mirror of
https://github.com/urbit/shrub.git
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303 lines
8.7 KiB
Haskell
303 lines
8.7 KiB
Haskell
module Deppy.Core where
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import ClassyPrelude
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import Bound
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import Data.Deriving (deriveEq1, deriveOrd1, deriveRead1, deriveShow1)
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import Data.Maybe (fromJust)
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import Data.Set (isSubsetOf)
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import qualified Data.Set as Set
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import Numeric.Natural
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type Typ = Exp
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data Exp a
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= Var a
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-- types
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| Typ
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| Fun (Abs a)
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| Cel (Abs a)
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| Wut (Set Tag)
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-- introduction forms
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| Lam (Abs a)
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| Cns (Exp a) (Exp a)
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| Tag Tag
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-- elimination forms
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| App (Exp a) (Exp a)
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| Hed (Exp a)
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| Tal (Exp a)
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| Cas (Typ a) (Exp a) (Map Tag (Exp a))
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-- recursion, flow control
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| Let (Exp a) (Scope () Exp a)
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| Rec (Abs a)
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deriving (Functor, Foldable, Traversable)
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type Tag = Natural
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data Abs a = Abs
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{ spec :: Typ a
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, body :: Scope () Exp a
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}
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deriving (Functor, Foldable, Traversable)
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deriveEq1 ''Abs
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deriveOrd1 ''Abs
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deriveRead1 ''Abs
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deriveShow1 ''Abs
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--makeBound ''Abs
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deriveEq1 ''Exp
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deriveOrd1 ''Exp
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deriveRead1 ''Exp
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deriveShow1 ''Exp
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--makeBound ''Exp
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deriving instance Eq a => Eq (Abs a)
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deriving instance Ord a => Ord (Abs a)
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deriving instance Read a => Read (Abs a)
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deriving instance Show a => Show (Abs a)
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deriving instance Eq a => Eq (Exp a)
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deriving instance Ord a => Ord (Exp a)
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deriving instance Read a => Read (Exp a)
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deriving instance Show a => Show (Exp a)
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instance Applicative Exp where
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pure = Var
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(<*>) = ap
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instance Monad Exp where
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return = Var
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Var a >>= f = f a
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Typ >>= _ = Typ
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Fun a >>= f = Fun (bindAbs a f)
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Cel a >>= f = Cel (bindAbs a f)
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Wut ls >>= _ = Wut ls
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Lam a >>= f = Lam (bindAbs a f)
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Cns x y >>= f = Cns (x >>= f) (y >>= f)
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Tag l >>= _ = Tag l
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App x y >>= f = App (x >>= f) (y >>= f)
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Hed x >>= f = Hed (x >>= f)
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Tal x >>= f = Tal (x >>= f)
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Cas t x cs >>= f = Cas (t >>= f) (x >>= f) (cs <&> (>>= f))
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Let a b >>= f = Let (a >>= f) (b >>>= f)
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Rec a >>= f = Rec (bindAbs a f)
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bindAbs :: Abs a -> (a -> Exp b) -> Abs b
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bindAbs (Abs s b) f = Abs (s >>= f) (b >>>= f)
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lam :: Eq a => a -> Typ a -> Exp a -> Exp a
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lam v t e = Lam (Abs t (abstract1 v e))
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fun :: Eq a => a -> Typ a -> Typ a -> Typ a
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fun v t u = Fun (Abs t (abstract1 v u))
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fun_ :: Typ a -> Typ a -> Typ a
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fun_ t u = Fun (Abs t (abstract (const Nothing) u))
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cel :: Eq a => a -> Typ a -> Typ a -> Typ a
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cel v t u = Cel (Abs t (abstract1 v u))
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cel_ :: Typ a -> Typ a -> Typ a
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cel_ t u = Cel (Abs t (abstract (const Nothing) u))
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rec :: Eq a => a -> Typ a -> Exp a -> Exp a
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rec v t e = Rec (Abs t (abstract1 v e))
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ledt :: Eq a => a -> Exp a -> Exp a -> Exp a
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ledt v e e' = Let e (abstract1 v e')
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wut = Wut . setFromList
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cas t e cs = Cas t e (mapFromList cs)
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infixl 9 @:
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(@:) = App
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-- | typing environment
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type Env a = a -> Typ a
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extend :: (b -> Typ a) -> Env a -> Env (Var b a)
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extend handleNewBindings oldEnv = \case
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-- TODO can we use Scope to decrease the cost of this?
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B v -> F <$> handleNewBindings v
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F v -> F <$> oldEnv v
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extend1 :: Typ a -> Env a -> Env (Var () a)
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extend1 t = extend \() -> t
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-- | amber rule assumptions
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type Asm a = Set (Typ a, Typ a)
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extendAsm :: (Ord a, Ord b) => Asm a -> Asm (Var b a)
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extendAsm = Set.map \(t, u) -> (F <$> t, F <$> u)
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-- | Remove types that mention variables that are no longer in scope
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retractAsm :: (Ord a, Ord b) => Asm (Var b a) -> Asm a
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retractAsm = foldMap wither
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where
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wither = \case
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(cleanTyp -> Just t, cleanTyp -> Just u) -> singleton (t, u)
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_ -> mempty
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cleanTyp = traverse \case
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F v -> pure v
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B _ -> Nothing
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type Typing = Maybe
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-- TODO
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-- - better errors
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-- - state monad for Asm (how to handle polymorphic recursion?)
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nest :: (Show a, Ord a) => Env a -> Typ a -> Typ a -> Typing ()
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nest env = fmap void . go env mempty
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where
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go :: (Show a, Ord a) => Env a -> Asm a -> Typ a -> Typ a -> Typing (Asm a)
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-- FIXME use a better more aggro normal form
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go env asm0 (whnf -> t0) (whnf -> u0) =
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if t0 == u0 || member (t0, u0) asm0
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then pure asm0
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else let asm = Set.insert (t0, u0) asm0 in
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case (t0, u0) of
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(Typ, Typ) -> pure asm
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-- FIXME yeah actually I think this is wrong
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-- we're comaring the type of a type variable with
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-- (Var v, u) -> go env asm (env v) u
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-- (t, Var v) -> go env asm t (env v)
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-- following Cardelli 80something, we check the RHSs assuming
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-- the putatively *lesser* of the LHSs for both
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(Fun (Abs a b), Fun (Abs a' b')) -> do
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asm' <- go env asm a' a
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retractAsm <$>
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go (extend1 a' env) (extendAsm asm') (fromScope b) (fromScope b')
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(Cel (Abs a b), Cel (Abs a' b')) -> do
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asm' <- go env asm a a'
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retractAsm <$>
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go (extend1 a env) (extendAsm asm') (fromScope b) (fromScope b')
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(Wut ls, Wut ls') -> do
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guard (ls `isSubsetOf` ls')
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pure asm
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-- TODO put into Typing errors
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(Lam{}, _) -> error "nest: lambda"
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(_, Lam{}) -> error "nest: lambda"
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(Cns{}, _) -> error "nest: cons"
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(_, Cns{}) -> error "nest: cons"
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(Tag{}, _) -> error "nest: tag"
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(_, Tag{}) -> error "nest: tag"
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-- Special rule for the Cas eliminator to enable sums and products
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(Cas _ e cs, Cas _ e' cs') -> do
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guard (whnf e == whnf e')
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Wut s <- infer env e
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-- TODO I should thread changing asm through the traversal
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-- but I can't be bothered right now. Perf regression.
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asm <$ traverse_ chk (setToList s)
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where
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chk tag = case (lookup tag cs, lookup tag cs') of
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(Just t, Just u) -> go env asm t u
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_ -> error "the Spanish inquisition"
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(Cas _ e cs, u) -> do
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Wut s <- infer env e
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-- TODO thread asms
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asm <$ traverse_
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(\tag -> go env asm (fromJust $ lookup tag cs) u)
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s
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(t, Cas _ e cs) -> do
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Wut s <- infer env e
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-- TODO thread asms
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asm <$ traverse_
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(\tag -> go env asm t (fromJust $ lookup tag cs))
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s
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(t@Cas{}, u) -> go env asm (whnf t) u
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(t, u@Cas{}) -> go env asm t (whnf u)
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(t@(Rec (Abs _ b)), u) -> go env asm (instantiate1 t b) u
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(t, u@(Rec (Abs _ b))) -> go env asm t (instantiate1 u b)
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_ -> Nothing
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check :: (Show a, Ord a) => Env a -> Exp a -> Typ a -> Typing ()
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check env e t = do
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t' <- infer env e
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nest env t' t
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infer :: forall a. (Show a, Ord a) => Env a -> Exp a -> Typing (Typ a)
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infer env = \case
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Var v -> pure $ env v
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Typ -> pure Typ
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Fun (Abs t b) -> do
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Typ <- infer env t
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Typ <- infer (extend1 t env) (fromScope b)
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pure Typ
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Cel (Abs t b) -> do
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Typ <- infer env t
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Typ <- infer (extend1 t env) (fromScope b)
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pure Typ
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Wut _ -> pure Typ
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Lam (Abs t b) -> do
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-- TODO do I need (whnf -> Typ)? (and elsewhere)
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Typ <- infer env t
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(toScope -> t') <- infer (extend1 t env) (fromScope b)
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pure $ Fun (Abs t t')
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Cns x y -> do
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-- Infer non-dependent pairs; if you want dependency, you must annotate
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t <- infer env x
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u <- infer env y
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pure $ Cel (Abs t (abstract (const Nothing) u))
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Tag t -> pure $ Wut (singleton t)
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App x y -> do
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Fun (Abs t b) <- infer env x
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check env y t
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pure $ whnf (instantiate1 y b)
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Hed x -> do
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Cel (Abs t _) <- infer env x
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pure t
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Tal x -> do
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Cel (Abs _ u) <- infer env x
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pure $ instantiate1 (whnf $ Hed $ x) u
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Cas t x cs -> do
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Typ <- infer env t
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Wut ts <- infer env x
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-- pretty restrictive - do we want?
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guard (ts == keysSet cs)
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traverse_ (\e -> check env e t) cs
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pure t
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-- Let e b -> do
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-- -- TODO is below faster, or infer env (instantiate1 e b)?
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-- t <- infer env e
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-- instantiate1 e $ infer (extend1 t env) (fromScope b)
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Rec (Abs t b) -> do
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Typ <- infer env t
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-- todo can F <$> be made faster?
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check (extend1 t env) (fromScope b) (F <$> t)
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pure t
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whnf :: (Show a, Eq a) => Exp a -> Exp a
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whnf = \case
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App (whnf -> Lam (Abs _ b)) x -> whnf $ instantiate1 x b
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Hed (whnf -> Cns x _) -> whnf x
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Tal (whnf -> Cns _ y) -> whnf y
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Cas _ (whnf -> Tag t) cs -> whnf $ fromJust $ lookup t cs
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e@(Rec (Abs _ b)) -> whnf $ instantiate1 e b
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e -> trace "sadface" e
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{-
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= Var a
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-- types
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| Typ
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| Fun (Abs a)
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| Cel (Abs a)
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| Wut (Set Tag)
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-- introduction forms
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| Lam (Abs a)
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| Cns (Exp a) (Exp a)
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| Tag Tag
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-- elimination forms
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| App (Exp a) (Exp a)
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| Hed (Exp a)
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| Tal (Exp a)
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| Cas (Typ a) (Exp a) (Map Tag (Exp a))
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-- recursion
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| Rec (Abs a)
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-}
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nf :: (Show a, Eq a) => Exp a -> Exp a
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nf = traceShowId . \case
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Typ -> Typ
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_ -> undefined
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