@@ -0,0 +1,953 @@
1+-----------------------------------------------------------------------------
3+-- Module : Language.PureScript.TypeChecker.Types
4+-- Copyright : (c) Phil Freeman 2013
7+-- Maintainer : Phil Freeman <paf31@cantab.net>
8+-- Stability : experimental
12+-- This module implements the type checker
14+-----------------------------------------------------------------------------
16+{-# OPTIONS_GHC -fno-warn-orphans #-}
17+{-# LANGUAGE DeriveDataTypeable #-}
18+{-# LANGUAGE FlexibleContexts #-}
19+{-# LANGUAGE MultiParamTypeClasses #-}
21+module Language.PureScript.TypeChecker.Types (
26+ The following functions represent the corresponding type checking judgements:
29+ Synthesize a type for a value
32+ Check a value has a given type
35+ Check an object with a given type contains specified properties
37+ checkFunctionApplication
38+ Check a function of a given type returns a value of another type when applied to its arguments
41+ Check a type subsumes another type
45+import Data.Maybe (maybeToList, isNothing, isJust, fromMaybe)
46+import qualified Data.Data as D
48+ (everythingWithContext, mkM, everywhereM, everything, mkT,
49+ something, everywhere, mkQ)
51+import Language.PureScript.Values
52+import Language.PureScript.Types
53+import Language.PureScript.Kinds
54+import Language.PureScript.Names
55+import Language.PureScript.TypeChecker.Monad
56+import Language.PureScript.TypeChecker.Kinds
57+import Language.PureScript.TypeChecker.Synonyms
58+import Language.PureScript.Pretty
60+import Control.Monad.State
61+import Control.Monad.Error
62+import Control.Monad.Reader
63+import Control.Monad.Unify
65+import Control.Applicative
66+import Control.Arrow (Arrow(..))
68+import qualified Data.Map as M
69+import Data.Function (on)
70+import Debug.Trace (trace)
72+instance Partial Type where
74+ isUnknown (TUnknown u) = Just u
75+ isUnknown _ = Nothing
77+instance Unifiable Check Type where
81+-- Unify two types, updating the current substitution
83+unifyTypes :: Type -> Type -> UnifyT Type Check ()
84+unifyTypes t1 t2 = rethrow (\e -> "Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2 ++ ":\n" ++ e) $ do
87+ unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
88+ unifyTypes' (TUnknown u) t = u =:= t
89+ unifyTypes' t (TUnknown u) = u =:= t
90+ unifyTypes' (SaturatedTypeSynonym name args) ty = do
91+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ args
93+ unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
94+ unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
96+ (Just sc1', Just sc2') -> do
97+ sko <- newSkolemConstant
98+ let sk1 = skolemize ident1 sko sc1' ty1
99+ let sk2 = skolemize ident2 sko sc2' ty2
100+ sk1 `unifyTypes` sk2
101+ _ -> throwError (prettyPrintType ty1)
102+ unifyTypes' (ForAll ident ty1 (Just sc)) ty2 = do
103+ sko <- newSkolemConstant
104+ let sk = skolemize ident sko sc ty1
106+ unifyTypes' (ForAll _ _ _) _ = throwError "Skolem variable scope is unspecified"
107+ unifyTypes' ty f@(ForAll _ _ _) = f `unifyTypes` ty
108+ unifyTypes' (Object row1) (Object row2) = row1 =?= row2
109+ unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
110+ unifyTypes' (TypeConstructor c1) (TypeConstructor c2) = do
112+ Just moduleName <- checkCurrentModule <$> get
113+ guardWith ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".") (typeConstructorsAreEqual env moduleName c1 c2)
114+ unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
117+ unifyTypes' (Skolem s1 _) (Skolem s2 _) | s1 == s2 = return ()
118+ unifyTypes' r1@(RCons _ _ _) r2 = unifyRows r1 r2
119+ unifyTypes' r1 r2@(RCons _ _ _) = unifyRows r1 r2
120+ unifyTypes' r1@REmpty r2 = unifyRows r1 r2
121+ unifyTypes' r1 r2@REmpty = unifyRows r1 r2
122+ unifyTypes' t3 t4 = throwError $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
125+-- Unify two rows, updating the current substitution
127+-- Common labels are first identified, and unified. Remaining labels and types are unified with a
128+-- trailing row unification variable, if appropriate, otherwise leftover labels result in a unification
131+unifyRows :: Type -> Type -> UnifyT Type Check ()
134+ (s1, r1') = rowToList r1
135+ (s2, r2') = rowToList r2
136+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
137+ sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
138+ sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
140+ forM_ int (uncurry (=?=))
141+ unifyRows' sd1 r1' sd2 r2'
143+ unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> UnifyT Type Check ()
144+ unifyRows' [] (TUnknown u) sd r = u =:= rowFromList (sd, r)
145+ unifyRows' sd r [] (TUnknown u) = u =:= rowFromList (sd, r)
146+ unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
148+ forM_ row $ \(_, t) -> occursCheck un t
150+ u =?= RCons name ty u'
151+ unifyRows' row r others u'
152+ unifyRows' [] REmpty [] REmpty = return ()
153+ unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
154+ unifyRows' [] (Skolem s1 _) [] (Skolem s2 _) | s1 == s2 = return ()
155+ unifyRows' sd3 r3 sd4 r4 = throwError $ "Cannot unify " ++ prettyPrintRow (rowFromList (sd3, r3)) ++ " with " ++ prettyPrintRow (rowFromList (sd4, r4)) ++ "."
158+-- Ensure type constructors are equal after canonicalization
160+typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
161+typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
164+-- Infer the types of multiple mutually-recursive values, and return elaborated values including
165+-- type class dictionaries and type annotations.
167+typesOf :: ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
168+typesOf moduleName vals = do
169+ tys <- fmap tidyUp . liftUnify $ do
170+ let es = map isTyped vals
171+ typed = filter (isJust . snd . snd) es
172+ untyped = filter (isNothing . snd . snd) es
173+ typedDict = map (\(ident, (_, Just ty)) -> (ident, ty)) typed
174+ untypedNames <- replicateM (length untyped) fresh
175+ let untypedDict = zip (map fst untyped) untypedNames
176+ dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable))) $ (map (id *** fst) typedDict) ++ untypedDict)
178+ triple@(_, (val, ty)) <- case e of
179+ (ident, (val, Just (ty, checkType))) -> do
180+ kind <- liftCheck $ kindOf moduleName ty
181+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
182+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
183+ val' <- bindNames dict $ if checkType
184+ then TypedValue True <$> check val ty' <*> pure ty'
185+ else return (TypedValue False val ty')
186+ return (ident, (val', ty'))
187+ (ident, (val, Nothing)) -> do
188+ TypedValue _ val' ty <- bindNames dict $ infer val
189+ ty =?= fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
190+ return (ident, (TypedValue True val' ty, ty))
191+ when (moduleName == ModuleName (ProperName "Main") && fst e == Ident "main") $ do
192+ [eff, a] <- replicateM 2 fresh
193+ ty =?= TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName (ProperName "Eff"))) (ProperName "Eff"))) eff) a
196+ forM tys $ \(ident, (val, ty)) -> do
197+ val' <- replaceTypeClassDictionaries moduleName val
198+ rethrow (("Error in " ++ show ident ++ ": \n") ++) $ skolemEscapeCheck val'
199+ return $ (ident, (overTypes (desaturateAllTypeSynonyms . setifyAll) $ val'
200+ , varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty))
202+ tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
205+-- Check if a value contains a type annotation
207+isTyped :: (Ident, Value) -> (Ident, (Value, Maybe (Type, Bool)))
208+isTyped (name, TypedValue checkType value ty) = (name, (value, Just (ty, checkType)))
209+isTyped (name, value) = (name, (value, Nothing))
212+-- Map a function over type annotations appearing inside a value
214+overTypes :: (Type -> Type) -> Value -> Value
215+overTypes f = everywhere (mkT f)
218+-- Replace type class dictionary placeholders with inferred type class dictionaries
220+replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
221+replaceTypeClassDictionaries mn = everywhereM (mkM go)
223+ go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
224+ go other = return other
227+-- Check that the current set of type class dictionaries entail the specified type class goal, and, if so,
228+-- return a type class dictionary reference.
230+entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, Type) -> Check Value
231+entails moduleName context goal@(className, ty) = do
234+ [] -> throwError $ "No " ++ show className ++ " instance found for " ++ prettyPrintType ty
235+ (dict : _) -> return dict
237+ go env (className', ty') =
238+ [ mkDictionary (canonicalizeDictionary tcd) args
241+ , typeConstructorsAreEqual env moduleName className' (tcdClassName tcd)
242+ , subst <- maybeToList $ typeHeadsAreEqual moduleName env ty' (tcdInstanceType tcd)
243+ , args <- solveSubgoals env subst (tcdDependencies tcd) ]
244+ solveSubgoals :: Environment -> [(String, Type)] -> Maybe [(Qualified ProperName, Type)] -> [Maybe [Value]]
245+ solveSubgoals _ _ Nothing = return Nothing
246+ solveSubgoals env subst (Just subgoals) = do
247+ dict <- mapM (go env) (replaceAllTypeVars subst subgoals)
249+ mkDictionary :: Qualified Ident -> Maybe [Value] -> Value
250+ mkDictionary fnName Nothing = Var fnName
251+ mkDictionary fnName (Just dicts) = foldl App (Var fnName) dicts
252+ filterModule :: TypeClassDictionaryInScope -> Bool
253+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
254+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
255+ filterModule _ = False
256+ canonicalizeDictionary :: TypeClassDictionaryInScope -> Qualified Ident
257+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDRegular, tcdName = nm }) = nm
258+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDAlias nm }) = nm
261+-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
262+-- and return a substitution from type variables to types which makes the type heads unify.
264+typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
265+typeHeadsAreEqual _ _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = Just []
266+typeHeadsAreEqual _ _ (TypeVar v) t = Just [(v, t)]
267+typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
268+typeHeadsAreEqual m e (TypeConstructor c1) (TypeConstructor c2) | typeConstructorsAreEqual e m c1 c2 = Just []
269+typeHeadsAreEqual m e (TypeApp h1 (TypeVar v)) (TypeApp h2 arg) = (:) (v, arg) <$> typeHeadsAreEqual m e h1 h2
270+typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
271+typeHeadsAreEqual _ _ _ _ = Nothing
274+-- Ensure unsolved unification variables do not escape
276+escapeCheck :: Value -> Type -> UnifyT Type Check ()
277+escapeCheck value ty = do
278+ subst <- unifyCurrentSubstitution <$> UnifyT get
279+ let visibleUnknowns = nub $ unknowns $ subst $? ty
280+ let allUnknowns = findAllTypes value
281+ forM_ allUnknowns $ \t -> do
282+ let unsolvedUnknowns = nub . unknowns $ subst $? t
283+ guardWith "Escape check fails" $ null $ unsolvedUnknowns \\ visibleUnknowns
286+-- Find all type annotations occuring inside a value
288+findAllTypes :: Value -> [Type]
289+findAllTypes = everything (++) (mkQ [] go)
291+ go (TypedValue _ _ ty) = [ty]
295+-- Ensure skolem variables do not escape their scope
297+skolemEscapeCheck :: Value -> Check ()
298+skolemEscapeCheck (TypedValue False _ _) = return ()
299+skolemEscapeCheck root@(TypedValue _ _ _) =
300+ case everythingWithContext [] (++) (mkQ ((,) []) go) root of
302+ ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
304+ go :: Value -> [(SkolemScope, Value)] -> ([(Maybe Value, Value)], [(SkolemScope, Value)])
305+ go val@(TypedValue _ _ (ForAll _ _ (Just sco))) scos = ([], (sco, val) : scos)
306+ go val@(TypedValue _ _ ty) scos = case collectSkolems ty \\ map fst scos of
307+ (sco : _) -> ([(findBindingScope sco, val)], scos)
310+ collectSkolems :: Type -> [SkolemScope]
311+ collectSkolems = nub . everything (++) (mkQ [] collect)
313+ collect (Skolem _ scope) = [scope]
315+ go _ scos = ([], scos)
316+ findBindingScope :: SkolemScope -> Maybe Value
317+ findBindingScope sco = something (mkQ Nothing go) root
319+ go val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
321+skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
324+-- Ensure a row contains no duplicate labels
326+setify :: Type -> Type
327+setify = rowFromList . first (M.toList . M.fromList) . rowToList
330+-- \"Setify\" all rows occuring inside a value
332+setifyAll :: (D.Data d) => d -> d
333+setifyAll = everywhere (mkT setify)
336+-- Replace outermost unsolved unification variables with named type variables
338+varIfUnknown :: Type -> Type
340+ let unks = nub $ unknowns ty
341+ toName = (:) 't' . show
342+ ty' = everywhere (mkT typeToVar) $ ty
343+ typeToVar :: Type -> Type
344+ typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
346+ in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
349+-- Replace named type variables with types
351+replaceAllTypeVars :: (D.Data d) => [(String, Type)] -> d -> d
352+replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
355+-- Replace named type variables with new unification variables
357+instantiatePolyTypeWithUnknowns :: Value -> Type -> UnifyT Type Check (Value, Type)
358+instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
359+ ty' <- replaceVarWithUnknown ident ty
360+ instantiatePolyTypeWithUnknowns val ty'
361+instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
363+ Just moduleName <- checkCurrentModule <$> get
364+ dicts <- getTypeClassDictionaries
365+ (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
366+ return (foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints)), ty')
367+instantiatePolyTypeWithUnknowns val ty = return (val, ty)
370+-- Replace a single type variable with a new unification variable
372+replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
373+replaceVarWithUnknown ident ty = do
375+ return $ replaceTypeVars ident tu $ ty
378+-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
379+-- better error messages during unification.
381+replaceAllTypeSynonyms :: (Functor m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
382+replaceAllTypeSynonyms d = do
384+ Just moduleName <- checkCurrentModule <$> get
385+ let syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
386+ either throwError return $ saturateAllTypeSynonyms env moduleName syns d
389+-- \"Desaturate\" @SaturatedTypeSynonym@s
391+desaturateAllTypeSynonyms :: (D.Data d) => d -> d
392+desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
394+ replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
395+ replaceSaturatedTypeSynonym t = t
398+-- Replace a type synonym and its arguments with the aliased type
400+expandTypeSynonym :: Qualified ProperName -> [Type] -> UnifyT Type Check Type
401+expandTypeSynonym name args = do
403+ Just moduleName <- checkCurrentModule <$> get
404+ case M.lookup (canonicalizeType moduleName env name) (typeSynonyms env) of
405+ Just (synArgs, body) -> return $ replaceAllTypeVars (zip synArgs args) body
406+ Nothing -> error "Type synonym was not defined"
409+-- Ensure a set of property names and value does not contain duplicate labels
411+ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
412+ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
415+-- Infer a type for a value, rethrowing any error to provide a more useful error message
417+infer :: Value -> UnifyT Type Check Value
418+infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
421+-- Infer a type for a value
423+infer' :: Value -> UnifyT Type Check Value
424+infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
425+infer' v@(StringLiteral _) = return $ TypedValue True v tyString
426+infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
427+infer' (ArrayLiteral vals) = do
428+ ts <- mapM infer vals
430+ forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
431+ return $ TypedValue True (ArrayLiteral ts) els
432+infer' (ObjectLiteral ps) = do
433+ ensureNoDuplicateProperties ps
434+ ts <- mapM (infer . snd) ps
435+ let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
436+ ty = Object $ rowFromList (fields, REmpty)
437+ return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
438+infer' (ObjectUpdate o ps) = do
439+ ensureNoDuplicateProperties ps
441+ newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
442+ let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
443+ oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
444+ let oldTy = Object $ rowFromList (oldTys, row)
445+ o' <- TypedValue True <$> check o oldTy <*> pure oldTy
446+ return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
447+infer' (Accessor prop val) = do
448+ typed@(TypedValue _ _ objTy) <- infer val
449+ propTy <- inferProperty objTy prop
454+ _ <- subsumes Nothing objTy (Object (RCons prop field rest))
455+ return $ TypedValue True (Accessor prop typed) field
456+ Just ty -> return $ TypedValue True (Accessor prop typed) ty
457+infer' (Abs arg ret) = do
459+ Just moduleName <- checkCurrentModule <$> get
460+ bindLocalVariables moduleName [(arg, ty)] $ do
461+ body@(TypedValue _ _ bodyTy) <- infer' ret
462+ return $ TypedValue True (Abs arg body) $ function ty bodyTy
463+infer' (App f arg) = do
464+ f'@(TypedValue _ _ ft) <- infer f
465+ (ret, app) <- checkFunctionApplication f' ft arg
466+ return $ TypedValue True app ret
467+infer' (Var var) = do
468+ Just moduleName <- checkCurrentModule <$> get
469+ ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
471+ ConstrainedType constraints ty' -> do
473+ dicts <- getTypeClassDictionaries
474+ return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) ty'
475+ _ -> return $ TypedValue True (Var var) ty
476+infer' (Block ss) = do
478+ (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
479+ guardWith "Block is missing a return statement" allCodePathsReturn
480+ return $ TypedValue True (Block ss') ret
481+infer' v@(Constructor c) = do
483+ Just moduleName <- checkCurrentModule <$> get
484+ case M.lookup (qualify moduleName c) (dataConstructors env) of
485+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
486+ Just (ty, _) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
487+ return $ TypedValue True v ty'
488+infer' (Case vals binders) = do
489+ ts <- mapM infer vals
491+ binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
492+ return $ TypedValue True (Case ts binders') ret
493+infer' (IfThenElse cond th el) = do
494+ cond' <- check cond tyBoolean
495+ v2@(TypedValue _ _ t2) <- infer th
496+ v3@(TypedValue _ _ t3) <- infer el
498+ return $ TypedValue True (IfThenElse cond' v2 v3) t2
499+infer' (TypedValue checkType val ty) = do
500+ Just moduleName <- checkCurrentModule <$> get
501+ kind <- liftCheck $ kindOf moduleName ty
502+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
503+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
504+ val' <- if checkType then check val ty' else return val
505+ return $ TypedValue True val' ty'
506+infer' _ = error "Invalid argument to infer"
509+-- Infer the type of a property inside a record with a given type
511+inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
512+inferProperty (Object row) prop = do
513+ let (props, _) = rowToList row
514+ return $ lookup prop props
515+inferProperty (SaturatedTypeSynonym name args) prop = do
516+ replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
517+ inferProperty replaced prop
518+inferProperty (ForAll ident ty _) prop = do
519+ replaced <- replaceVarWithUnknown ident ty
520+ inferProperty replaced prop
521+inferProperty _ _ = return Nothing
524+-- Infer the types of variables brought into scope by a binder
526+inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
527+inferBinder _ NullBinder = return M.empty
528+inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
529+inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
530+inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
531+inferBinder val (VarBinder name) = return $ M.singleton name val
532+inferBinder val (NullaryBinder ctor) = do
534+ Just moduleName <- checkCurrentModule <$> get
535+ case M.lookup (qualify moduleName ctor) (dataConstructors env) of
537+ _ <- subsumes Nothing ty val
539+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
540+inferBinder val (UnaryBinder ctor binder) = do
542+ Just moduleName <- checkCurrentModule <$> get
543+ case M.lookup (qualify moduleName ctor) (dataConstructors env) of
545+ (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contains constraints") ty
547+ TypeApp (TypeApp t obj) ret | t == tyFunction -> do
548+ _ <- subsumes Nothing val ret
549+ inferBinder obj binder
550+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not a unary constructor"
551+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
552+inferBinder val (ObjectBinder props) = do
555+ m1 <- inferRowProperties row rest props
559+ inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
560+ inferRowProperties nrow row [] = nrow =?= row >> return M.empty
561+ inferRowProperties nrow row ((name, binder):binders) = do
563+ m1 <- inferBinder propTy binder
564+ m2 <- inferRowProperties nrow (RCons name propTy row) binders
565+ return $ m1 `M.union` m2
566+inferBinder val (ArrayBinder binders) = do
568+ m1 <- M.unions <$> mapM (inferBinder el) binders
569+ val =?= TypeApp tyArray el
571+inferBinder val (ConsBinder headBinder tailBinder) = do
573+ m1 <- inferBinder el headBinder
574+ m2 <- inferBinder val tailBinder
575+ val =?= TypeApp tyArray el
576+ return $ m1 `M.union` m2
577+inferBinder val (NamedBinder name binder) = do
578+ m <- inferBinder val binder
579+ return $ M.insert name val m
582+-- Check the types of the return values in a set of binders in a case statement
584+checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> UnifyT Type Check [([Binder], Maybe Guard, Value)]
585+checkBinders _ _ [] = return []
586+checkBinders nvals ret ((binders, grd, val):bs) = do
587+ Just moduleName <- checkCurrentModule <$> get
588+ m1 <- M.unions <$> zipWithM inferBinder nvals binders
589+ r <- bindLocalVariables moduleName (M.toList m1) $ do
590+ val' <- TypedValue True <$> check val ret <*> pure ret
592+ Nothing -> return (binders, Nothing, val')
594+ g' <- check g tyBoolean
595+ return (binders, Just g', val')
596+ rs <- checkBinders nvals ret bs
600+-- Check that a local variable name is not already used
602+assignVariable :: Ident -> UnifyT Type Check ()
603+assignVariable name = do
604+ env <- checkEnv <$> get
605+ Just moduleName <- checkCurrentModule <$> get
606+ case M.lookup (moduleName, name) (names env) of
607+ Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
611+-- Check the type of the return values of a statement, returning whether or not the statement returns on
614+checkStatement :: M.Map Ident Type -> Type -> Statement -> UnifyT Type Check (Bool, M.Map Ident Type, Statement)
615+checkStatement mass _ (VariableIntroduction name val) = do
617+ val'@(TypedValue _ _ t) <- infer val
618+ return (False, M.insert name t mass, VariableIntroduction name val')
619+checkStatement mass _ (Assignment ident val) = do
620+ val'@(TypedValue _ _ t) <- infer val
621+ case M.lookup ident mass of
622+ Nothing -> throwError $ "No local variable with name " ++ show ident
623+ Just ty -> do t =?= ty
624+ return (False, mass, Assignment ident val')
625+checkStatement mass ret (While val inner) = do
626+ val' <- check val tyBoolean
627+ (allCodePathsReturn, _, inner') <- checkBlock mass ret inner
628+ return (allCodePathsReturn, mass, While val' inner')
629+checkStatement mass ret (If ifst) = do
630+ (allCodePathsReturn, ifst') <- checkIfStatement mass ret ifst
631+ return (allCodePathsReturn, mass, If ifst')
632+checkStatement mass ret (For ident start end inner) = do
633+ Just moduleName <- checkCurrentModule <$> get
634+ assignVariable ident
635+ start' <- check start tyNumber
636+ end' <- check end tyNumber
637+ (allCodePathsReturn, _, inner') <- bindLocalVariables moduleName [(ident, tyNumber)] $ checkBlock mass ret inner
638+ return (allCodePathsReturn, mass, For ident start' end' inner')
639+checkStatement mass ret (Return val) = do
640+ val' <- check val ret
641+ return (True, mass, Return (TypedValue True val' ret))
644+-- Check the type of an if-then-else statement
646+checkIfStatement :: M.Map Ident Type -> Type -> IfStatement -> UnifyT Type Check (Bool, IfStatement)
647+checkIfStatement mass ret (IfStatement val thens Nothing) = do
648+ val' <- check val tyBoolean
649+ (_, _, thens') <- checkBlock mass ret thens
650+ return (False, IfStatement val' thens' Nothing)
651+checkIfStatement mass ret (IfStatement val thens (Just elses)) = do
652+ val' <- check val tyBoolean
653+ (allCodePathsReturn1, _, thens') <- checkBlock mass ret thens
654+ (allCodePathsReturn2, elses') <- checkElseStatement mass ret elses
655+ return (allCodePathsReturn1 && allCodePathsReturn2, IfStatement val' thens' (Just elses'))
658+-- Check the type of an else statement
660+checkElseStatement :: M.Map Ident Type -> Type -> ElseStatement -> UnifyT Type Check (Bool, ElseStatement)
661+checkElseStatement mass ret (Else elses) = do
662+ (allCodePathsReturn, _, elses') <- checkBlock mass ret elses
663+ return (allCodePathsReturn, Else elses')
664+checkElseStatement mass ret (ElseIf ifst) = (id *** ElseIf) <$> checkIfStatement mass ret ifst
667+-- Check the type of the return value of a block of statements
669+checkBlock :: M.Map Ident Type -> Type -> [Statement] -> UnifyT Type Check (Bool, M.Map Ident Type, [Statement])
670+checkBlock mass _ [] = return (False, mass, [])
671+checkBlock mass ret (s:ss) = do
672+ Just moduleName <- checkCurrentModule <$> get
673+ (b1, mass1, s') <- checkStatement mass ret s
674+ bindLocalVariables moduleName (M.toList mass1) $ case (b1, ss) of
675+ (True, []) -> return (True, mass1, [s'])
676+ (True, _) -> throwError "Unreachable code"
678+ (b, m, ss'') <- checkBlock mass1 ret ss'
679+ return (b, m, s':ss'')
682+-- Generate a new skolem constant
684+newSkolemConstant :: UnifyT Type Check Int
685+newSkolemConstant = runUnknown <$> fresh'
688+-- Generate a new skolem scope
690+newSkolemScope :: UnifyT Type Check SkolemScope
691+newSkolemScope = SkolemScope . runUnknown <$> fresh'
694+-- Skolemize a type variable by replacing its instances with fresh skolem constants
696+skolemize :: (D.Data d) => String -> Int -> SkolemScope -> d -> d
697+skolemize ident sko scope d = replaceTypeVars ident (Skolem sko scope) d
700+-- Introduce skolem scope at every occurence of a ForAll
702+introduceSkolemScope :: Type -> UnifyT Type Check Type
703+introduceSkolemScope = everywhereM (mkM go)
705+ go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
706+ go other = return other
709+-- Check the type of a value, rethrowing errors to provide a better error message
711+check :: Value -> Type -> UnifyT Type Check Value
712+check val ty = rethrow errorMessage $ check' val ty
715+ "Error checking type of term " ++
716+ prettyPrintValue val ++
718+ prettyPrintType ty ++
723+-- Check the type of a value
725+check' :: Value -> Type -> UnifyT Type Check Value
726+check' val t@(ForAll ident ty _) = do
727+ scope <- newSkolemScope
728+ sko <- newSkolemConstant
729+ let sk = skolemize ident sko scope ty
730+ val' <- check val sk
731+ return $ TypedValue True val' (ForAll ident ty (Just scope))
732+check' val t@(ConstrainedType constraints ty) = do
734+ Just moduleName <- checkCurrentModule <$> get
735+ dictNames <- flip mapM constraints $ \(Qualified _ (ProperName className), _) -> do
736+ n <- liftCheck freshDictionaryName
737+ return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
738+ val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
739+ TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
740+ (qualifyAllUnqualifiedNames moduleName env constraints)) $
742+ return $ TypedValue True (foldr Abs val' dictNames) t
743+check' val t@(SaturatedTypeSynonym name args) = do
744+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
745+ val' <- check val ty
746+ return $ TypedValue True val' ty
747+check' val u@(TUnknown _) = do
748+ val'@(TypedValue _ _ ty) <- infer val
749+ -- Don't unify an unknown with an inferred polytype
750+ (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
752+ return $ TypedValue True val'' ty'
753+check' v@(NumericLiteral _) t | t == tyNumber =
754+ return $ TypedValue True v t
755+check' v@(StringLiteral _) t | t == tyString =
756+ return $ TypedValue True v t
757+check' v@(BooleanLiteral _) t | t == tyBoolean =
758+ return $ TypedValue True v t
759+check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
760+ arr <- ArrayLiteral <$> forM vals (\val -> check val ty)
761+ return $ TypedValue True arr t
762+check' (Abs arg ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
763+ Just moduleName <- checkCurrentModule <$> get
764+ ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
765+ return $ TypedValue True (Abs arg ret') ty
766+check' (App f arg) ret = do
767+ f'@(TypedValue _ _ ft) <- infer f
768+ (ret', app) <- checkFunctionApplication f' ft arg
769+ subsumes Nothing ret' ret
770+ return $ TypedValue True app ret
771+check' v@(Var var) ty = do
772+ Just moduleName <- checkCurrentModule <$> get
773+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
774+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
775+ v' <- subsumes (Just v) repl ty'
777+ Nothing -> throwError "Unable to check type subsumption"
778+ Just v'' -> return $ TypedValue True v'' ty'
779+check' (TypedValue checkType val ty1) ty2 = do
780+ Just moduleName <- checkCurrentModule <$> get
781+ kind <- liftCheck $ kindOf moduleName ty1
782+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
783+ val' <- subsumes (Just val) ty1 ty2
785+ Nothing -> throwError "Unable to check type subsumption"
787+ val''' <- if checkType then check val'' ty1 else return val''
788+ return $ TypedValue checkType (TypedValue True val''' ty1) ty2
789+check' (Case vals binders) ret = do
790+ vals' <- mapM infer vals
791+ let ts = map (\(TypedValue _ _ t) -> t) vals'
792+ binders' <- checkBinders ts ret binders
793+ return $ TypedValue True (Case vals' binders') ret
794+check' (IfThenElse cond th el) ty = do
795+ cond' <- check cond tyBoolean
798+ return $ TypedValue True (IfThenElse cond' th' el') ty
799+check' (ObjectLiteral ps) t@(Object row) = do
800+ ensureNoDuplicateProperties ps
801+ ps' <- checkProperties ps row False
802+ return $ TypedValue True (ObjectLiteral ps') t
803+check' (ObjectUpdate obj ps) t@(Object row) = do
804+ ensureNoDuplicateProperties ps
805+ us <- zip (map fst ps) <$> replicateM (length ps) fresh
806+ let (propsToCheck, rest) = rowToList row
807+ propsToRemove = map fst ps
808+ remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
809+ obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
810+ ps' <- checkProperties ps row True
811+ return $ TypedValue True (ObjectUpdate obj' ps') t
812+check' (Accessor prop val) ty = do
814+ val' <- check val (Object (RCons prop ty rest))
815+ return $ TypedValue True (Accessor prop val') ty
816+check' (Block ss) ret = do
817+ (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
818+ guardWith "Block is missing a return statement" allCodePathsReturn
819+ return $ TypedValue True (Block ss') ret
820+check' (Constructor c) ty = do
822+ Just moduleName <- checkCurrentModule <$> get
823+ case M.lookup (qualify moduleName c) (dataConstructors env) of
824+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
826+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
827+ _ <- subsumes Nothing repl ty
828+ return $ TypedValue True (Constructor c) ty
829+check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
832+-- Check the type of a collection of named record fields
834+-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
836+checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
837+checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
838+ go [] [] REmpty = return []
839+ go [] [] u@(TUnknown _) = do u =?= REmpty
841+ go [] [] (Skolem _ _) | lax = return []
842+ go [] ((p, _): _) _ | lax = return []
843+ | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
844+ go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
845+ go ((p,v):ps') [] u@(TUnknown _) = do
846+ v'@(TypedValue _ _ ty) <- infer v
848+ u =?= RCons p ty rest
849+ ps'' <- go ps' [] rest
850+ return $ (p, v') : ps''
851+ go ((p,v):ps') ts r =
854+ v'@(TypedValue _ _ ty) <- infer v
856+ r =?= RCons p ty rest
857+ ps'' <- go ps' ts rest
858+ return $ (p, v') : ps''
861+ ps'' <- go ps' (delete (p, ty) ts) r
862+ return $ (p, v') : ps''
863+ go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
866+-- Check the type of a function application, rethrowing errors to provide a better error message
868+checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
869+checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
871+ errorMessage msg = "Error applying function of type "
872+ ++ prettyPrintType fnTy
873+ ++ " to argument " ++ prettyPrintValue arg
877+-- Check the type of a function application
879+checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
880+checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
881+ tyFunction' =?= tyFunction
882+ arg' <- check arg argTy
883+ return (retTy, App fn arg')
884+checkFunctionApplication' fn (ForAll ident ty _) arg = do
885+ replaced <- replaceVarWithUnknown ident ty
886+ checkFunctionApplication fn replaced arg
887+checkFunctionApplication' fn u@(TUnknown _) arg = do
889+ TypedValue _ v t <- infer arg
890+ (v', t') <- instantiatePolyTypeWithUnknowns arg t
891+ return $ TypedValue True v' t'
892+ let ty = (\(TypedValue _ _ t) -> t) arg'
894+ u =?= function ty ret
895+ return (ret, App fn arg')
896+checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
897+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
898+ checkFunctionApplication fn ty arg
899+checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
901+ dicts <- getTypeClassDictionaries
902+ Just moduleName <- checkCurrentModule <$> get
903+ checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) fnTy arg
904+checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
905+ ++ prettyPrintType fnTy
906+ ++ " to argument " ++ prettyPrintValue arg
909+-- Check whether one type subsumes another, rethrowing errors to provide a better error message
911+subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
912+subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
914+ errorMessage msg = "Error checking that type "
915+ ++ prettyPrintType ty1
916+ ++ " subsumes type "
917+ ++ prettyPrintType ty2
921+-- Check whether one type subsumes another
923+subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
924+subsumes' val (ForAll ident ty1 _) ty2 = do
925+ replaced <- replaceVarWithUnknown ident ty1
926+ subsumes val replaced ty2
927+subsumes' val ty1 (ForAll ident ty2 sco) =
930+ sko <- newSkolemConstant
931+ let sk = skolemize ident sko sco' ty2
933+ Nothing -> throwError "Skolem variable scope is unspecified"
934+subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
935+ subsumes Nothing arg2 arg1
936+ subsumes Nothing ret1 ret2
938+subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
939+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
940+ subsumes val ty1 ty2
941+subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
942+ ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
943+ subsumes val ty1 ty2
944+subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
946+ dicts <- getTypeClassDictionaries
947+ Just moduleName <- checkCurrentModule <$> get
948+ _ <- subsumes' Nothing ty1 ty2
949+ return . Just $ foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))
950+subsumes' val ty1 ty2 = do