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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 DeriveDataTypeable #-}
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, isNothing, isJust, fromMaybe)
46−import qualified Data.Data as D
47−import Data.Generics
48− (everythingWithContext, mkM, everywhereM, everything, mkT,
49− something, everywhere, mkQ)
50−
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
59−
60−import Control.Monad.State
61−import Control.Monad.Error
62−import Control.Monad.Reader
63−import Control.Monad.Unify
64−
65−import Control.Applicative
66−import Control.Arrow (Arrow(..))
67−
68−import qualified Data.Map as M
69−import Data.Function (on)
70−import Debug.Trace (trace)
71−
72−instance Partial Type where
73− unknown = TUnknown
74− isUnknown (TUnknown u) = Just u
75− isUnknown _ = Nothing
76−
77−instance Unifiable Check Type where
78− (=?=) = unifyTypes
79−
80−-- |
81−-- Unify two types, updating the current substitution
82−--
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
85− unifyTypes' t1 t2
86− where
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
92− ty1 `unifyTypes` ty
93− unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
94− unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
95− case (sc1, sc2) of
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
105− sk `unifyTypes` ty2
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
111− env <- getEnv
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
115− t3 `unifyTypes` t5
116− t4 `unifyTypes` t6
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 ++ "."
123−
124−-- |
125−-- Unify two rows, updating the current substitution
126−--
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
129−-- error.
130−--
131−unifyRows :: Type -> Type -> UnifyT Type Check ()
132−unifyRows r1 r2 =
133− let
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 ]
139− in do
140− forM_ int (uncurry (=?=))
141− unifyRows' sd1 r1' sd2 r2'
142− where
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
147− occursCheck un ty
148− forM_ row $ \(_, t) -> occursCheck un t
149− u' <- fresh
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)) ++ "."
156−
157−-- |
158−-- Ensure type constructors are equal after canonicalization
159−--
160−typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
161−typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
162−
163−-- |
164−-- Infer the types of multiple mutually-recursive values, and return elaborated values including
165−-- type class dictionaries and type annotations.
166−--
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)
177− forM es $ \e -> do
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
194− escapeCheck val ty
195− return triple
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))
201− where
202− tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
203−
204−-- |
205−-- Check if a value contains a type annotation
206−--
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))
210−
211−-- |
212−-- Map a function over type annotations appearing inside a value
213−--
214−overTypes :: (Type -> Type) -> Value -> Value
215−overTypes f = everywhere (mkT f)
216−
217−-- |
218−-- Replace type class dictionary placeholders with inferred type class dictionaries
219−--
220−replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
221−replaceTypeClassDictionaries mn = everywhereM (mkM go)
222− where
223− go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
224− go other = return other
225−
226−-- |
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.
229−--
230−entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, Type) -> Check Value
231−entails moduleName context goal@(className, ty) = do
232− env <- getEnv
233− case go env goal of
234− [] -> throwError $ "No " ++ show className ++ " instance found for " ++ prettyPrintType ty
235− (dict : _) -> return dict
236− where
237− go env (className', ty') =
238− [ mkDictionary (canonicalizeDictionary tcd) args
239− | tcd <- context
240− , filterModule tcd
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)
248− return $ Just dict
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
259−
260−-- |
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.
263−--
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) <$> typeHeadsAreEqual m e h1 h2
270−typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
271−typeHeadsAreEqual _ _ _ _ = Nothing
272−
273−-- |
274−-- Ensure unsolved unification variables do not escape
275−--
276−escapeCheck :: Value -> Type -> UnifyT Type Check ()
277−escapeCheck value ty = do
278− subst <- unifyCurrentSubstitution <$> 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
284−
285−-- |
286−-- Find all type annotations occuring inside a value
287−--
288−findAllTypes :: Value -> [Type]
289−findAllTypes = everything (++) (mkQ [] go)
290− where
291− go (TypedValue _ _ ty) = [ty]
292− go _ = []
293−
294−-- |
295−-- Ensure skolem variables do not escape their scope
296−--
297−skolemEscapeCheck :: Value -> Check ()
298−skolemEscapeCheck (TypedValue False _ _) = return ()
299−skolemEscapeCheck root@(TypedValue _ _ _) =
300− case everythingWithContext [] (++) (mkQ ((,) []) go) root of
301− [] -> return ()
302− ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
303− where
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)
308− _ -> ([], scos)
309− where
310− collectSkolems :: Type -> [SkolemScope]
311− collectSkolems = nub . everything (++) (mkQ [] collect)
312− where
313− collect (Skolem _ scope) = [scope]
314− collect _ = []
315− go _ scos = ([], scos)
316− findBindingScope :: SkolemScope -> Maybe Value
317− findBindingScope sco = something (mkQ Nothing go) root
318− where
319− go val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
320− go _ = Nothing
321−skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
322−
323−-- |
324−-- Ensure a row contains no duplicate labels
325−--
326−setify :: Type -> Type
327−setify = rowFromList . first (M.toList . M.fromList) . rowToList
328−
329−-- |
330−-- \"Setify\" all rows occuring inside a value
331−--
332−setifyAll :: (D.Data d) => d -> d
333−setifyAll = everywhere (mkT setify)
334−
335−-- |
336−-- Replace outermost unsolved unification variables with named type variables
337−--
338−varIfUnknown :: Type -> Type
339−varIfUnknown ty =
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)
345− typeToVar t = t
346− in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
347−
348−-- |
349−-- Replace named type variables with types
350−--
351−replaceAllTypeVars :: (D.Data d) => [(String, Type)] -> d -> d
352−replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
353−
354−-- |
355−-- Replace named type variables with new unification variables
356−--
357−replaceAllVarsWithUnknowns :: Type -> UnifyT Type Check Type
358−replaceAllVarsWithUnknowns (ForAll ident ty _) = replaceVarWithUnknown ident ty >>= replaceAllVarsWithUnknowns
359−replaceAllVarsWithUnknowns ty = return ty
360−
361−-- |
362−-- Replace a single type variable with a new unification variable
363−--
364−replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
365−replaceVarWithUnknown ident ty = do
366− tu <- fresh
367− return $ replaceTypeVars ident tu $ ty
368−
369−-- |
370−-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
371−-- better error messages during unification.
372−--
373−replaceAllTypeSynonyms :: (Functor m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
374−replaceAllTypeSynonyms d = do
375− env <- getEnv
376− Just moduleName <- checkCurrentModule <$> get
377− let syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
378− either throwError return $ saturateAllTypeSynonyms env moduleName syns d
379−
380−-- |
381−-- \"Desaturate\" @SaturatedTypeSynonym@s
382−--
383−desaturateAllTypeSynonyms :: (D.Data d) => d -> d
384−desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
385− where
386− replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
387− replaceSaturatedTypeSynonym t = t
388−
389−-- |
390−-- Replace a type synonym and its arguments with the aliased type
391−--
392−expandTypeSynonym :: Qualified ProperName -> [Type] -> UnifyT Type Check Type
393−expandTypeSynonym name args = do
394− env <- getEnv
395− Just moduleName <- checkCurrentModule <$> get
396− case M.lookup (canonicalizeType moduleName env name) (typeSynonyms env) of
397− Just (synArgs, body) -> return $ replaceAllTypeVars (zip synArgs args) body
398− Nothing -> error "Type synonym was not defined"
399−
400−-- |
401−-- Ensure a set of property names and value does not contain duplicate labels
402−--
403−ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
404−ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
405−
406−-- |
407−-- Infer a type for a value, rethrowing any error to provide a more useful error message
408−--
409−infer :: Value -> UnifyT Type Check Value
410−infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
411−
412−-- |
413−-- Infer a type for a value
414−--
415−infer' :: Value -> UnifyT Type Check Value
416−infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
417−infer' v@(StringLiteral _) = return $ TypedValue True v tyString
418−infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
419−infer' (ArrayLiteral vals) = do
420− ts <- mapM infer vals
421− els <- fresh
422− forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
423− return $ TypedValue True (ArrayLiteral ts) els
424−infer' (ObjectLiteral ps) = do
425− ensureNoDuplicateProperties ps
426− ts <- mapM (infer . snd) ps
427− let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
428− ty = Object $ rowFromList (fields, REmpty)
429− return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
430−infer' (ObjectUpdate o ps) = do
431− ensureNoDuplicateProperties ps
432− row <- fresh
433− newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
434− let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
435− oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
436− let oldTy = Object $ rowFromList (oldTys, row)
437− o' <- TypedValue True <$> check o oldTy <*> pure oldTy
438− return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
439−infer' (Accessor prop val) = do
440− typed@(TypedValue _ _ objTy) <- infer val
441− propTy <- inferProperty objTy prop
442− case propTy of
443− Nothing -> do
444− field <- fresh
445− rest <- fresh
446− _ <- subsumes Nothing objTy (Object (RCons prop field rest))
447− return $ TypedValue True (Accessor prop typed) field
448− Just ty -> return $ TypedValue True (Accessor prop typed) ty
449−infer' (Abs arg ret) = do
450− ty <- fresh
451− Just moduleName <- checkCurrentModule <$> get
452− bindLocalVariables moduleName [(arg, ty)] $ do
453− body@(TypedValue _ _ bodyTy) <- infer' ret
454− return $ TypedValue True (Abs arg body) $ function ty bodyTy
455−infer' (App f arg) = do
456− f'@(TypedValue _ _ ft) <- infer f
457− (ret, app) <- checkFunctionApplication f' ft arg
458− return $ TypedValue True app ret
459−infer' (Var var) = do
460− Just moduleName <- checkCurrentModule <$> get
461− ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
462− case ty of
463− ConstrainedType constraints _ -> do
464− env <- getEnv
465− dicts <- getTypeClassDictionaries
466− return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) ty
467− _ -> return $ TypedValue True (Var var) ty
468−infer' (Block ss) = do
469− ret <- fresh
470− (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
471− guardWith "Block is missing a return statement" allCodePathsReturn
472− return $ TypedValue True (Block ss') ret
473−infer' v@(Constructor c) = do
474− env <- getEnv
475− Just moduleName <- checkCurrentModule <$> get
476− case M.lookup (qualify moduleName c) (dataConstructors env) of
477− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
478− Just (ty, _) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
479− return $ TypedValue True v ty'
480−infer' (Case vals binders) = do
481− ts <- mapM infer vals
482− ret <- fresh
483− binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
484− return $ TypedValue True (Case ts binders') ret
485−infer' (IfThenElse cond th el) = do
486− cond' <- check cond tyBoolean
487− v2@(TypedValue _ _ t2) <- infer th
488− v3@(TypedValue _ _ t3) <- infer el
489− t2 =?= t3
490− return $ TypedValue True (IfThenElse cond' v2 v3) t2
491−infer' (TypedValue checkType val ty) = do
492− Just moduleName <- checkCurrentModule <$> get
493− kind <- liftCheck $ kindOf moduleName ty
494− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
495− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
496− val' <- if checkType then check val ty' else return val
497− return $ TypedValue True val' ty'
498−infer' _ = error "Invalid argument to infer"
499−
500−-- |
501−-- Infer the type of a property inside a record with a given type
502−--
503−inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
504−inferProperty (Object row) prop = do
505− let (props, _) = rowToList row
506− return $ lookup prop props
507−inferProperty (SaturatedTypeSynonym name args) prop = do
508− replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
509− inferProperty replaced prop
510−inferProperty (ForAll ident ty _) prop = do
511− replaced <- replaceVarWithUnknown ident ty
512− inferProperty replaced prop
513−inferProperty _ _ = return Nothing
514−
515−-- |
516−-- Infer the types of variables brought into scope by a binder
517−--
518−inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
519−inferBinder _ NullBinder = return M.empty
520−inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
521−inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
522−inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
523−inferBinder val (VarBinder name) = return $ M.singleton name val
524−inferBinder val (NullaryBinder ctor) = do
525− env <- getEnv
526− Just moduleName <- checkCurrentModule <$> get
527− case M.lookup (qualify moduleName ctor) (dataConstructors env) of
528− Just (ty, _) -> do
529− _ <- subsumes Nothing ty val
530− return M.empty
531− _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
532−inferBinder val (UnaryBinder ctor binder) = do
533− env <- getEnv
534− Just moduleName <- checkCurrentModule <$> get
535− case M.lookup (qualify moduleName ctor) (dataConstructors env) of
536− Just (ty, _) -> do
537− fn <- replaceAllVarsWithUnknowns ty
538− case fn of
539− TypeApp (TypeApp t obj) ret | t == tyFunction -> do
540− _ <- subsumes Nothing val ret
541− inferBinder obj binder
542− _ -> throwError $ "Constructor " ++ show ctor ++ " is not a unary constructor"
543− _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
544−inferBinder val (ObjectBinder props) = do
545− row <- fresh
546− rest <- fresh
547− m1 <- inferRowProperties row rest props
548− val =?= Object row
549− return m1
550− where
551− inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
552− inferRowProperties nrow row [] = nrow =?= row >> return M.empty
553− inferRowProperties nrow row ((name, binder):binders) = do
554− propTy <- fresh
555− m1 <- inferBinder propTy binder
556− m2 <- inferRowProperties nrow (RCons name propTy row) binders
557− return $ m1 `M.union` m2
558−inferBinder val (ArrayBinder binders) = do
559− el <- fresh
560− m1 <- M.unions <$> mapM (inferBinder el) binders
561− val =?= TypeApp tyArray el
562− return m1
563−inferBinder val (ConsBinder headBinder tailBinder) = do
564− el <- fresh
565− m1 <- inferBinder el headBinder
566− m2 <- inferBinder val tailBinder
567− val =?= TypeApp tyArray el
568− return $ m1 `M.union` m2
569−inferBinder val (NamedBinder name binder) = do
570− m <- inferBinder val binder
571− return $ M.insert name val m
572−
573−-- |
574−-- Check the types of the return values in a set of binders in a case statement
575−--
576−checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> UnifyT Type Check [([Binder], Maybe Guard, Value)]
577−checkBinders _ _ [] = return []
578−checkBinders nvals ret ((binders, grd, val):bs) = do
579− Just moduleName <- checkCurrentModule <$> get
580− m1 <- M.unions <$> zipWithM inferBinder nvals binders
581− r <- bindLocalVariables moduleName (M.toList m1) $ do
582− val' <- TypedValue True <$> check val ret <*> pure ret
583− case grd of
584− Nothing -> return (binders, Nothing, val')
585− Just g -> do
586− g' <- check g tyBoolean
587− return (binders, Just g', val')
588− rs <- checkBinders nvals ret bs
589− return $ r : rs
590−
591−-- |
592−-- Check that a local variable name is not already used
593−--
594−assignVariable :: Ident -> UnifyT Type Check ()
595−assignVariable name = do
596− env <- checkEnv <$> get
597− Just moduleName <- checkCurrentModule <$> get
598− case M.lookup (moduleName, name) (names env) of
599− Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
600− _ -> return ()
601−
602−-- |
603−-- Check the type of the return values of a statement, returning whether or not the statement returns on
604−-- all code paths
605−--
606−checkStatement :: M.Map Ident Type -> Type -> Statement -> UnifyT Type Check (Bool, M.Map Ident Type, Statement)
607−checkStatement mass _ (VariableIntroduction name val) = do
608− assignVariable name
609− val'@(TypedValue _ _ t) <- infer val
610− return (False, M.insert name t mass, VariableIntroduction name val')
611−checkStatement mass _ (Assignment ident val) = do
612− val'@(TypedValue _ _ t) <- infer val
613− case M.lookup ident mass of
614− Nothing -> throwError $ "No local variable with name " ++ show ident
615− Just ty -> do t =?= ty
616− return (False, mass, Assignment ident val')
617−checkStatement mass ret (While val inner) = do
618− val' <- check val tyBoolean
619− (allCodePathsReturn, _, inner') <- checkBlock mass ret inner
620− return (allCodePathsReturn, mass, While val' inner')
621−checkStatement mass ret (If ifst) = do
622− (allCodePathsReturn, ifst') <- checkIfStatement mass ret ifst
623− return (allCodePathsReturn, mass, If ifst')
624−checkStatement mass ret (For ident start end inner) = do
625− Just moduleName <- checkCurrentModule <$> get
626− assignVariable ident
627− start' <- check start tyNumber
628− end' <- check end tyNumber
629− (allCodePathsReturn, _, inner') <- bindLocalVariables moduleName [(ident, tyNumber)] $ checkBlock mass ret inner
630− return (allCodePathsReturn, mass, For ident start' end' inner')
631−checkStatement mass ret (Return val) = do
632− val' <- check val ret
633− return (True, mass, Return (TypedValue True val' ret))
634−
635−-- |
636−-- Check the type of an if-then-else statement
637−--
638−checkIfStatement :: M.Map Ident Type -> Type -> IfStatement -> UnifyT Type Check (Bool, IfStatement)
639−checkIfStatement mass ret (IfStatement val thens Nothing) = do
640− val' <- check val tyBoolean
641− (_, _, thens') <- checkBlock mass ret thens
642− return (False, IfStatement val' thens' Nothing)
643−checkIfStatement mass ret (IfStatement val thens (Just elses)) = do
644− val' <- check val tyBoolean
645− (allCodePathsReturn1, _, thens') <- checkBlock mass ret thens
646− (allCodePathsReturn2, elses') <- checkElseStatement mass ret elses
647− return (allCodePathsReturn1 && allCodePathsReturn2, IfStatement val' thens' (Just elses'))
648−
649−-- |
650−-- Check the type of an else statement
651−--
652−checkElseStatement :: M.Map Ident Type -> Type -> ElseStatement -> UnifyT Type Check (Bool, ElseStatement)
653−checkElseStatement mass ret (Else elses) = do
654− (allCodePathsReturn, _, elses') <- checkBlock mass ret elses
655− return (allCodePathsReturn, Else elses')
656−checkElseStatement mass ret (ElseIf ifst) = (id *** ElseIf) <$> checkIfStatement mass ret ifst
657−
658−-- |
659−-- Check the type of the return value of a block of statements
660−--
661−checkBlock :: M.Map Ident Type -> Type -> [Statement] -> UnifyT Type Check (Bool, M.Map Ident Type, [Statement])
662−checkBlock mass _ [] = return (False, mass, [])
663−checkBlock mass ret (s:ss) = do
664− Just moduleName <- checkCurrentModule <$> get
665− (b1, mass1, s') <- checkStatement mass ret s
666− bindLocalVariables moduleName (M.toList mass1) $ case (b1, ss) of
667− (True, []) -> return (True, mass1, [s'])
668− (True, _) -> throwError "Unreachable code"
669− (False, ss') -> do
670− (b, m, ss'') <- checkBlock mass1 ret ss'
671− return (b, m, s':ss'')
672−
673−-- |
674−-- Generate a new skolem constant
675−--
676−newSkolemConstant :: UnifyT Type Check Int
677−newSkolemConstant = runUnknown <$> fresh'
678−
679−-- |
680−-- Generate a new skolem scope
681−--
682−newSkolemScope :: UnifyT Type Check SkolemScope
683−newSkolemScope = SkolemScope . runUnknown <$> fresh'
684−
685−-- |
686−-- Skolemize a type variable by replacing its instances with fresh skolem constants
687−--
688−skolemize :: (D.Data d) => String -> Int -> SkolemScope -> d -> d
689−skolemize ident sko scope d = replaceTypeVars ident (Skolem sko scope) d
690−
691−-- |
692−-- Introduce skolem scope at every occurence of a ForAll
693−--
694−introduceSkolemScope :: Type -> UnifyT Type Check Type
695−introduceSkolemScope = everywhereM (mkM go)
696− where
697− go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
698− go other = return other
699−
700−-- |
701−-- Check the type of a value, rethrowing errors to provide a better error message
702−--
703−check :: Value -> Type -> UnifyT Type Check Value
704−check val ty = rethrow errorMessage $ check' val ty
705− where
706− errorMessage msg =
707− "Error checking type of term " ++
708− prettyPrintValue val ++
709− " against type " ++
710− prettyPrintType ty ++
711− ":\n" ++
712− msg
713−
714−-- |
715−-- Check the type of a value
716−--
717−check' :: Value -> Type -> UnifyT Type Check Value
718−check' val t@(ForAll ident ty _) = do
719− scope <- newSkolemScope
720− sko <- newSkolemConstant
721− let sk = skolemize ident sko scope ty
722− val' <- check val sk
723− return $ TypedValue True val' (ForAll ident ty (Just scope))
724−check' val t@(ConstrainedType constraints ty) = do
725− env <- getEnv
726− Just moduleName <- checkCurrentModule <$> get
727− dictNames <- flip mapM constraints $ \(Qualified _ (ProperName className), _) -> do
728− n <- liftCheck freshDictionaryName
729− return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
730− val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
731− TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
732− (qualifyAllUnqualifiedNames moduleName env constraints)) $
733− check val ty
734− return $ TypedValue True (foldr Abs val' dictNames) t
735−check' val t@(SaturatedTypeSynonym name args) = do
736− ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
737− val' <- check val ty
738− return $ TypedValue True val' ty
739−check' val u@(TUnknown _) = do
740− val'@(TypedValue _ _ ty) <- infer val
741− -- Don't unify an unknown with an inferred polytype
742− ty' <- replaceAllVarsWithUnknowns ty
743− ty' =?= u
744− return $ TypedValue True val' ty'
745−check' v@(NumericLiteral _) t | t == tyNumber =
746− return $ TypedValue True v t
747−check' v@(StringLiteral _) t | t == tyString =
748− return $ TypedValue True v t
749−check' v@(BooleanLiteral _) t | t == tyBoolean =
750− return $ TypedValue True v t
751−check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
752− arr <- ArrayLiteral <$> forM vals (\val -> check val ty)
753− return $ TypedValue True arr t
754−check' (Abs arg ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
755− Just moduleName <- checkCurrentModule <$> get
756− ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
757− return $ TypedValue True (Abs arg ret') ty
758−check' (App f arg) ret = do
759− f'@(TypedValue _ _ ft) <- infer f
760− (ret', app) <- checkFunctionApplication f' ft arg
761− subsumes Nothing ret' ret
762− return $ TypedValue True app ret
763−check' v@(Var var) ty = do
764− Just moduleName <- checkCurrentModule <$> get
765− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
766− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
767− v' <- subsumes (Just v) repl ty'
768− case v' of
769− Nothing -> throwError "Unable to check type subsumption"
770− Just v'' -> return $ TypedValue True v'' ty'
771−check' (TypedValue checkType val ty1) ty2 = do
772− Just moduleName <- checkCurrentModule <$> get
773− kind <- liftCheck $ kindOf moduleName ty1
774− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
775− val' <- subsumes (Just val) ty1 ty2
776− case val' of
777− Nothing -> throwError "Unable to check type subsumption"
778− Just val'' -> do
779− val''' <- if checkType then check val'' ty1 else return val''
780− return $ TypedValue checkType (TypedValue True val''' ty1) ty2
781−check' (Case vals binders) ret = do
782− vals' <- mapM infer vals
783− let ts = map (\(TypedValue _ _ t) -> t) vals'
784− binders' <- checkBinders ts ret binders
785− return $ TypedValue True (Case vals' binders') ret
786−check' (IfThenElse cond th el) ty = do
787− cond' <- check cond tyBoolean
788− th' <- check th ty
789− el' <- check el ty
790− return $ TypedValue True (IfThenElse cond' th' el') ty
791−check' (ObjectLiteral ps) t@(Object row) = do
792− ensureNoDuplicateProperties ps
793− ps' <- checkProperties ps row False
794− return $ TypedValue True (ObjectLiteral ps') t
795−check' (ObjectUpdate obj ps) t@(Object row) = do
796− ensureNoDuplicateProperties ps
797− us <- zip (map fst ps) <$> replicateM (length ps) fresh
798− let (propsToCheck, rest) = rowToList row
799− propsToRemove = map fst ps
800− remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
801− obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
802− ps' <- checkProperties ps row True
803− return $ TypedValue True (ObjectUpdate obj' ps') t
804−check' (Accessor prop val) ty = do
805− rest <- fresh
806− val' <- check val (Object (RCons prop ty rest))
807− return $ TypedValue True (Accessor prop val') ty
808−check' (Block ss) ret = do
809− (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
810− guardWith "Block is missing a return statement" allCodePathsReturn
811− return $ TypedValue True (Block ss') ret
812−check' (Constructor c) ty = do
813− env <- getEnv
814− Just moduleName <- checkCurrentModule <$> get
815− case M.lookup (qualify moduleName c) (dataConstructors env) of
816− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
817− Just (ty1, _) -> do
818− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
819− _ <- subsumes Nothing repl ty
820− return $ TypedValue True (Constructor c) ty
821−check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
822−
823−-- |
824−-- Check the type of a collection of named record fields
825−--
826−-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
827−--
828−checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
829−checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
830− go [] [] REmpty = return []
831− go [] [] u@(TUnknown _) = do u =?= REmpty
832− return []
833− go [] [] (Skolem _ _) | lax = return []
834− go [] ((p, _): _) _ | lax = return []
835− | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
836− go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
837− go ((p,v):ps') [] u@(TUnknown _) = do
838− v'@(TypedValue _ _ ty) <- infer v
839− rest <- fresh
840− u =?= RCons p ty rest
841− ps'' <- go ps' [] rest
842− return $ (p, v') : ps''
843− go ((p,v):ps') ts r =
844− case lookup p ts of
845− Nothing -> do
846− v'@(TypedValue _ _ ty) <- infer v
847− rest <- fresh
848− r =?= RCons p ty rest
849− ps'' <- go ps' ts rest
850− return $ (p, v') : ps''
851− Just ty -> do
852− v' <- check v ty
853− ps'' <- go ps' (delete (p, ty) ts) r
854− return $ (p, v') : ps''
855− go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
856−
857−-- |
858−-- Check the type of a function application, rethrowing errors to provide a better error message
859−--
860−checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
861−checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
862− where
863− errorMessage msg = "Error applying function of type "
864− ++ prettyPrintType fnTy
865− ++ " to argument " ++ prettyPrintValue arg
866− ++ ":\n" ++ msg
867−
868−-- |
869−-- Check the type of a function application
870−--
871−checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
872−checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
873− tyFunction' =?= tyFunction
874− arg' <- check arg argTy
875− return (retTy, App fn arg')
876−checkFunctionApplication' fn (ForAll ident ty _) arg = do
877− replaced <- replaceVarWithUnknown ident ty
878− checkFunctionApplication fn replaced arg
879−checkFunctionApplication' fn u@(TUnknown _) arg = do
880− arg' <- do
881− TypedValue _ v t <- infer arg
882− TypedValue True v <$> replaceAllVarsWithUnknowns t
883− let ty = (\(TypedValue _ _ t) -> t) arg'
884− ret <- fresh
885− u =?= function ty ret
886− return (ret, App fn arg')
887−checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
888− ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
889− checkFunctionApplication fn ty arg
890−checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
891− env <- getEnv
892− dicts <- getTypeClassDictionaries
893− Just moduleName <- checkCurrentModule <$> get
894− checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) fnTy arg
895−checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
896− ++ prettyPrintType fnTy
897− ++ " to argument " ++ prettyPrintValue arg
898−
899−-- |
900−-- Check whether one type subsumes another, rethrowing errors to provide a better error message
901−--
902−subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
903−subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
904− where
905− errorMessage msg = "Error checking that type "
906− ++ prettyPrintType ty1
907− ++ " subsumes type "
908− ++ prettyPrintType ty2
909− ++ ":\n" ++ msg
910−
911−-- |
912−-- Check whether one type subsumes another
913−--
914−subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
915−subsumes' val (ForAll ident ty1 _) ty2 = do
916− replaced <- replaceVarWithUnknown ident ty1
917− subsumes val replaced ty2
918−subsumes' val ty1 (ForAll ident ty2 sco) =
919− case sco of
920− Just sco' -> do
921− sko <- newSkolemConstant
922− let sk = skolemize ident sko sco' ty2
923− subsumes val ty1 sk
924− Nothing -> throwError "Skolem variable scope is unspecified"
925−subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
926− subsumes Nothing arg2 arg1
927− subsumes Nothing ret1 ret2
928− return val
929−subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
930− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
931− subsumes val ty1 ty2
932−subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
933− ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
934− subsumes val ty1 ty2
935−subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
936− env <- getEnv
937− dicts <- getTypeClassDictionaries
938− Just moduleName <- checkCurrentModule <$> get
939− _ <- subsumes' Nothing ty1 ty2
940− return . Just $ foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))
941−subsumes' val ty1 ty2 = do
942− ty1 =?= ty2
943− return val
944−