@@ -1,1040 +0,0 @@
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)
50−import Data.Generics.Extras
52−import Language.PureScript.Values
53−import Language.PureScript.Types
54−import Language.PureScript.Kinds
55−import Language.PureScript.Names
56−import Language.PureScript.TypeChecker.Monad
57−import Language.PureScript.TypeChecker.Kinds
58−import Language.PureScript.TypeChecker.Synonyms
59−import Language.PureScript.Pretty
61−import Control.Monad.State
62−import Control.Monad.Error
63−import Control.Monad.Reader
64−import Control.Monad.Unify
66−import Control.Applicative
67−import Control.Arrow (Arrow(..))
69−import qualified Data.Map as M
70−import Data.Function (on)
71−import Data.Ord (comparing)
73−instance Partial Type where
75− isUnknown (TUnknown u) = Just u
76− isUnknown _ = Nothing
78−instance Unifiable Check Type where
82−-- Unify two types, updating the current substitution
84−unifyTypes :: Type -> Type -> UnifyT Type Check ()
85−unifyTypes t1 t2 = rethrow (\e -> "Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2 ++ ":\n" ++ e) $ do
88− unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
89− unifyTypes' (TUnknown u) t = u =:= t
90− unifyTypes' t (TUnknown u) = u =:= t
91− unifyTypes' (SaturatedTypeSynonym name args) ty = do
92− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ args
94− unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
95− unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
97− (Just sc1', Just sc2') -> do
98− sko <- newSkolemConstant
99− let sk1 = skolemize ident1 sko sc1' ty1
100− let sk2 = skolemize ident2 sko sc2' ty2
101− sk1 `unifyTypes` sk2
102− _ -> throwError (prettyPrintType ty1)
103− unifyTypes' (ForAll ident ty1 (Just sc)) ty2 = do
104− sko <- newSkolemConstant
105− let sk = skolemize ident sko sc ty1
107− unifyTypes' (ForAll _ _ _) _ = throwError "Skolem variable scope is unspecified"
108− unifyTypes' ty f@(ForAll _ _ _) = f `unifyTypes` ty
109− unifyTypes' (Object row1) (Object row2) = row1 =?= row2
110− unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
111− unifyTypes' (TypeConstructor c1) (TypeConstructor c2) = do
113− Just moduleName <- checkCurrentModule <$> get
114− guardWith ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".") (typeConstructorsAreEqual env moduleName c1 c2)
115− unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
118− unifyTypes' (Skolem s1 _) (Skolem s2 _) | s1 == s2 = return ()
119− unifyTypes' r1@(RCons _ _ _) r2 = unifyRows r1 r2
120− unifyTypes' r1 r2@(RCons _ _ _) = unifyRows r1 r2
121− unifyTypes' r1@REmpty r2 = unifyRows r1 r2
122− unifyTypes' r1 r2@REmpty = unifyRows r1 r2
123− unifyTypes' t3 t4 = throwError $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
126−-- Unify two rows, updating the current substitution
128−-- Common labels are first identified, and unified. Remaining labels and types are unified with a
129−-- trailing row unification variable, if appropriate, otherwise leftover labels result in a unification
132−unifyRows :: Type -> Type -> UnifyT Type Check ()
135− (s1, r1') = rowToList r1
136− (s2, r2') = rowToList r2
137− int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
138− sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
139− sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
141− forM_ int (uncurry (=?=))
142− unifyRows' sd1 r1' sd2 r2'
144− unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> UnifyT Type Check ()
145− unifyRows' [] (TUnknown u) sd r = u =:= rowFromList (sd, r)
146− unifyRows' sd r [] (TUnknown u) = u =:= rowFromList (sd, r)
147− unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
149− forM_ row $ \(_, t) -> occursCheck un t
151− u =?= RCons name ty u'
152− unifyRows' row r others u'
153− unifyRows' [] REmpty [] REmpty = return ()
154− unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
155− unifyRows' [] (Skolem s1 _) [] (Skolem s2 _) | s1 == s2 = return ()
156− unifyRows' sd3 r3 sd4 r4 = throwError $ "Cannot unify (" ++ prettyPrintRow (rowFromList (sd3, r3)) ++ ") with (" ++ prettyPrintRow (rowFromList (sd4, r4)) ++ ")."
159−-- Ensure type constructors are equal after canonicalization
161−typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
162−typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
165−-- Infer the types of multiple mutually-recursive values, and return elaborated values including
166−-- type class dictionaries and type annotations.
168−typesOf :: Maybe ModuleName -> ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
169−typesOf mainModuleName moduleName vals = do
170− tys <- fmap tidyUp . liftUnify $ do
172− -- Map each declaration to a name/value pair, with an optional type, if the declaration is typed
173− es = map isTyped vals
174− -- Filter the typed and untyped declarations
175− typed = filter (isJust . snd . snd) es
176− untyped = filter (isNothing . snd . snd) es
177− -- Make a map of names to typed declarations
178− typedDict = map (\(ident, (_, Just (ty, _))) -> (ident, ty)) typed
179− -- Create fresh unification variables for the types of untyped declarations
180− untypedNames <- replicateM (length untyped) fresh
182− -- Make a map of names to the unification variables of untyped declarations
183− untypedDict = zip (map fst untyped) untypedNames
184− -- Create the dictionary of all name/type pairs, which will be added to the environment during type checking
185− dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable))) $ typedDict ++ untypedDict)
186− forM es $ \e@(_, (val, _)) -> do
187− -- If the declaration is a function, it has access to other values in the binding group.
188− -- If not, the generated code might fail at runtime since those values might be undefined.
189− let dict' = if isFunction val then dict else M.empty
190− triple@(_, (val, ty)) <- case e of
191− -- Typed declarations
192− (ident, (val, Just (ty, checkType))) -> do
194− kind <- liftCheck $ kindOf moduleName ty
195− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
196− -- Check the type with the new names in scope
197− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
198− val' <- bindNames dict' $ if checkType
199− then TypedValue True <$> check val ty' <*> pure ty'
200− else return (TypedValue False val ty')
201− return (ident, (val', ty'))
202− -- Untyped declarations
203− (ident, (val, Nothing)) -> do
204− -- Infer the type with the new names in scope
205− TypedValue _ val' ty <- bindNames dict' $ infer val
206− ty =?= fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
207− return (ident, (TypedValue True val' ty, ty))
208− -- If --main is enabled, need to check that `main` has type Eff eff a for some eff, a
209− when (Just moduleName == mainModuleName && fst e == Ident "main") $ do
210− [eff, a] <- replicateM 2 fresh
211− ty =?= TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName (ProperName "Eff"))) (ProperName "Eff"))) eff) a
212− -- Make sure unification variables do not escape
215− forM tys $ \(ident, (val, ty)) -> do
216− -- Replace type class dictionary placeholders with actual dictionaries
217− val' <- replaceTypeClassDictionaries moduleName val
218− -- Check skolem variables did not escape their scope
219− skolemEscapeCheck val'
220− -- Remove type synonyms placeholders, remove duplicate row fields, and replace
221− -- top-level unification variables with named type variables.
222− let val'' = overTypes (desaturateAllTypeSynonyms . setifyAll) val'
223− ty' = varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty
224− return $ (ident, (val'', ty'))
226− -- Apply the substitution that was returned from runUnify to both types and (type-annotated) values
227− tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
230−-- Check if a value introduces a function
232−isFunction :: Value -> Bool
233−isFunction (Abs _ _) = True
234−isFunction (TypedValue _ val _) = isFunction val
238−-- Check if a value contains a type annotation
240−isTyped :: (Ident, Value) -> (Ident, (Value, Maybe (Type, Bool)))
241−isTyped (name, TypedValue checkType value ty) = (name, (value, Just (ty, checkType)))
242−isTyped (name, value) = (name, (value, Nothing))
245−-- Map a function over type annotations appearing inside a value
247−overTypes :: (Type -> Type) -> Value -> Value
248−overTypes f = everywhere (mkT f)
251−-- Replace type class dictionary placeholders with inferred type class dictionaries
253−replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
254−replaceTypeClassDictionaries mn = everywhereM' (mkM go)
256− go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
257− go other = return other
260−-- Check that the current set of type class dictionaries entail the specified type class goal, and, if so,
261−-- return a type class dictionary reference.
263−entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, Type) -> Check Value
264−entails moduleName context goal@(className, ty) = do
267− [] -> throwError $ "No " ++ show className ++ " instance found for " ++ prettyPrintType ty
268− (dict : _) -> return dict
270− go env (className', ty') =
271− [ mkDictionary (canonicalizeDictionary tcd) args
273− -- Choose type class dictionaries in scope in the current module
275− -- Make sure the type class name matches the one we are trying to satisfy
276− , typeConstructorsAreEqual env moduleName className' (tcdClassName tcd)
277− -- Make sure the type unifies with the type in the type instance definition
278− , subst <- maybeToList $ typeHeadsAreEqual moduleName env ty' (tcdInstanceType tcd)
279− -- Solve any necessary subgoals
280− , args <- solveSubgoals env subst (tcdDependencies tcd) ]
281− -- Create dictionaries for subgoals which still need to be solved by calling go recursively
282− -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type
283− -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively.
284− solveSubgoals :: Environment -> [(String, Type)] -> Maybe [(Qualified ProperName, Type)] -> [Maybe [Value]]
285− solveSubgoals _ _ Nothing = return Nothing
286− solveSubgoals env subst (Just subgoals) = do
287− dict <- mapM (go env) (map (id *** replaceAllTypeVars subst) subgoals)
289− -- Make a dictionary from subgoal dictionaries by applying the correct function
290− mkDictionary :: Qualified Ident -> Maybe [Value] -> Value
291− mkDictionary fnName Nothing = Var fnName
292− mkDictionary fnName (Just []) = App (Var fnName) (ObjectLiteral [])
293− mkDictionary fnName (Just dicts) = foldl App (Var fnName) dicts
294− -- Filter out type dictionaries which are in scope in the current module
295− filterModule :: TypeClassDictionaryInScope -> Bool
296− filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
297− filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
298− filterModule _ = False
299− -- Resolve a type class dictionary in scope to an actual value by following any (TCDAlias) pointers
300− -- which originated from module imports
301− canonicalizeDictionary :: TypeClassDictionaryInScope -> Qualified Ident
302− canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDRegular, tcdName = nm }) = nm
303− canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDAlias nm }) = nm
306−-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
307−-- and return a substitution from type variables to types which makes the type heads unify.
309−typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
310−typeHeadsAreEqual _ _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = Just []
311−typeHeadsAreEqual _ _ (TypeVar v) t = Just [(v, t)]
312−typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
313−typeHeadsAreEqual m e (TypeConstructor c1) (TypeConstructor c2) | typeConstructorsAreEqual e m c1 c2 = Just []
314−typeHeadsAreEqual m e (TypeApp h1 (TypeVar v)) (TypeApp h2 arg) = (:) (v, arg) <$> typeHeadsAreEqual m e h1 h2
315−typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
316−typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e m name args of
318− Right t1 -> typeHeadsAreEqual m e t1 t2
319−typeHeadsAreEqual _ _ _ _ = Nothing
322−-- Ensure unsolved unification variables do not escape
324−escapeCheck :: Value -> Type -> UnifyT Type Check ()
325−escapeCheck value ty = do
326− subst <- unifyCurrentSubstitution <$> UnifyT get
327− let visibleUnknowns = nub $ unknowns $ subst $? ty
328− let allUnknowns = findAllTypes value
329− forM_ allUnknowns $ \t -> do
330− let unsolvedUnknowns = nub . unknowns $ subst $? t
331− guardWith "Escape check fails" $ null $ unsolvedUnknowns \\ visibleUnknowns
334−-- Find all type annotations occuring inside a value
336−findAllTypes :: Value -> [Type]
337−findAllTypes = everything (++) (mkQ [] go)
339− go (TypedValue _ _ ty) = [ty]
343−-- Ensure skolem variables do not escape their scope
345−skolemEscapeCheck :: Value -> Check ()
346−skolemEscapeCheck (TypedValue False _ _) = return ()
347−skolemEscapeCheck root@(TypedValue _ _ _) =
348− -- Every skolem variable is created when a ForAll type is skolemized.
349− -- This determines the scope of that skolem variable, which is copied from the SkolemScope
350− -- field of the ForAll constructor.
351− -- We traverse the tree top-down, and collect any SkolemScopes introduced by ForAlls.
352− -- If a Skolem is encountered whose SkolemScope is not in the current list, we have found
353− -- an escaped skolem variable.
354− case everythingWithContext [] (++) (mkQ ((,) []) go) root of
356− ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
358− go :: Value -> [(SkolemScope, Value)] -> ([(Maybe Value, Value)], [(SkolemScope, Value)])
359− go val@(TypedValue _ _ (ForAll _ _ (Just sco))) scos = ([], (sco, val) : scos)
360− go val@(TypedValue _ _ ty) scos = case collectSkolems ty \\ map fst scos of
361− (sco : _) -> ([(findBindingScope sco, val)], scos)
364− collectSkolems :: Type -> [SkolemScope]
365− collectSkolems = nub . everything (++) (mkQ [] collect)
367− collect (Skolem _ scope) = [scope]
369− go _ scos = ([], scos)
370− findBindingScope :: SkolemScope -> Maybe Value
371− findBindingScope sco = something (mkQ Nothing go) root
373− go val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
375−skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
378−-- Ensure a row contains no duplicate labels
380−setify :: Type -> Type
381−setify = rowFromList . first (M.toList . M.fromList) . rowToList
384−-- \"Setify\" all rows occuring inside a value
386−setifyAll :: (D.Data d) => d -> d
387−setifyAll = everywhere (mkT setify)
390−-- Replace outermost unsolved unification variables with named type variables
392−varIfUnknown :: Type -> Type
394− let unks = nub $ unknowns ty
395− toName = (:) 't' . show
396− ty' = everywhere (mkT typeToVar) $ ty
397− typeToVar :: Type -> Type
398− typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
400− in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
403−-- Replace named type variables with types
405−replaceAllTypeVars :: [(String, Type)] -> Type -> Type
406−replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
409−-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
410−-- or TypeClassDictionary values.
412−-- This is necessary during type checking to avoid unifying a polymorphic type with a
413−-- unification variable.
415−instantiatePolyTypeWithUnknowns :: Value -> Type -> UnifyT Type Check (Value, Type)
416−instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
417− ty' <- replaceVarWithUnknown ident ty
418− instantiatePolyTypeWithUnknowns val ty'
419−instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
421− Just moduleName <- checkCurrentModule <$> get
422− dicts <- getTypeClassDictionaries
423− (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
424− return (foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints)), ty')
425−instantiatePolyTypeWithUnknowns val ty = return (val, ty)
428−-- Replace a single type variable with a new unification variable
430−replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
431−replaceVarWithUnknown ident ty = do
433− return $ replaceTypeVars ident tu $ ty
436−-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
437−-- better error messages during unification.
439−replaceAllTypeSynonyms' :: (D.Data d) => Environment -> ModuleName -> d -> Either String d
440−replaceAllTypeSynonyms' env moduleName d =
442− syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
444− saturateAllTypeSynonyms env moduleName syns d
446−replaceAllTypeSynonyms :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
447−replaceAllTypeSynonyms d = do
449− Just moduleName <- checkCurrentModule <$> get
450− either throwError return $ replaceAllTypeSynonyms' env moduleName d
453−-- \"Desaturate\" @SaturatedTypeSynonym@s
455−desaturateAllTypeSynonyms :: (D.Data d) => d -> d
456−desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
458− replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
459− replaceSaturatedTypeSynonym t = t
462−-- Replace a type synonym and its arguments with the aliased type
464−expandTypeSynonym' :: Environment -> ModuleName -> Qualified ProperName -> [Type] -> Either String Type
465−expandTypeSynonym' env moduleName name args =
466− case M.lookup (canonicalizeType moduleName env name) (typeSynonyms env) of
467− Just (synArgs, body) -> do
468− let repl = replaceAllTypeVars (zip synArgs args) body
469− replaceAllTypeSynonyms' env moduleName repl
470− Nothing -> error "Type synonym was not defined"
472−expandTypeSynonym :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => Qualified ProperName -> [Type] -> m Type
473−expandTypeSynonym name args = do
475− Just moduleName <- checkCurrentModule <$> get
476− either throwError return $ expandTypeSynonym' env moduleName name args
479−-- Ensure a set of property names and value does not contain duplicate labels
481−ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
482−ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
485−-- Infer a type for a value, rethrowing any error to provide a more useful error message
487−infer :: Value -> UnifyT Type Check Value
488−infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
491−-- Infer a type for a value
493−infer' :: Value -> UnifyT Type Check Value
494−infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
495−infer' v@(StringLiteral _) = return $ TypedValue True v tyString
496−infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
497−infer' (ArrayLiteral vals) = do
498− ts <- mapM infer vals
500− forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
501− return $ TypedValue True (ArrayLiteral ts) els
502−infer' (ObjectLiteral ps) = do
503− ensureNoDuplicateProperties ps
504− ts <- mapM (infer . snd) ps
505− let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
506− ty = Object $ rowFromList (fields, REmpty)
507− return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
508−infer' (ObjectUpdate o ps) = do
509− ensureNoDuplicateProperties ps
511− newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
512− let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
513− oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
514− let oldTy = Object $ rowFromList (oldTys, row)
515− o' <- TypedValue True <$> check o oldTy <*> pure oldTy
516− return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
517−infer' (Accessor prop val) = do
518− typed@(TypedValue _ _ objTy) <- infer val
519− propTy <- inferProperty objTy prop
524− _ <- subsumes Nothing objTy (Object (RCons prop field rest))
525− return $ TypedValue True (Accessor prop typed) field
526− Just ty -> return $ TypedValue True (Accessor prop typed) ty
527−infer' (Abs arg ret) = do
529− Just moduleName <- checkCurrentModule <$> get
530− bindLocalVariables moduleName [(arg, ty)] $ do
531− body@(TypedValue _ _ bodyTy) <- infer' ret
532− return $ TypedValue True (Abs arg body) $ function ty bodyTy
533−infer' (App f arg) = do
534− f'@(TypedValue _ _ ft) <- infer f
535− (ret, app) <- checkFunctionApplication f' ft arg
536− return $ TypedValue True app ret
537−infer' (Var var) = do
538− Just moduleName <- checkCurrentModule <$> get
539− ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
541− ConstrainedType constraints ty' -> do
543− dicts <- getTypeClassDictionaries
544− return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) ty'
545− _ -> return $ TypedValue True (Var var) ty
546−infer' (Block ss) = do
548− (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
549− guardWith "Block is missing a return statement" allCodePathsReturn
550− return $ TypedValue True (Block ss') ret
551−infer' v@(Constructor c) = do
553− Just moduleName <- checkCurrentModule <$> get
554− case M.lookup (qualify moduleName c) (dataConstructors env) of
555− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
556− Just (ty, _) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
557− return $ TypedValue True v ty'
558−infer' (Case vals binders) = do
559− ts <- mapM infer vals
561− binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
562− return $ TypedValue True (Case ts binders') ret
563−infer' (IfThenElse cond th el) = do
564− cond' <- check cond tyBoolean
565− v2@(TypedValue _ _ t2) <- infer th
566− v3@(TypedValue _ _ t3) <- infer el
568− return $ TypedValue True (IfThenElse cond' v2 v3) t2
569−infer' (TypedValue checkType val ty) = do
570− Just moduleName <- checkCurrentModule <$> get
571− kind <- liftCheck $ kindOf moduleName ty
572− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
573− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
574− val' <- if checkType then check val ty' else return val
575− return $ TypedValue True val' ty'
576−infer' _ = error "Invalid argument to infer"
579−-- Infer the type of a property inside a record with a given type
581−inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
582−inferProperty (Object row) prop = do
583− let (props, _) = rowToList row
584− return $ lookup prop props
585−inferProperty (SaturatedTypeSynonym name args) prop = do
586− replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
587− inferProperty replaced prop
588−inferProperty (ForAll ident ty _) prop = do
589− replaced <- replaceVarWithUnknown ident ty
590− inferProperty replaced prop
591−inferProperty _ _ = return Nothing
594−-- Infer the types of variables brought into scope by a binder
596−inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
597−inferBinder _ NullBinder = return M.empty
598−inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
599−inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
600−inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
601−inferBinder val (VarBinder name) = return $ M.singleton name val
602−inferBinder val (ConstructorBinder ctor binders) = do
604− Just moduleName <- checkCurrentModule <$> get
605− case M.lookup (qualify moduleName ctor) (dataConstructors env) of
607− (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contains constraints") ty
611− subsumes Nothing val ty
613− go (binder : binders) (TypeApp (TypeApp t obj) ret) | t == tyFunction =
614− M.union <$> inferBinder obj binder <*> go binders ret
615− go _ _ = throwError $ "Wrong number of arguments to constructor " ++ show ctor
616− _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
617−inferBinder val (ObjectBinder props) = do
620− m1 <- inferRowProperties row rest props
624− inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
625− inferRowProperties nrow row [] = nrow =?= row >> return M.empty
626− inferRowProperties nrow row ((name, binder):binders) = do
628− m1 <- inferBinder propTy binder
629− m2 <- inferRowProperties nrow (RCons name propTy row) binders
630− return $ m1 `M.union` m2
631−inferBinder val (ArrayBinder binders) = do
633− m1 <- M.unions <$> mapM (inferBinder el) binders
634− val =?= TypeApp tyArray el
636−inferBinder val (ConsBinder headBinder tailBinder) = do
638− m1 <- inferBinder el headBinder
639− m2 <- inferBinder val tailBinder
640− val =?= TypeApp tyArray el
641− return $ m1 `M.union` m2
642−inferBinder val (NamedBinder name binder) = do
643− m <- inferBinder val binder
644− return $ M.insert name val m
647−-- Check the types of the return values in a set of binders in a case statement
649−checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> UnifyT Type Check [([Binder], Maybe Guard, Value)]
650−checkBinders _ _ [] = return []
651−checkBinders nvals ret ((binders, grd, val):bs) = do
652− Just moduleName <- checkCurrentModule <$> get
653− m1 <- M.unions <$> zipWithM inferBinder nvals binders
654− r <- bindLocalVariables moduleName (M.toList m1) $ do
655− val' <- TypedValue True <$> check val ret <*> pure ret
657− Nothing -> return (binders, Nothing, val')
659− g' <- check g tyBoolean
660− return (binders, Just g', val')
661− rs <- checkBinders nvals ret bs
665−-- Check that a local variable name is not already used
667−assignVariable :: Ident -> UnifyT Type Check ()
668−assignVariable name = do
669− env <- checkEnv <$> get
670− Just moduleName <- checkCurrentModule <$> get
671− case M.lookup (moduleName, name) (names env) of
672− Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
676−-- Check the type of the return values of a statement, returning whether or not the statement returns on
679−checkStatement :: M.Map Ident Type -> Type -> Statement -> UnifyT Type Check (Bool, M.Map Ident Type, Statement)
680−checkStatement mass _ (VariableIntroduction name val) = do
682− val'@(TypedValue _ _ t) <- infer val
683− return (False, M.insert name t mass, VariableIntroduction name val')
684−checkStatement mass _ (Assignment ident val) = do
685− val'@(TypedValue _ _ t) <- infer val
686− case M.lookup ident mass of
687− Nothing -> throwError $ "No local variable with name " ++ show ident
688− Just ty -> do t =?= ty
689− return (False, mass, Assignment ident val')
690−checkStatement mass ret (While val inner) = do
691− val' <- check val tyBoolean
692− (allCodePathsReturn, _, inner') <- checkBlock mass ret inner
693− return (allCodePathsReturn, mass, While val' inner')
694−checkStatement mass ret (If ifst) = do
695− (allCodePathsReturn, ifst') <- checkIfStatement mass ret ifst
696− return (allCodePathsReturn, mass, If ifst')
697−checkStatement mass ret (For ident start end inner) = do
698− Just moduleName <- checkCurrentModule <$> get
699− assignVariable ident
700− start' <- check start tyNumber
701− end' <- check end tyNumber
702− (allCodePathsReturn, _, inner') <- bindLocalVariables moduleName [(ident, tyNumber)] $ checkBlock mass ret inner
703− return (allCodePathsReturn, mass, For ident start' end' inner')
704−checkStatement mass ret (Return val) = do
705− val' <- check val ret
706− return (True, mass, Return (TypedValue True val' ret))
709−-- Check the type of an if-then-else statement
711−checkIfStatement :: M.Map Ident Type -> Type -> IfStatement -> UnifyT Type Check (Bool, IfStatement)
712−checkIfStatement mass ret (IfStatement val thens Nothing) = do
713− val' <- check val tyBoolean
714− (_, _, thens') <- checkBlock mass ret thens
715− return (False, IfStatement val' thens' Nothing)
716−checkIfStatement mass ret (IfStatement val thens (Just elses)) = do
717− val' <- check val tyBoolean
718− (allCodePathsReturn1, _, thens') <- checkBlock mass ret thens
719− (allCodePathsReturn2, elses') <- checkElseStatement mass ret elses
720− return (allCodePathsReturn1 && allCodePathsReturn2, IfStatement val' thens' (Just elses'))
723−-- Check the type of an else statement
725−checkElseStatement :: M.Map Ident Type -> Type -> ElseStatement -> UnifyT Type Check (Bool, ElseStatement)
726−checkElseStatement mass ret (Else elses) = do
727− (allCodePathsReturn, _, elses') <- checkBlock mass ret elses
728− return (allCodePathsReturn, Else elses')
729−checkElseStatement mass ret (ElseIf ifst) = (id *** ElseIf) <$> checkIfStatement mass ret ifst
732−-- Check the type of the return value of a block of statements
734−checkBlock :: M.Map Ident Type -> Type -> [Statement] -> UnifyT Type Check (Bool, M.Map Ident Type, [Statement])
735−checkBlock mass _ [] = return (False, mass, [])
736−checkBlock mass ret (s:ss) = do
737− Just moduleName <- checkCurrentModule <$> get
738− (b1, mass1, s') <- checkStatement mass ret s
739− bindLocalVariables moduleName (M.toList mass1) $ case (b1, ss) of
740− (True, []) -> return (True, mass1, [s'])
741− (True, _) -> throwError "Unreachable code"
743− (b, m, ss'') <- checkBlock mass1 ret ss'
744− return (b, m, s':ss'')
747−-- Generate a new skolem constant
749−newSkolemConstant :: UnifyT Type Check Int
750−newSkolemConstant = runUnknown <$> fresh'
753−-- Generate a new skolem scope
755−newSkolemScope :: UnifyT Type Check SkolemScope
756−newSkolemScope = SkolemScope . runUnknown <$> fresh'
759−-- Skolemize a type variable by replacing its instances with fresh skolem constants
761−skolemize :: String -> Int -> SkolemScope -> Type -> Type
762−skolemize ident sko scope = replaceTypeVars ident (Skolem sko scope)
765−-- Introduce skolem scope at every occurence of a ForAll
767−introduceSkolemScope :: Type -> UnifyT Type Check Type
768−introduceSkolemScope = everywhereM (mkM go)
770− go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
771− go other = return other
774−-- Check the type of a value, rethrowing errors to provide a better error message
776−check :: Value -> Type -> UnifyT Type Check Value
777−check val ty = rethrow errorMessage $ check' val ty
780− "Error checking type of term " ++
781− prettyPrintValue val ++
783− prettyPrintType ty ++
788−-- Check the type of a value
790−check' :: Value -> Type -> UnifyT Type Check Value
791−check' val t@(ForAll ident ty _) = do
792− scope <- newSkolemScope
793− sko <- newSkolemConstant
794− let sk = skolemize ident sko scope ty
795− val' <- check val sk
796− return $ TypedValue True val' (ForAll ident ty (Just scope))
797−check' val t@(ConstrainedType constraints ty) = do
799− Just moduleName <- checkCurrentModule <$> get
800− dictNames <- flip mapM constraints $ \(Qualified _ (ProperName className), _) -> do
801− n <- liftCheck freshDictionaryName
802− return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
803− val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
804− TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
805− (qualifyAllUnqualifiedNames moduleName env constraints)) $
807− return $ TypedValue True (foldr Abs val' dictNames) t
808−check' val t@(SaturatedTypeSynonym name args) = do
809− ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
810− val' <- check val ty
811− return $ TypedValue True val' ty
812−check' val u@(TUnknown _) = do
813− val'@(TypedValue _ _ ty) <- infer val
814− -- Don't unify an unknown with an inferred polytype
815− (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
817− return $ TypedValue True val'' ty'
818−check' v@(NumericLiteral _) t | t == tyNumber =
819− return $ TypedValue True v t
820−check' v@(StringLiteral _) t | t == tyString =
821− return $ TypedValue True v t
822−check' v@(BooleanLiteral _) t | t == tyBoolean =
823− return $ TypedValue True v t
824−check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
825− arr <- ArrayLiteral <$> forM vals (\val -> check val ty)
826− return $ TypedValue True arr t
827−check' (Abs arg ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
828− Just moduleName <- checkCurrentModule <$> get
829− ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
830− return $ TypedValue True (Abs arg ret') ty
831−check' (App f arg) ret = do
832− f'@(TypedValue _ _ ft) <- infer f
833− (ret', app) <- checkFunctionApplication f' ft arg
834− subsumes Nothing ret' ret
835− return $ TypedValue True app ret
836−check' v@(Var var) ty = do
837− Just moduleName <- checkCurrentModule <$> get
838− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
839− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
840− v' <- subsumes (Just v) repl ty'
842− Nothing -> throwError "Unable to check type subsumption"
843− Just v'' -> return $ TypedValue True v'' ty'
844−check' (TypedValue checkType val ty1) ty2 = do
845− Just moduleName <- checkCurrentModule <$> get
846− kind <- liftCheck $ kindOf moduleName ty1
847− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
848− ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
849− val' <- subsumes (Just val) ty1' ty2
851− Nothing -> throwError "Unable to check type subsumption"
853− val''' <- if checkType then check val'' ty1 else return val''
854− return $ TypedValue checkType (TypedValue True val''' ty1) ty2
855−check' (Case vals binders) ret = do
856− vals' <- mapM infer vals
857− let ts = map (\(TypedValue _ _ t) -> t) vals'
858− binders' <- checkBinders ts ret binders
859− return $ TypedValue True (Case vals' binders') ret
860−check' (IfThenElse cond th el) ty = do
861− cond' <- check cond tyBoolean
864− return $ TypedValue True (IfThenElse cond' th' el') ty
865−check' (ObjectLiteral ps) t@(Object row) = do
866− ensureNoDuplicateProperties ps
867− ps' <- checkProperties ps row False
868− return $ TypedValue True (ObjectLiteral ps') t
869−check' (ObjectUpdate obj ps) t@(Object row) = do
870− ensureNoDuplicateProperties ps
871− us <- zip (map fst ps) <$> replicateM (length ps) fresh
872− let (propsToCheck, rest) = rowToList row
873− propsToRemove = map fst ps
874− remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
875− obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
876− ps' <- checkProperties ps row True
877− return $ TypedValue True (ObjectUpdate obj' ps') t
878−check' (Accessor prop val) ty = do
880− val' <- check val (Object (RCons prop ty rest))
881− return $ TypedValue True (Accessor prop val') ty
882−check' (Block ss) ret = do
883− (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
884− guardWith "Block is missing a return statement" allCodePathsReturn
885− return $ TypedValue True (Block ss') ret
886−check' (Constructor c) ty = do
888− Just moduleName <- checkCurrentModule <$> get
889− case M.lookup (qualify moduleName c) (dataConstructors env) of
890− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
892− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
893− _ <- subsumes Nothing repl ty
894− return $ TypedValue True (Constructor c) ty
895−check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
898−-- Check the type of a collection of named record fields
900−-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
902−checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
903−checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
904− go [] [] REmpty = return []
905− go [] [] u@(TUnknown _) = do u =?= REmpty
907− go [] [] (Skolem _ _) | lax = return []
908− go [] ((p, _): _) _ | lax = return []
909− | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
910− go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
911− go ((p,v):ps') [] u@(TUnknown _) = do
912− v'@(TypedValue _ _ ty) <- infer v
914− u =?= RCons p ty rest
915− ps'' <- go ps' [] rest
916− return $ (p, v') : ps''
917− go ((p,v):ps') ts r =
920− v'@(TypedValue _ _ ty) <- infer v
922− r =?= RCons p ty rest
923− ps'' <- go ps' ts rest
924− return $ (p, v') : ps''
927− ps'' <- go ps' (delete (p, ty) ts) r
928− return $ (p, v') : ps''
929− go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
932−-- Check the type of a function application, rethrowing errors to provide a better error message
934−checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
935−checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
937− errorMessage msg = "Error applying function of type "
938− ++ prettyPrintType fnTy
939− ++ " to argument " ++ prettyPrintValue arg
943−-- Check the type of a function application
945−checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
946−checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
947− tyFunction' =?= tyFunction
948− arg' <- check arg argTy
949− return (retTy, App fn arg')
950−checkFunctionApplication' fn (ForAll ident ty _) arg = do
951− replaced <- replaceVarWithUnknown ident ty
952− checkFunctionApplication fn replaced arg
953−checkFunctionApplication' fn u@(TUnknown _) arg = do
955− TypedValue _ arg' t <- infer arg
956− (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
957− return $ TypedValue True arg'' t'
958− let ty = (\(TypedValue _ _ t) -> t) arg'
960− u =?= function ty ret
961− return (ret, App fn arg')
962−checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
963− ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
964− checkFunctionApplication fn ty arg
965−checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
967− dicts <- getTypeClassDictionaries
968− Just moduleName <- checkCurrentModule <$> get
969− checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) fnTy arg
970−checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
971− ++ prettyPrintType fnTy
972− ++ " to argument " ++ prettyPrintValue arg
975−-- Check whether one type subsumes another, rethrowing errors to provide a better error message
977−subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
978−subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
980− errorMessage msg = "Error checking that type "
981− ++ prettyPrintType ty1
982− ++ " subsumes type "
983− ++ prettyPrintType ty2
987−-- Check whether one type subsumes another
989−subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
990−subsumes' val (ForAll ident ty1 _) ty2 = do
991− replaced <- replaceVarWithUnknown ident ty1
992− subsumes val replaced ty2
993−subsumes' val ty1 (ForAll ident ty2 sco) =
996− sko <- newSkolemConstant
997− let sk = skolemize ident sko sco' ty2
999− Nothing -> throwError "Skolem variable scope is unspecified"
1000−subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
1001− subsumes Nothing arg2 arg1
1002− subsumes Nothing ret1 ret2
1004−subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
1005− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
1006− subsumes val ty1 ty2
1007−subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
1008− ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
1009− subsumes val ty1 ty2
1010−subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
1012− dicts <- getTypeClassDictionaries
1013− Just moduleName <- checkCurrentModule <$> get
1014− _ <- subsumes' Nothing ty1 ty2
1015− return . Just $ foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))
1016−subsumes' val (Object r1) (Object r2) = do
1018− (ts1, r1') = rowToList r1
1019− (ts2, r2') = rowToList r2
1020− ts1' = sortBy (comparing fst) ts1
1021− ts2' = sortBy (comparing fst) ts2
1022− go ts1' ts2' r1' r2'
1025− go [] ts2 r1 r2 = r1 =?= rowFromList (ts2, r2)
1026− go ts1 [] r1 r2 = r2 =?= rowFromList (ts1, r1)
1027− go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1 r2
1028− | p1 == p2 = do subsumes Nothing ty1 ty2
1030− | p1 < p2 = do rest <- fresh
1031− r2 =?= RCons p1 ty1 rest
1032− go ts1 ((p2, ty2) : ts2) r1 rest
1033− | p1 > p2 = do rest <- fresh
1034− r1 =?= RCons p2 ty2 rest
1035− go ((p1, ty1) : ts1) ts2 rest r2
1036−subsumes' val ty1 ty2@(Object _) = subsumes val ty2 ty1
1037−subsumes' val ty1 ty2 = do