Re: [Haskell-cafe] Flipping *->*->* kinds, or monadic finally-tagless madness
>Kim-Ee Yeoh wrote: >> As for fixing the original bug, I've found that the real magic lies >> in the incantation (Y . unY) inserted at the appropriate places. >Aka unsafeCoerce, changing the phantom type |a|. The type of (Y . unY) is (Y . unY) :: forall a b c. Y c a -> Y c b so modulo (Y c), it is indeed unsafeCoerce. >The need to do it is caused by wanting to erase the existential introduced >by Za/MkZa. That's not the primary reason. The earlier version of the code in my original message doesn't use existentials. We still however, need to "wobble" the type via (Y . unY) in order to typecheck. >Depending on what the phantom type is supposed to represent, this may or >may not give the semantics/safety you're after. If you're referring to the safety of the object/target language, then even without any Symantics instances, only type-correct code can compile, thanks to the finally-tagless embedding that "lifts" type-checking in the meta-language (Haskell) into type-checking for the target language. That safety isn't in the least bit compromised. The pretty-printing Symantics instance in question actually type-checks fine without unsafeCoerce or its like when written out without the additional Monad type-class abstraction and Y-Z isomorphism. Translating to the latter was entirely straightforward. Thanks to all who responded. -- View this message in context: http://www.nabble.com/Flipping-*-%3E*-%3E*-kinds%2C-or-monadic-finally-tagless-madness-tp24314553p24439023.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Flipping *->*->* kinds, or monadic finally-tagless madness
Kim-Ee Yeoh wrote:
> > type VarCount = int
> > newtype Y b a = Y {unY :: VarCount -> (b, VarCount)}
>
Hi Edward,
Your runPretty version fits the bill nicely, thank you. I might still retain
the state monad version because it allows generalizations beyond
pretty-printing.
As for fixing the original bug, I've found that the real magic lies
in the incantation (Y . unY) inserted at the appropriate places.
Aka unsafeCoerce, changing the phantom type |a|. The need to do it is
caused by wanting to erase the existential introduced by Za/MkZa.
Depending on what the phantom type is supposed to represent, this may or
may not give the semantics/safety you're after.
--
Live well,
~wren
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Re: [Haskell-cafe] Flipping *->*->* kinds, or monadic finally-tagless madness
Hi Edward,
Your runPretty version fits the bill nicely, thank you. I might still retain
the state monad version because it allows generalizations beyond
pretty-printing.
As for fixing the original bug, I've found that the real magic lies
in the incantation (Y . unY) inserted at the appropriate places. Indeed,
I've removed type signatures because try as I might, I couldn't
write something the type-checker would accept. This is for 6.8.2.
FWIW, the final version:
instance Symantics (Y String) where
int = unZ . return . show
bool = unZ . return . show
lam f = unZ $ do
show_c0 <- get
let
vname = "v" ++ show_c0
c0 = read show_c0 :: VarCount
c1 = succ c0
put (show c1)
bodyf <- (Z . Y . unY . f . unZ . return) vname
return $ "(\\" ++ vname ++ " -> " ++ bodyf ++ ")"
fix f= pr3 [MkZa $ lam f] ["(fix ", ")"]
app e1 e2= pr3 [MkZa e1,MkZa e2] ["("," " ,")"]
add e1 e2= pr3 [MkZa e1,MkZa e2] ["("," + " ,")"]
mul e1 e2= pr3 [MkZa e1,MkZa e2] ["("," * " ,")"]
leq e1 e2= pr3 [MkZa e1,MkZa e2] ["("," <= ",")"]
if_ be et ee = pr3 [MkZa be,MkZa et,MkZa ee] ["(if "," then "," else
",")"]
-- Suppress the Symantics phantom type by casting to an existential
data Za where
MkZa :: Y String a -> Za
pr3 a b = unZ $ pr2 a b
pr2 :: forall a. [Za] -> [String] -> Z a String
pr2 _ [] = return ""
pr2 [] ts = (return . concat) ts
pr2 ((MkZa e):es) (t:ts) = do
s1 <- (Z . Y . unY) e -- that (Y . unY) magical
incantation again!
s2 <- pr2 es ts
return $ t ++ s1 ++ s2
Edward Kmett wrote:
>
> You might also look at doing it without all the State monad noise with
> something like:
>> class Symantics repr where
>>int :: Int -> repr Int
>>add :: repr Int -> repr Int -> repr Int
>>lam :: (repr a -> repr b) -> repr (a->b)
>>app :: repr (a -> b) -> repr a -> repr b
>
>> newtype Pretty a = Pretty { runPretty :: [String] -> String }
>
>> pretty :: Pretty a -> String
>> pretty (Pretty f) = f vars where
>> vars = [ [i] | i <- ['a'..'z']] ++ [i : show j | j <- [1..], i <-
> ['a'..'z'] ]
>
>> instance Symantics Pretty where
>>int = Pretty . const . show
>>add x y = Pretty $ \vars -> "(" ++ runPretty x vars ++ " + " ++
> runPretty y vars ++ ")"
>>lam f = Pretty $ \ (v:vars) -> "(\\" ++ v ++ ". " ++ runPretty (f (var
> v)) vars ++ ")" where
>>var = Pretty . const
>>app f x = Pretty $ \vars -> "(" ++ runPretty f vars ++ " " ++
>> runPretty
> x vars ++ ")"
>
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Re: [Haskell-cafe] Flipping *->*->* kinds, or monadic finally-tagless madness
You might also look at doing it without all the State monad noise with
something like:
> class Symantics repr where
>int :: Int -> repr Int
>add :: repr Int -> repr Int -> repr Int
>lam :: (repr a -> repr b) -> repr (a->b)
>app :: repr (a -> b) -> repr a -> repr b
> newtype Pretty a = Pretty { runPretty :: [String] -> String }
> pretty :: Pretty a -> String
> pretty (Pretty f) = f vars where
> vars = [ [i] | i <- ['a'..'z']] ++ [i : show j | j <- [1..], i <-
['a'..'z'] ]
> instance Symantics Pretty where
>int = Pretty . const . show
>add x y = Pretty $ \vars -> "(" ++ runPretty x vars ++ " + " ++
runPretty y vars ++ ")"
>lam f = Pretty $ \ (v:vars) -> "(\\" ++ v ++ ". " ++ runPretty (f (var
v)) vars ++ ")" where
>var = Pretty . const
>app f x = Pretty $ \vars -> "(" ++ runPretty f vars ++ " " ++ runPretty
x vars ++ ")"
-Edward Kmett
On Thu, Jul 2, 2009 at 5:52 PM, Kim-Ee Yeoh wrote:
>
> I'm trying to write HOAS Show instances for the finally-tagless
> type-classes using actual State monads.
>
> The original code:
> http://okmij.org/ftp/Computation/FLOLAC/EvalTaglessF.hs
>
> Two type variables are needed: one to vary over the Symantics
> class (but only as a phantom type) and another to vary over the
> Monad class. Hence, the use of 2-variable type constructors.
>
> > type VarCount = int
> > newtype Y b a = Y {unY :: VarCount -> (b, VarCount)}
>
> Not knowing of a type-level 'flip', I resort to newtype isomorphisms:
>
> > newtype Z a b = Z {unZ :: Y b a}
> > instance Monad (Z a) where
> >return x = Z $ Y $ \c -> (x,c)
> >(Z (Y m)) >>= f = Z $ Y $ \c0 -> let (x,c1) = m c0 in (unY . unZ) (f
> > x) c1-- Pace, too-strict puritans
> > instance MonadState String (Z a) where
> >get = Z $ Y $ \c -> (show c, c)
> >put x = Z $ Y $ \_ -> ((), read x)
>
> So far so good. Now for the Symantics instances (abridged).
>
> > class Symantics repr where
> >int :: Int -> repr Int -- int literal
> >add :: repr Int -> repr Int -> repr Int
> >lam :: (repr a -> repr b) -> repr (a->b)
>
> > instance Symantics (Y String) where
> >int = unZ . return . show
> >add x y = unZ $ do
> > sx <- Z x
> > sy <- Z y
> > return $ "(" ++ sx ++ " + " ++ sy ++ ")"
>
> The add function illustrates the kind of do-sugaring we know and love
> that I want to use for Symantics.
>
> >lam f = unZ $ do
> > show_c0 <- get
> > let
> > vname = "v" ++ show_c0
> > c0 = read show_c0 :: VarCount
> > c1 = succ c0
> > fz :: Z a String -> Z b String
> > fz = Z . f . unZ
> > put (show c1)
> > s <- (fz . return) vname
> > return $ "(\\" ++ vname ++ " -> " ++ s ++ ")"
>
> Now with lam, I get this cryptic error message (under 6.8.2):
>
>Occurs check: cannot construct the infinite type: b = a -> b
>When trying to generalise the type inferred for `lam'
> Signature type: forall a1 b1.
> (Y String a1 -> Y String b1) -> Y String (a1 ->
> b1)
> Type to generalise: forall a1 b1.
> (Y String a1 -> Y String b1) -> Y String (a1 ->
> b1)
>In the instance declaration for `Symantics (Y String)'
>
> Both the two types in the error message are identical, which suggests
> no generalization is needed. I'm puzzled why ghc sees an infinite type.
>
> Any ideas on how to proceed?
>
> --
> View this message in context:
> http://www.nabble.com/Flipping-*-%3E*-%3E*-kinds%2C-or-monadic-finally-tagless-madness-tp24314553p24314553.html
> Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.
>
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[Haskell-cafe] Flipping *->*->* kinds, or monadic finally-tagless madness
I'm trying to write HOAS Show instances for the finally-tagless
type-classes using actual State monads.
The original code:
http://okmij.org/ftp/Computation/FLOLAC/EvalTaglessF.hs
Two type variables are needed: one to vary over the Symantics
class (but only as a phantom type) and another to vary over the
Monad class. Hence, the use of 2-variable type constructors.
> type VarCount = int
> newtype Y b a = Y {unY :: VarCount -> (b, VarCount)}
Not knowing of a type-level 'flip', I resort to newtype isomorphisms:
> newtype Z a b = Z {unZ :: Y b a}
> instance Monad (Z a) where
>return x = Z $ Y $ \c -> (x,c)
>(Z (Y m)) >>= f = Z $ Y $ \c0 -> let (x,c1) = m c0 in (unY . unZ) (f
> x) c1-- Pace, too-strict puritans
> instance MonadState String (Z a) where
>get = Z $ Y $ \c -> (show c, c)
>put x = Z $ Y $ \_ -> ((), read x)
So far so good. Now for the Symantics instances (abridged).
> class Symantics repr where
>int :: Int -> repr Int -- int literal
>add :: repr Int -> repr Int -> repr Int
>lam :: (repr a -> repr b) -> repr (a->b)
> instance Symantics (Y String) where
>int = unZ . return . show
>add x y = unZ $ do
> sx <- Z x
> sy <- Z y
> return $ "(" ++ sx ++ " + " ++ sy ++ ")"
The add function illustrates the kind of do-sugaring we know and love
that I want to use for Symantics.
>lam f = unZ $ do
> show_c0 <- get
> let
> vname = "v" ++ show_c0
> c0 = read show_c0 :: VarCount
> c1 = succ c0
> fz :: Z a String -> Z b String
> fz = Z . f . unZ
> put (show c1)
> s <- (fz . return) vname
> return $ "(\\" ++ vname ++ " -> " ++ s ++ ")"
Now with lam, I get this cryptic error message (under 6.8.2):
Occurs check: cannot construct the infinite type: b = a -> b
When trying to generalise the type inferred for `lam'
Signature type: forall a1 b1.
(Y String a1 -> Y String b1) -> Y String (a1 ->
b1)
Type to generalise: forall a1 b1.
(Y String a1 -> Y String b1) -> Y String (a1 ->
b1)
In the instance declaration for `Symantics (Y String)'
Both the two types in the error message are identical, which suggests
no generalization is needed. I'm puzzled why ghc sees an infinite type.
Any ideas on how to proceed?
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