTypeSynonyms = everythingOnTypes (||) go where
1019− go (SaturatedTypeSynonym _ _) = True
1020− go _ = False
1021−
1022−-- |
1023−-- Check the type of a collection of named record fields
1024−--
1025−-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
1026−--
1027−checkProperties :: [(String, Expr)] -> Type -> Bool -> UnifyT Type Check [(String, Expr)]
1028−checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
1029− go [] [] REmpty = return []
1030− go [] [] u@(TUnknown _) = do u =?= REmpty
1031− return []
1032− go [] [] (Skolem _ _ _) | lax = return []
1033− go [] ((p, _): _) _ | lax = return []
1034− | otherwise = throwError $ mkErrorStack ("Object does not have property " ++ p) (Just (ExprError (ObjectLiteral ps)))
1035− go ((p,_):_) [] REmpty = throwError $ mkErrorStack ("Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row) (Just (ExprError (ObjectLiteral ps)))
1036− go ((p,v):ps') [] u@(TUnknown _) = do
1037− v'@(TypedValue _ _ ty) <- infer v
1038− rest <- fresh
1039− u =?= RCons p ty rest
1040− ps'' <- go ps' [] rest
1041− return $ (p, v') : ps''
1042− go ((p,v):ps') ts r =
1043− case lookup p ts of
1044− Nothing -> do
1045− v'@(TypedValue _ _ ty) <- infer v
1046− rest <- fresh
1047− r =?= RCons p ty rest
1048− ps'' <- go ps' ts rest
1049− return $ (p, v') : ps''
1050− Just ty -> do
1051− v' <- check v ty
1052− ps'' <- go ps' (delete (p, ty) ts) r
1053− return $ (p, v') : ps''
1054− go _ _ _ = throwError $ mkErrorStack ("Object does not have type " ++ prettyPrintType (TypeApp tyObject row)) (Just (ExprError (ObjectLiteral ps)))
1055−
1056−-- |
1057−-- Check the type of a function application, rethrowing errors to provide a better error message
1058−--
1059−checkFunctionApplication :: Expr -> Type -> Expr -> Maybe Type -> UnifyT Type Check (Type, Expr)
1060−checkFunctionApplication fn fnTy arg ret = rethrow (mkErrorStack errorMessage (Just (ExprError fn)) <>) $ do
1061− subst <- unifyCurrentSubstitution <$> UnifyT get
1062− checkFunctionApplication' fn (subst $? fnTy) arg (($?) subst <$> ret)
1063− where
1064− errorMessage = "Error applying function of type "
1065− ++ prettyPrintType fnTy
1066− ++ " to argument " ++ prettyPrintValue arg
1067−
1068−-- |
1069−-- Check the type of a function application
1070−--
1071−checkFunctionApplication' :: Expr -> Type -> Expr -> Maybe Type -> UnifyT Type Check (Type, Expr)
1072−checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg ret = do
1073− tyFunction' =?= tyFunction
1074− arg' <- check arg argTy
1075− case ret of
1076− Nothing -> return (retTy, App fn arg')
1077− Just ret' -> do
1078− Just app' <- subsumes (Just (App fn arg')) retTy ret'
1079− return (retTy, app')
1080−checkFunctionApplication' fn (ForAll ident ty _) arg ret = do
1081− replaced <- replaceVarWithUnknown ident ty
1082− checkFunctionApplication fn replaced arg ret
1083−checkFunctionApplication' fn u@(TUnknown _) arg ret = do
1084− arg' <- do
1085− TypedValue _ arg' t <- infer arg
1086− (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
1087− return $ TypedValue True arg'' t'
1088− let ty = (\(TypedValue _ _ t) -> t) arg'
1089− ret' <- maybe fresh return ret
1090− u =?= function ty ret'
1091− return (ret', App fn arg')
1092−checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg ret = do
1093− ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
1094− checkFunctionApplication fn ty arg ret
1095−checkFunctionApplication' fn (KindedType ty _) arg ret = do
1096− checkFunctionApplication fn ty arg ret
1097−checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg ret = do
1098− dicts <- getTypeClassDictionaries
1099− checkFunctionApplication' (foldl App fn (map (flip (TypeClassDictionary True) dicts) constraints)) fnTy arg ret
1100−checkFunctionApplication' fn fnTy dict@(TypeClassDictionary _ _ _) _ =
1101− return (fnTy, App fn dict)
1102−checkFunctionApplication' _ fnTy arg _ = throwError . strMsg $ "Cannot apply a function of type "
1103− ++ prettyPrintType fnTy
1104− ++ " to argument " ++ prettyPrintValue arg
1105−
1106−-- |
1107−-- Check whether one type subsumes another, rethrowing errors to provide a better error message
1108−--
1109−subsumes :: Maybe Expr -> Type -> Type -> UnifyT Type Check (Maybe Expr)
1110−subsumes val ty1 ty2 = rethrow (mkErrorStack errorMessage (ExprError <$> val) <>) $ subsumes' val ty1 ty2
1111− where
1112− errorMessage = "Error checking that type "
1113− ++ prettyPrintType ty1
1114− ++ " subsumes type "
1115− ++ prettyPrintType ty2
1116−
1117−-- |
1118−-- Check whether one type subsumes another
1119−--
1120−subsumes' :: Maybe Expr -> Type -> Type -> UnifyT Type Check (Maybe Expr)
1121−subsumes' val (ForAll ident ty1 _) ty2 = do
1122− replaced <- replaceVarWithUnknown ident ty1
1123− subsumes val replaced ty2
1124−subsumes' val ty1 (ForAll ident ty2 sco) =
1125− case sco of
1126− Just sco' -> do
1127− sko <- newSkolemConstant
1128− let sk = skolemize ident sko sco' ty2
1129− subsumes val ty1 sk
1130− Nothing -> throwError . strMsg $ "Skolem variable scope is unspecified"
1131−subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
1132− _ <- subsumes Nothing arg2 arg1
1133− _ <- subsumes Nothing ret1 ret2
1134− return val
1135−subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
1136− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
1137− subsumes val ty1 ty2
1138−subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
1139− ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
1140− subsumes val ty1 ty2
1141−subsumes' val (KindedType ty1 _) ty2 = do
1142− subsumes val ty1 ty2
1143−subsumes' val ty1 (KindedType ty2 _) = do
1144− subsumes val ty1 ty2
1145−subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
1146− dicts <- getTypeClassDictionaries
1147− subsumes' (Just $ foldl App val (map (flip (TypeClassDictionary True) dicts) constraints)) ty1 ty2
1148−subsumes' val (TypeApp f1 r1) (TypeApp f2 r2) | f1 == tyObject && f2 == tyObject = do
1149− let
1150− (ts1, r1') = rowToList r1
1151− (ts2, r2') = rowToList r2
1152− ts1' = sortBy (comparing fst) ts1
1153− ts2' = sortBy (comparing fst) ts2
1154− go ts1' ts2' r1' r2'
1155− return val
1156− where
1157− go [] ts2 r1' r2' = r1' =?= rowFromList (ts2, r2')
1158− go ts1 [] r1' r2' = r2' =?= rowFromList (ts1, r1')
1159− go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1' r2'
1160− | p1 == p2 = do _ <- subsumes Nothing ty1 ty2
1161− go ts1 ts2 r1' r2'
1162− | p1 < p2 = do rest <- fresh
1163− r2' =?= RCons p1 ty1 rest
1164− go ts1 ((p2, ty2) : ts2) r1' rest
1165− | otherwise = do rest <- fresh
1166− r1' =?= RCons p2 ty2 rest
1167− go ((p1, ty1) : ts1) ts2 rest r2'
1168−subsumes' val ty1 ty2@(TypeApp obj _) | obj == tyObject = subsumes val ty2 ty1
1169−subsumes' val ty1 ty2 = do
1170− ty1 =?= ty2
1171− return val
1172−
1173−-- |
1174−-- Compute the meet of two types, i.e. the most general type which both types subsume.
1175−-- TODO: handle constrained types
1176−--
1177−meet :: Expr -> Expr -> Type -> Type -> UnifyT Type Check (Expr, Expr, Type)
1178−meet e1 e2 (ForAll ident t1 _) t2 = do
1179− t1' <- replaceVarWithUnknown ident t1
1180− meet e1 e2 t1' t2
1181−meet e1 e2 t1 (ForAll ident t2 _) = do
1182− t2' <- replaceVarWithUnknown ident t2
1183− meet e1 e2 t1 t2'
1184−meet e1 e2 t1 t2 = do
1185− t1 =?= t2
1186− return (e1, e2, t1)
1187−
1188−
1189−
1190−
1191−
1192−
1193−