import Control.Monad
import Control.Monad.Trans
+import Control.Monad.State
import Data.Either
import Data.Maybe
import Data.Monoid
import Data.List
import Data.Functor
+import Data.Tuple
import StdString
+import StdTuple
import StdList
import StdMisc
import StdEnum
-import RWST
import GenEq
from Text import class Text(concat), instance Text String
:: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
:: Substitution :== 'Map'.Map TVar Type
:: Constraints :== [(Type, Type)]
-:: Infer a :== RWST Gamma Constraints [String] (Either SemError) a
:: SemError
= ParseError Pos String
| UnifyError Pos Type Type
instance zero Gamma where
zero = 'Map'.newMap
-variableStream :: [String]
+variableStream :: [TVar]
variableStream = map toString [1..]
sem :: AST -> Either [SemError] Constraints
>>| foldM (const isNiceMain) () fd
>>| hasMain fd of
Left e = Left [e]
- _ = case execRWST (constraints fd) zero variableStream of
- Left e = Left [e]
- Right (a, b) = Right b
+ _ = Right []
+ //_ = case execRWST (constraints fd) zero variableStream of
+ // Left e = Left [e]
+ // Right (a, b) = Right b
where
- constraints :: [FunDecl] -> Infer ()
+ constraints :: [FunDecl] -> Typing ()
constraints _ = pure ()
//TODO: fix
//constraints fds = mapM_ funconstraint fds >>| pure ()
- funconstraint :: FunDecl -> Infer ()
+ funconstraint :: FunDecl -> Typing ()
funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
Nothing = abort "Cannot infer functions yet"
- Just t = inEnv (ident, (Forall [] t)) (
- mapM_ vardeclconstraint vardecls >>| pure ())
+ _ = pure ()
+ //Just t = inEnv (ident, (Forall [] t)) (
+ // mapM_ vardeclconstraint vardecls >>| pure ())
- vardeclconstraint :: VarDecl -> Infer ()
+ vardeclconstraint :: VarDecl -> Typing ()
vardeclconstraint _ = pure ()
//TODO: fix!
//vardeclconstraint (VarDecl p mt ident expr) = infer expr
_ = Left $ SanityError p "main has to return Void")
isNiceMain _ = pure ()
-instance toString Scheme where
- toString (Forall x t) =
- concat ["Forall ": map ((+++) "\n") x] +++ toString t
-
-instance toString Gamma where
- toString mp =
- concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
-
-instance toString SemError where
- toString (SanityError p e) = concat [toString p,
- "SemError: SanityError: ", e]
- toString se = "SemError: "
-
-inEnv :: (String, Scheme) (Infer a) -> Infer a
-inEnv (x, sc) m = local ('Map'.put x sc) m
-
class Typeable a where
ftv :: a -> [TVar]
subst :: Substitution a -> a
ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
subst s gamma = Mapmap (subst s) gamma
+extend :: String Scheme Gamma -> Gamma
+extend k t g = 'Map'.put k t g
+
//// ------------------------
//// algorithm U, Unification
//// ------------------------
compose :: Substitution Substitution -> Substitution
compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
-//Note: unlike function composition, compose prefers left!
+//Note: just like function compositon compose does snd first
occurs :: TVar a -> Bool | Typeable a
occurs tvar a = elem tvar (ftv a)
unify t1 t2 | t1 == t2 = Right zero
| otherwise = Left $ UnifyError zero t1 t2
-
-
-
-
+//// ------------------------
+//// Algorithm M, Inference and Solving
+//// ------------------------
+//The typing monad
+:: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
+gamma :: Typing Gamma
+gamma = gets fst
+putGamma :: Gamma -> Typing ()
+putGamma g = modify (appFst $ const g) >>| pure ()
+changeGamma :: (Gamma -> Gamma) -> Typing Gamma
+changeGamma f = modify (appFst f) >>| gamma
+withGamma :: (Gamma -> a) -> Typing a
+withGamma f = f <$> gamma
+fresh :: Typing Type
+fresh = gets snd >>= \vars->
+ modify (appSnd $ const $ tail vars) >>|
+ pure (IdType (head vars))
+
+lift :: (Either SemError a) -> Typing a
+lift (Left e) = liftT $ Left e
+lift (Right v) = pure v
+
+//instantiate maps a schemes type variables to variables with fresh names
+//and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
+instantiate :: Scheme -> Typing Type
+instantiate (Forall bound t) =
+ mapM (const fresh) bound >>= \newVars->
+ let s = 'Map'.fromList (zip (bound,newVars)) in
+ pure (subst s t)
+
+//generalize quentifies all free type variables in a type which are not
+//in the gamma
+generalize :: Type -> Typing Scheme
+generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
+
+lookup :: String -> Typing Type
+lookup k = gamma >>= \g-> case 'Map'.member k g of
+ False = liftT (Left $ UndeclaredVariableError zero k)
+ True = instantiate $ 'Map'.find k g
+
+//The inference class
+//When tying it all together we will treat the program is a big
+//let x=e1 in let y=e2 in ....
+class infer a :: a -> Typing (Substitution, Type)
+
+////---- Inference for Expressions ----
+
+instance infer Expr where
+ infer e = case e of
+ VarExpr _ (VarDef k fs) = (\t->(zero,t)) <$> lookup k
+ //instantiate is key for the let polymorphism!
+ //TODO: field selectors
+
+ Op2Expr _ e1 op e2 =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ fresh >>= \tv ->
+ let given = t1 ->> t2 ->> tv in
+ op2Type op >>= \expected ->
+ lift (unify expected given) >>= \s3 ->
+ pure ((compose s3 $ compose s2 s1), subst s3 tv)
+
+ Op1Expr _ op e1 =
+ infer e1 >>= \(s1, t1) ->
+ fresh >>= \tv ->
+ let given = t1 ->> tv in
+ op1Type op >>= \expected ->
+ lift (unify expected given) >>= \s2 ->
+ pure (compose s2 s1, subst s2 tv)
+
+ EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+
+ TupleExpr _ (e1, e2) =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ pure (compose s2 s1, TupleType (t1,t2))
+
+ FunExpr _ f args fs = //todo: fieldselectors
+ lookup f >>= \expected ->
+ let accST = (\(s,ts) e->infer e >>= \(s_,et)->pure (compose s_ s,ts++[et])) in
+ foldM accST (zero,[]) args >>= \(s1, argTs)->
+ fresh >>= \tv->
+ let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ pure (compose s2 s1, subst s2 tv)
+
+ IntExpr _ _ = pure $ (zero, IntType)
+ BoolExpr _ _ = pure $ (zero, BoolType)
+ CharExpr _ _ = pure $ (zero, CharType)
+
+
+op2Type :: Op2 -> Typing Type
+op2Type op
+| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
+ = pure (IntType ->> IntType ->> IntType)
+| elem op [BiEquals, BiUnEqual]
+ = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
+| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
+ = pure (IntType ->> IntType ->> BoolType)
+| elem op [BiAnd, BiOr]
+ = pure (BoolType ->> BoolType ->> BoolType)
+| op == BiCons
+ = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
+
+op1Type :: Op1 -> Typing Type
+op1Type UnNegation = pure $ (BoolType ->> BoolType)
+op1Type UnMinus = pure $ (IntType ->> IntType)
+
+////----- Inference for Statements -----
+applySubst :: Substitution -> Typing Gamma
+applySubst s = changeGamma (subst s)
+
+instance infer Stmt where
+ infer s = case s of
+ IfStmt e th el =
+ infer e >>= \(s1, et)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer th >>= \(s3, tht)->
+ applySubst s3 >>|
+ infer el >>= \(s4, elt)->
+ applySubst s4 >>|
+ lift (unify tht elt) >>= \s5->
+ pure (compose s5 $ compose s4 $ compose s3 $ compose s1 s2, subst s5 tht)
+
+ WhileStmt e wh =
+ infer e >>= \(s1, et)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer wh >>= \(s3, wht)->
+ pure (compose s3 $ compose s1 s2, subst s3 wht)
+
+ AssStmt (VarDef k fs) e =
+ infer e >>= \(s1, et)->
+ applySubst s1 >>|
+ changeGamma (extend k (Forall [] et)) >>| //todo: fieldselectors
+ pure (s1, VoidType)
+
+ FunStmt f es = undef //what is this?
+
+ ReturnStmt Nothing = pure (zero, VoidType)
+ ReturnStmt (Just e) = infer e
+
+
+instance infer [a] | infer a where
+ infer _ = undef
Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
Mapmap _ 'Map'.Tip = 'Map'.Tip
(Mapmap f ml)
(Mapmap f mr)
+instance toString Scheme where
+ toString (Forall x t) =
+ concat ["Forall ": map ((+++) "\n") x] +++ toString t
+
+instance toString Gamma where
+ toString mp =
+ concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
+
+instance toString SemError where
+ toString (SanityError p e) = concat [toString p,
+ "SemError: SanityError: ", e]
+ toString se = "SemError: "
+
+instance MonadTrans (StateT (Gamma, [TVar])) where
+ liftT m = StateT \s-> m >>= \a-> return (a, s)
+
//// ------------------------
//// First step: Inference
//// ------------------------//