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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−import Data.Generics.Extras
51−
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
60−
61−import Control.Monad.State
62−import Control.Monad.Error
63−import Control.Monad.Reader
64−import Control.Monad.Unify
65−
66−import Control.Applicative
67−import Control.Arrow (Arrow(..))
68−
69−import qualified Data.Map as M
70−import Data.Function (on)
71−import Data.Ord (comparing)
72−
73−instance Partial Type where
74− unknown = TUnknown
75− isUnknown (TUnknown u) = Just u
76− isUnknown _ = Nothing
77−
78−instance Unifiable Check Type where
79− (=?=) = unifyTypes
80−
81−-- |
82−-- Unify two types, updating the current substitution
83−--
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
86− unifyTypes' t1 t2
87− where
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
93− ty1 `unifyTypes` ty
94− unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
95− unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
96− case (sc1, sc2) of
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
106− sk `unifyTypes` ty2
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
112− env <- getEnv
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
116− t3 `unifyTypes` t5
117− t4 `unifyTypes` t6
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 ++ "."
124−
125−-- |
126−-- Unify two rows, updating the current substitution
127−--
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
130−-- error.
131−--
132−unifyRows :: Type -> Type -> UnifyT Type Check ()
133−unifyRows r1 r2 =
134− let
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 ]
140− in do
141− forM_ int (uncurry (=?=))
142− unifyRows' sd1 r1' sd2 r2'
143− where
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
148− occursCheck un ty
149− forM_ row $ \(_, t) -> occursCheck un t
150− u' <- fresh
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)) ++ ")."
157−
158−-- |
159−-- Ensure type constructors are equal after canonicalization
160−--
161−typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
162−typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
163−
164−-- |
165−-- Infer the types of multiple mutually-recursive values, and return elaborated values including
166−-- type class dictionaries and type annotations.
167−--
168−typesOf :: Maybe ModuleName -> ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
169−typesOf mainModuleName moduleName vals = do
170− tys <- fmap tidyUp . liftUnify $ do
171− let
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
181− let
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
193− -- Kind check
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 "Control", ProperName "Monad", ProperName "Eff"])) (ProperName "Eff"))) eff) a
212− -- Make sure unification variables do not escape
213− escapeCheck val ty
214− return triple
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'))
225− where
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
228−
229−-- |
230−-- Check if a value introduces a function
231−--
232−isFunction :: Value -> Bool
233−isFunction (Abs _ _) = True
234−isFunction (TypedValue _ val _) = isFunction val
235−isFunction _ = False
236−
237−-- |
238−-- Check if a value contains a type annotation
239−--
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))
243−
244−-- |
245−-- Map a function over type annotations appearing inside a value
246−--
247−overTypes :: (Type -> Type) -> Value -> Value
248−overTypes f = everywhere (mkT f)
249−
250−-- |
251−-- Replace type class dictionary placeholders with inferred type class dictionaries
252−--
253−replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
254−replaceTypeClassDictionaries mn = everywhereM' (mkM go)
255− where
256− go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
257− go other = return other
258−
259−-- |
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.
262−--
263−entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, Type) -> Check Value
264−entails moduleName context goal@(className, ty) = do
265− env <- getEnv
266− case go env goal of
267− [] -> throwError $ "No " ++ show className ++ " instance found for " ++ prettyPrintType ty
268− (dict : _) -> return dict
269− where
270− go env (className', ty') =
271− [ mkDictionary (canonicalizeDictionary tcd) args
272− | tcd <- context
273− -- Choose type class dictionaries in scope in the current module
274− , filterModule tcd
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)
288− return $ Just dict
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
304−
305−-- |
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.
308−--
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) <$> typeHeadsAreEqual m e h1 h2
315−typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
316−typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e m name args of
317− Left err -> Nothing
318− Right t1 -> typeHeadsAreEqual m e t1 t2
319−typeHeadsAreEqual _ _ _ _ = Nothing
320−
321−-- |
322−-- Ensure unsolved unification variables do not escape
323−--
324−escapeCheck :: Value -> Type -> UnifyT Type Check ()
325−escapeCheck value ty = do
326− subst <- unifyCurrentSubstitution <$> 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
332−
333−-- |
334−-- Find all type annotations occuring inside a value
335−--
336−findAllTypes :: Value -> [Type]
337−findAllTypes = everything (++) (mkQ [] go)
338− where
339− go (TypedValue _ _ ty) = [ty]
340− go _ = []
341−
342−-- |
343−-- Ensure skolem variables do not escape their scope
344−--
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
355− [] -> return ()
356− ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
357− where
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)
362− _ -> ([], scos)
363− where
364− collectSkolems :: Type -> [SkolemScope]
365− collectSkolems = nub . everything (++) (mkQ [] collect)
366− where
367− collect (Skolem _ scope) = [scope]
368− collect _ = []
369− go _ scos = ([], scos)
370− findBindingScope :: SkolemScope -> Maybe Value
371− findBindingScope sco = something (mkQ Nothing go) root
372− where
373− go val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
374− go _ = Nothing
375−skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
376−
377−-- |
378−-- Ensure a row contains no duplicate labels
379−--
380−setify :: Type -> Type
381−setify = rowFromList . first (M.toList . M.fromList) . rowToList
382−
383−-- |
384−-- \"Setify\" all rows occuring inside a value
385−--
386−setifyAll :: (D.Data d) => d -> d
387−setifyAll = everywhere (mkT setify)
388−
389−-- |
390−-- Replace outermost unsolved unification variables with named type variables
391−--
392−varIfUnknown :: Type -> Type
393−varIfUnknown ty =
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)
399− typeToVar t = t
400− in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
401−
402−-- |
403−-- Replace named type variables with types
404−--
405−replaceAllTypeVars :: [(String, Type)] -> Type -> Type
406−replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
407−
408−-- |
409−-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
410−-- or TypeClassDictionary values.
411−--
412−-- This is necessary during type checking to avoid unifying a polymorphic type with a
413−-- unification variable.
414−--
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
420− env <- getEnv
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)
426−
427−-- |
428−-- Replace a single type variable with a new unification variable
429−--
430−replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
431−replaceVarWithUnknown ident ty = do
432− tu <- fresh
433− return $ replaceTypeVars ident tu $ ty
434−
435−-- |
436−-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
437−-- better error messages during unification.
438−--
439−replaceAllTypeSynonyms' :: (D.Data d) => Environment -> ModuleName -> d -> Either String d
440−replaceAllTypeSynonyms' env moduleName d =
441− let
442− syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
443− in
444− saturateAllTypeSynonyms env moduleName syns d
445−
446−replaceAllTypeSynonyms :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
447−replaceAllTypeSynonyms d = do
448− env <- getEnv
449− Just moduleName <- checkCurrentModule <$> get
450− either throwError return $ replaceAllTypeSynonyms' env moduleName d
451−
452−-- |
453−-- \"Desaturate\" @SaturatedTypeSynonym@s
454−--
455−desaturateAllTypeSynonyms :: (D.Data d) => d -> d
456−desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
457− where
458− replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
459− replaceSaturatedTypeSynonym t = t
460−
461−-- |
462−-- Replace a type synonym and its arguments with the aliased type
463−--
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"
471−
472−expandTypeSynonym :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => Qualified ProperName -> [Type] -> m Type
473−expandTypeSynonym name args = do
474− env <- getEnv
475− Just moduleName <- checkCurrentModule <$> get
476− either throwError return $ expandTypeSynonym' env moduleName name args
477−
478−-- |
479−-- Ensure a set of property names and value does not contain duplicate labels
480−--
481−ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
482−ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
483−
484−-- |
485−-- Infer a type for a value, rethrowing any error to provide a more useful error message
486−--
487−infer :: Value -> UnifyT Type Check Value
488−infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
489−
490−-- |
491−-- Infer a type for a value
492−--
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
499− els <- fresh
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
510− row <- fresh
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
520− case propTy of
521− Nothing -> do
522− field <- fresh
523− rest <- fresh
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 (Left arg) ret) = do
528− ty <- fresh
529− Just moduleName <- checkCurrentModule <$> get
530− bindLocalVariables moduleName [(arg, ty)] $ do
531− body@(TypedValue _ _ bodyTy) <- infer' ret
532− return $ TypedValue True (Abs (Left arg) body) $ function ty bodyTy
533−infer' (Abs (Right _) _) = error "Binder was not desugared"
534−infer' (App f arg) = do
535− f'@(TypedValue _ _ ft) <- infer f
536− (ret, app) <- checkFunctionApplication f' ft arg
537− return $ TypedValue True app ret
538−infer' (Var var) = do
539− Just moduleName <- checkCurrentModule <$> get
540− ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
541− case ty of
542− ConstrainedType constraints ty' -> do
543− env <- getEnv
544− dicts <- getTypeClassDictionaries
545− return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) ty'
546− _ -> return $ TypedValue True (Var var) ty
547−infer' v@(Constructor c) = do
548− env <- getEnv
549− Just moduleName <- checkCurrentModule <$> get
550− case M.lookup (qualify moduleName c) (dataConstructors env) of
551− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
552− Just (ty, _) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
553− return $ TypedValue True v ty'
554−infer' (Case vals binders) = do
555− ts <- mapM infer vals
556− ret <- fresh
557− binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
558− return $ TypedValue True (Case ts binders') ret
559−infer' (IfThenElse cond th el) = do
560− cond' <- check cond tyBoolean
561− v2@(TypedValue _ _ t2) <- infer th
562− v3@(TypedValue _ _ t3) <- infer el
563− t2 =?= t3
564− return $ TypedValue True (IfThenElse cond' v2 v3) t2
565−infer' (TypedValue checkType val ty) = do
566− Just moduleName <- checkCurrentModule <$> get
567− kind <- liftCheck $ kindOf moduleName ty
568− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
569− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
570− val' <- if checkType then check val ty' else return val
571− return $ TypedValue True val' ty'
572−infer' _ = error "Invalid argument to infer"
573−
574−-- |
575−-- Infer the type of a property inside a record with a given type
576−--
577−inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
578−inferProperty (Object row) prop = do
579− let (props, _) = rowToList row
580− return $ lookup prop props
581−inferProperty (SaturatedTypeSynonym name args) prop = do
582− replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
583− inferProperty replaced prop
584−inferProperty (ForAll ident ty _) prop = do
585− replaced <- replaceVarWithUnknown ident ty
586− inferProperty replaced prop
587−inferProperty _ _ = return Nothing
588−
589−-- |
590−-- Infer the types of variables brought into scope by a binder
591−--
592−inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
593−inferBinder _ NullBinder = return M.empty
594−inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
595−inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
596−inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
597−inferBinder val (VarBinder name) = return $ M.singleton name val
598−inferBinder val (ConstructorBinder ctor binders) = do
599− env <- getEnv
600− Just moduleName <- checkCurrentModule <$> get
601− case M.lookup (qualify moduleName ctor) (dataConstructors env) of
602− Just (ty, _) -> do
603− (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contains constraints") ty
604− go binders fn
605− where
606− go [] ty = do
607− subsumes Nothing val ty
608− return M.empty
609− go (binder : binders) (TypeApp (TypeApp t obj) ret) | t == tyFunction =
610− M.union <$> inferBinder obj binder <*> go binders ret
611− go _ _ = throwError $ "Wrong number of arguments to constructor " ++ show ctor
612− _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
613−inferBinder val (ObjectBinder props) = do
614− row <- fresh
615− rest <- fresh
616− m1 <- inferRowProperties row rest props
617− val =?= Object row
618− return m1
619− where
620− inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
621− inferRowProperties nrow row [] = nrow =?= row >> return M.empty
622− inferRowProperties nrow row ((name, binder):binders) = do
623− propTy <- fresh
624− m1 <- inferBinder propTy binder
625− m2 <- inferRowProperties nrow (RCons name propTy row) binders
626− return $ m1 `M.union` m2
627−inferBinder val (ArrayBinder binders) = do
628− el <- fresh
629− m1 <- M.unions <$> mapM (inferBinder el) binders
630− val =?= TypeApp tyArray el
631− return m1
632−inferBinder val (ConsBinder headBinder tailBinder) = do
633− el <- fresh
634− m1 <- inferBinder el headBinder
635− m2 <- inferBinder val tailBinder
636− val =?= TypeApp tyArray el
637− return $ m1 `M.union` m2
638−inferBinder val (NamedBinder name binder) = do
639− m <- inferBinder val binder
640− return $ M.insert name val m
641−
642−-- |
643−-- Check the types of the return values in a set of binders in a case statement
644−--
645−checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> UnifyT Type Check [([Binder], Maybe Guard, Value)]
646−checkBinders _ _ [] = return []
647−checkBinders nvals ret ((binders, grd, val):bs) = do
648− Just moduleName <- checkCurrentModule <$> get
649− m1 <- M.unions <$> zipWithM inferBinder nvals binders
650− r <- bindLocalVariables moduleName (M.toList m1) $ do
651− val' <- TypedValue True <$> check val ret <*> pure ret
652− case grd of
653− Nothing -> return (binders, Nothing, val')
654− Just g -> do
655− g' <- check g tyBoolean
656− return (binders, Just g', val')
657− rs <- checkBinders nvals ret bs
658− return $ r : rs
659−
660−-- |
661−-- Check that a local variable name is not already used
662−--
663−assignVariable :: Ident -> UnifyT Type Check ()
664−assignVariable name = do
665− env <- checkEnv <$> get
666− Just moduleName <- checkCurrentModule <$> get
667− case M.lookup (moduleName, name) (names env) of
668− Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
669− _ -> return ()
670−
671−-- |
672−-- Generate a new skolem constant
673−--
674−newSkolemConstant :: UnifyT Type Check Int
675−newSkolemConstant = runUnknown <$> fresh'
676−
677−-- |
678−-- Generate a new skolem scope
679−--
680−newSkolemScope :: UnifyT Type Check SkolemScope
681−newSkolemScope = SkolemScope . runUnknown <$> fresh'
682−
683−-- |
684−-- Skolemize a type variable by replacing its instances with fresh skolem constants
685−--
686−skolemize :: String -> Int -> SkolemScope -> Type -> Type
687−skolemize ident sko scope = replaceTypeVars ident (Skolem sko scope)
688−
689−-- |
690−-- Introduce skolem scope at every occurence of a ForAll
691−--
692−introduceSkolemScope :: Type -> UnifyT Type Check Type
693−introduceSkolemScope = everywhereM (mkM go)
694− where
695− go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
696− go other = return other
697−
698−-- |
699−-- Check the type of a value, rethrowing errors to provide a better error message
700−--
701−check :: Value -> Type -> UnifyT Type Check Value
702−check val ty = rethrow errorMessage $ check' val ty
703− where
704− errorMessage msg =
705− "Error checking type of term " ++
706− prettyPrintValue val ++
707− " against type " ++
708− prettyPrintType ty ++
709− ":\n" ++
710− msg
711−
712−-- |
713−-- Check the type of a value
714−--
715−check' :: Value -> Type -> UnifyT Type Check Value
716−check' val t@(ForAll ident ty _) = do
717− scope <- newSkolemScope
718− sko <- newSkolemConstant
719− let sk = skolemize ident sko scope ty
720− val' <- check val sk
721− return $ TypedValue True val' (ForAll ident ty (Just scope))
722−check' val t@(ConstrainedType constraints ty) = do
723− env <- getEnv
724− Just moduleName <- checkCurrentModule <$> get
725− dictNames <- flip mapM constraints $ \(Qualified _ (ProperName className), _) -> do
726− n <- liftCheck freshDictionaryName
727− return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
728− val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
729− TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
730− (qualifyAllUnqualifiedNames moduleName env constraints)) $
731− check val ty
732− return $ TypedValue True (foldr Abs val' (map Left dictNames)) t
733−check' val t@(SaturatedTypeSynonym name args) = do
734− ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
735− val' <- check val ty
736− return $ TypedValue True val' ty
737−check' val u@(TUnknown _) = do
738− val'@(TypedValue _ _ ty) <- infer val
739− -- Don't unify an unknown with an inferred polytype
740− (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
741− ty' =?= u
742− return $ TypedValue True val'' ty'
743−check' v@(NumericLiteral _) t | t == tyNumber =
744− return $ TypedValue True v t
745−check' v@(StringLiteral _) t | t == tyString =
746− return $ TypedValue True v t
747−check' v@(BooleanLiteral _) t | t == tyBoolean =
748− return $ TypedValue True v t
749−check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
750− arr <- ArrayLiteral <$> forM vals (\val -> check val ty)
751− return $ TypedValue True arr t
752−check' (Abs (Left arg) ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
753− Just moduleName <- checkCurrentModule <$> get
754− ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
755− return $ TypedValue True (Abs (Left arg) ret') ty
756−check' (Abs (Right _) _) _ = error "Binder was not desugared"
757−check' (App f arg) ret = do
758− f'@(TypedValue _ _ ft) <- infer f
759− (ret', app) <- checkFunctionApplication f' ft arg
760− subsumes Nothing ret' ret
761− return $ TypedValue True app ret
762−check' v@(Var var) ty = do
763− Just moduleName <- checkCurrentModule <$> get
764− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
765− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
766− v' <- subsumes (Just v) repl ty'
767− case v' of
768− Nothing -> throwError "Unable to check type subsumption"
769− Just v'' -> return $ TypedValue True v'' ty'
770−check' (TypedValue checkType val ty1) ty2 = do
771− Just moduleName <- checkCurrentModule <$> get
772− kind <- liftCheck $ kindOf moduleName ty1
773− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
774− ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
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' (Constructor c) ty = do
809− env <- getEnv
810− Just moduleName <- checkCurrentModule <$> get
811− case M.lookup (qualify moduleName c) (dataConstructors env) of
812− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
813− Just (ty1, _) -> do
814− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
815− _ <- subsumes Nothing repl ty
816− return $ TypedValue True (Constructor c) ty
817−check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
818−
819−-- |
820−-- Check the type of a collection of named record fields
821−--
822−-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
823−--
824−checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
825−checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
826− go [] [] REmpty = return []
827− go [] [] u@(TUnknown _) = do u =?= REmpty
828− return []
829− go [] [] (Skolem _ _) | lax = return []
830− go [] ((p, _): _) _ | lax = return []
831− | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
832− go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
833− go ((p,v):ps') [] u@(TUnknown _) = do
834− v'@(TypedValue _ _ ty) <- infer v
835− rest <- fresh
836− u =?= RCons p ty rest
837− ps'' <- go ps' [] rest
838− return $ (p, v') : ps''
839− go ((p,v):ps') ts r =
840− case lookup p ts of
841− Nothing -> do
842− v'@(TypedValue _ _ ty) <- infer v
843− rest <- fresh
844− r =?= RCons p ty rest
845− ps'' <- go ps' ts rest
846− return $ (p, v') : ps''
847− Just ty -> do
848− v' <- check v ty
849− ps'' <- go ps' (delete (p, ty) ts) r
850− return $ (p, v') : ps''
851− go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
852−
853−-- |
854−-- Check the type of a function application, rethrowing errors to provide a better error message
855−--
856−checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
857−checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
858− where
859− errorMessage msg = "Error applying function of type "
860− ++ prettyPrintType fnTy
861− ++ " to argument " ++ prettyPrintValue arg
862− ++ ":\n" ++ msg
863−
864−-- |
865−-- Check the type of a function application
866−--
867−checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
868−checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
869− tyFunction' =?= tyFunction
870− arg' <- check arg argTy
871− return (retTy, App fn arg')
872−checkFunctionApplication' fn (ForAll ident ty _) arg = do
873− replaced <- replaceVarWithUnknown ident ty
874− checkFunctionApplication fn replaced arg
875−checkFunctionApplication' fn u@(TUnknown _) arg = do
876− arg' <- do
877− TypedValue _ arg' t <- infer arg
878− (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
879− return $ TypedValue True arg'' t'
880− let ty = (\(TypedValue _ _ t) -> t) arg'
881− ret <- fresh
882− u =?= function ty ret
883− return (ret, App fn arg')
884−checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
885− ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
886− checkFunctionApplication fn ty arg
887−checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
888− env <- getEnv
889− dicts <- getTypeClassDictionaries
890− Just moduleName <- checkCurrentModule <$> get
891− checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) fnTy arg
892−checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
893− ++ prettyPrintType fnTy
894− ++ " to argument " ++ prettyPrintValue arg
895−
896−-- |
897−-- Check whether one type subsumes another, rethrowing errors to provide a better error message
898−--
899−subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
900−subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
901− where
902− errorMessage msg = "Error checking that type "
903− ++ prettyPrintType ty1
904− ++ " subsumes type "
905− ++ prettyPrintType ty2
906− ++ ":\n" ++ msg
907−
908−-- |
909−-- Check whether one type subsumes another
910−--
911−subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
912−subsumes' val (ForAll ident ty1 _) ty2 = do
913− replaced <- replaceVarWithUnknown ident ty1
914− subsumes val replaced ty2
915−subsumes' val ty1 (ForAll ident ty2 sco) =
916− case sco of
917− Just sco' -> do
918− sko <- newSkolemConstant
919− let sk = skolemize ident sko sco' ty2
920− subsumes val ty1 sk
921− Nothing -> throwError "Skolem variable scope is unspecified"
922−subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
923− subsumes Nothing arg2 arg1
924− subsumes Nothing ret1 ret2
925− return val
926−subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
927− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
928− subsumes val ty1 ty2
929−subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
930− ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
931− subsumes val ty1 ty2
932−subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
933− env <- getEnv
934− dicts <- getTypeClassDictionaries
935− Just moduleName <- checkCurrentModule <$> get
936− _ <- subsumes' Nothing ty1 ty2
937− return . Just $ foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))
938−subsumes' val (Object r1) (Object r2) = do
939− let
940− (ts1, r1') = rowToList r1
941− (ts2, r2') = rowToList r2
942− ts1' = sortBy (comparing fst) ts1
943− ts2' = sortBy (comparing fst) ts2
944− go ts1' ts2' r1' r2'
945− return val
946− where
947− go [] ts2 r1 r2 = r1 =?= rowFromList (ts2, r2)
948− go ts1 [] r1 r2 = r2 =?= rowFromList (ts1, r1)
949− go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1 r2
950− | p1 == p2 = do subsumes Nothing ty1 ty2
951− go ts1 ts2 r1 r2
952− | p1 < p2 = do rest <- fresh
953− r2 =?= RCons p1 ty1 rest
954− go ts1 ((p2, ty2) : ts2) r1 rest
955− | p1 > p2 = do rest <- fresh
956− r1 =?= RCons p2 ty2 rest
957− go ((p1, ty1) : ts1) ts2 rest r2
958−subsumes' val ty1 ty2@(Object _) = subsumes val ty2 ty1
959−subsumes' val ty1 ty2 = do
960− ty1 =?= ty2
961− return val
962−