Started working on algorithm M

diff --git a/sem.icl b/sem.icl
index 16a426c..8cc3df9 100644 (file)
--- a/sem.icl
+++ b/sem.icl
@@ -99,19 +99,6 @@ where
                                _ = 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: "
-
 class Typeable a where
     ftv :: a -> [TVar]
     subst :: Substitution a -> a
@@ -147,8 +134,8 @@ instance Typeable Gamma where
 instance zero Substitution where zero = 'Map'.newMap
 
 compose :: Substitution Substitution -> Substitution
-compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
-//Note: unlike function composition, compose is left biased!
+compose s1 s2 = 'Map'.union (Mapmap (subst s2) s1) s2
+//Note: just like function compositon compose does snd first
 
 occurs :: TVar a -> Bool | Typeable a
 occurs tvar a = elem tvar (ftv a)
@@ -177,13 +164,19 @@ gamma :: Typing Gamma
 gamma = gets fst
 putGamma :: Gamma -> Typing ()
 putGamma g = modify (appFst $ const g) >>| pure ()
-withGamma :: (Gamma -> Gamma) -> Typing ()
-withGamma f = modify (appFst f) >>| pure ()
+changeGamma :: (Gamma -> Gamma) -> Typing ()
+changeGamma f = modify (appFst f) >>| pure ()
+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
@@ -191,13 +184,67 @@ 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 Scheme 
+lookup k = gamma >>= \g-> case 'Map'.member k g of
+    False = liftT (Left $ UndeclaredVariableError zero k)
+    True = pure ('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)
+
+instance infer Expr where 
+ infer e = case e of
+    VarExpr _ (VarDef k fs) = (\t->(zero,t)) <$> (lookup k >>= instantiate)
+    //instantiate is key for the let polymorphism!
+
+    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 s1 $ compose s2 s3), 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 s1 s2), 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)
 
 
 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
@@ -206,6 +253,22 @@ Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
                                         (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
 //// ------------------------//