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{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeSynonymInstances #-}
module CC.Typecheck(runPass) where
import Control.Monad.State.Strict
import Control.Monad.Except
import qualified Data.Map.Strict as Map
import Data.Map.Strict (Map)
import Data.Maybe
import qualified Data.Set as Set
import Data.Set (Set)
import qualified CC.AST.Source as S
import qualified CC.AST.Typed as T
import CC.Context
import CC.Pretty
import CC.Types
-- Inspiration: https://github.com/kritzcreek/fby19
data TCError = TypeError SourceRange T.Type T.Type
| RefError SourceRange Name
deriving (Show)
instance Pretty TCError where
pretty (TypeError sr real expect) =
"Type error: Expression at " ++ pretty sr ++
" has type " ++ pretty real ++
", but should have type " ++ pretty expect
pretty (RefError sr name) =
"Reference error: Variable '" ++ name ++ "' out of scope at " ++ pretty sr
type TM a = ExceptT TCError (State Int) a
genId :: TM Int
genId = state (\idval -> (idval, idval + 1))
genTyVar :: TM T.Type
genTyVar = T.TyVar <$> genId
runTM :: TM a -> Either TCError a
runTM m = evalState (runExceptT m) 1
newtype Env = Env (Map Name T.TypeScheme)
newtype Subst = Subst (Map Int T.Type)
class FreeTypeVars a where
freeTypeVars :: a -> Set Int
instance FreeTypeVars T.Type where
freeTypeVars (T.TFun t1 t2) = freeTypeVars t1 <> freeTypeVars t2
freeTypeVars T.TInt = mempty
freeTypeVars (T.TTup ts) = Set.unions (map freeTypeVars ts)
freeTypeVars (T.TyVar var) = Set.singleton var
instance FreeTypeVars T.TypeScheme where
freeTypeVars (T.TypeScheme bnds ty) = foldr Set.delete (freeTypeVars ty) bnds
instance FreeTypeVars Env where
freeTypeVars (Env mp) = foldMap freeTypeVars (Map.elems mp)
infixr >>!
class Substitute a where
(>>!) :: Subst -> a -> a
instance Substitute T.Type where
theta@(Subst mp) >>! ty = case ty of
T.TFun t1 t2 -> T.TFun (theta >>! t1) (theta >>! t2)
T.TInt -> T.TInt
T.TTup ts -> T.TTup (map (theta >>!) ts)
T.TyVar i -> fromMaybe ty (Map.lookup i mp)
instance Substitute T.TypeScheme where
Subst mp >>! T.TypeScheme bnds ty =
T.TypeScheme bnds (Subst (foldr Map.delete mp bnds) >>! ty)
instance Substitute Env where
theta >>! Env mp = Env (Map.map (theta >>!) mp)
-- TODO: make this instance unnecessary
instance Substitute T.Expr where
theta >>! T.Lam ty (T.Occ name ty2) body =
T.Lam (theta >>! ty) (T.Occ name (theta >>! ty2)) (theta >>! body)
theta >>! T.Let (T.Occ name ty) rhs body =
T.Let (T.Occ name (theta >>! ty)) (theta >>! rhs) (theta >>! body)
theta >>! T.Call ty e1 e2 =
T.Call (theta >>! ty) (theta >>! e1) (theta >>! e2)
_ >>! expr@(T.Int _) = expr
theta >>! T.Tup es = T.Tup (map (theta >>!) es)
theta >>! T.Var (T.Occ name ty) = T.Var (T.Occ name (theta >>! ty))
instance Semigroup Subst where
s2@(Subst m2) <> Subst m1 = Subst (Map.union (Map.map (s2 >>!) m1) m2)
instance Monoid Subst where
mempty = Subst mempty
emptyEnv :: Env
emptyEnv = Env mempty
envAdd :: Name -> T.TypeScheme -> Env -> Env
envAdd name sty (Env mp) = Env (Map.insert name sty mp)
envFind :: Name -> Env -> Maybe T.TypeScheme
envFind name (Env mp) = Map.lookup name mp
substVar :: Int -> T.Type -> Subst
substVar var ty = Subst (Map.singleton var ty)
generalise :: Env -> T.Type -> T.TypeScheme
generalise env ty =
T.TypeScheme (Set.toList (freeTypeVars ty Set.\\ freeTypeVars env)) ty
instantiate :: T.TypeScheme -> TM T.Type
instantiate (T.TypeScheme bnds ty) = do
vars <- traverse (const genTyVar) bnds
let theta = Subst (Map.fromList (zip bnds vars))
return (theta >>! ty)
data UnifyContext = UnifyContext SourceRange T.Type T.Type
unify :: SourceRange -> T.Type -> T.Type -> TM Subst
unify sr t1 t2 = unify' (UnifyContext sr t1 t2) t1 t2
unify' :: UnifyContext -> T.Type -> T.Type -> TM Subst
unify' _ T.TInt T.TInt = return mempty
unify' ctx (T.TFun t1 t2) (T.TFun u1 u2) = (<>) <$> unify' ctx t1 u1 <*> unify' ctx t2 u2
unify' ctx (T.TTup ts) (T.TTup us)
| length ts == length us = mconcat <$> zipWithM (unify' ctx) ts us
unify' _ (T.TyVar var) ty = return (substVar var ty)
unify' _ ty (T.TyVar var) = return (substVar var ty)
unify' (UnifyContext sr t1 t2) _ _ = throwError (TypeError sr t1 t2)
convertType :: S.Type -> T.Type
convertType (S.TFun t1 t2) = T.TFun (convertType t1) (convertType t2)
convertType S.TInt = T.TInt
convertType (S.TTup ts) = T.TTup (map convertType ts)
infer :: Env -> S.Expr -> TM (Subst, T.Expr)
infer env expr = case expr of
S.Lam _ [] body -> infer env body
S.Lam sr args@(_:_:_) body -> infer env (foldr (S.Lam sr . pure) body args)
S.Lam _ [(arg, _)] body -> do
argVar <- genTyVar
let augEnv = envAdd arg (T.TypeScheme [] argVar) env
(theta, body') <- infer augEnv body
let argType = theta >>! argVar
return (theta, T.Lam (T.TFun argType (T.exprType body'))
(T.Occ arg argType) body')
S.Let _ (name, _) rhs body -> do
(theta1, rhs') <- infer env rhs
let varType = T.exprType rhs'
let augEnv = envAdd name (T.TypeScheme [] varType) env
(theta2, body') <- infer augEnv body
return (theta2 <> theta1, T.Let (T.Occ name varType) rhs' body')
S.Call sr func arg -> do
(theta1, func') <- infer env func
(theta2, arg') <- infer (theta1 >>! env) arg
resVar <- genTyVar
theta3 <- unify sr (theta2 >>! T.exprType func')
(T.TFun (T.exprType arg') resVar)
return (theta3 <> theta2 <> theta1
,T.Call (theta3 >>! resVar)
((theta3 <> theta2) >>! func') -- TODO: quadratic complexity
(theta3 >>! arg')) -- TODO: quadratic complexity
S.Int _ val -> return (mempty, T.Int val)
S.Tup _ es -> fmap T.Tup <$> inferList env es
S.Var sr name
| Just sty <- envFind name env -> do
ty <- instantiate sty
return (mempty, T.Var (T.Occ name ty))
| otherwise ->
throwError (RefError sr name)
S.Annot sr subex ty -> do
(theta1, subex') <- infer env subex
theta2 <- unify sr (T.exprType subex') (convertType ty)
return (theta2 <> theta1, theta2 >>! subex') -- TODO: quadratic complexity
inferList :: Env -> [S.Expr] -> TM (Subst, [T.Expr])
inferList _ [] = return (mempty, [])
inferList env (expr : exprs) = do
(theta, expr') <- infer env expr
(theta', res) <- inferList (theta >>! env) exprs
return (theta <> theta', expr' : res)
runPass :: Context -> S.Program -> Either TCError T.Program
runPass (Context _ (Builtins builtins)) prog =
let env = Env (Map.fromList [(name, generalise emptyEnv ty) | (name, ty) <- builtins])
in runTM (typeCheck env prog)
typeCheck :: Env -> S.Program -> TM T.Program
typeCheck startEnv (S.Program decls) =
let defs = [(name, ty)
| S.Def (S.Function (Just ty) (name, _) _ _) <- decls]
env = foldl (\env' (name, ty) -> envAdd name (generalise env' (convertType ty)) env')
startEnv defs
in T.Program <$> mapM (typeCheckDef env . (\(S.Def def) -> def)) decls
typeCheckDef :: Env -> S.Def -> TM T.Def
typeCheckDef env (S.Function mannot (name, sr) args@(_:_) body) =
typeCheckDef env (S.Function mannot (name, sr) [] (S.Lam sr args body))
typeCheckDef env (S.Function (Just annot) (name, sr) [] body) =
typeCheckDef env (S.Function Nothing (name, sr) [] (S.Annot sr body annot))
typeCheckDef env (S.Function Nothing (name, _) [] body) = do
(_, body') <- infer env body
return (T.Def name body')
|
