-- Haskell98!
-- Embedding a higher-order domain-specific language (simply-typed
-- lambda-calculus with constants) with a selectable evaluation order:
-- Call-by-value, call-by-name, call-by-need in the same Final Tagless framework
-- This is the Haskell98 version of the code CB.hs located in the
-- same directory as this file
module CB98 where
import Data.IORef
import Control.Monad
import Control.Monad.Trans
-- The (higher-order abstract) syntax of our DSL
type Arr exp a b = exp a -> exp b
class EDSL exp where
lam :: (exp a -> exp b) -> exp (Arr exp a b)
app :: exp (Arr exp a b) -> exp a -> exp b
int :: Int -> exp Int -- Integer literal
add :: exp Int -> exp Int -> exp Int
sub :: exp Int -> exp Int -> exp Int
-- A convenient abbreviation
let_ :: EDSL exp => exp a -> (exp a -> exp b) -> exp b
let_ x y = (lam y) `app` x
-- A sample EDSL term
t :: EDSL exp => exp Int
t = (lam $ \x -> let_ (x `add` x)
$ \y -> y `add` y) `app` int 10
-- Interpretation of EDSL expressions as values of the host language (Haskell)
-- An EDSL expression of type a is interpreted as a Haskell value
-- of the type SName m a, SValue m a or SLazy m a, where
-- m is a Monad (the parameter of the interpretation).
newtype SName m a = SN { unSN :: m a }
-- Could be automatically derived by GHC. But we stick to Haskell98
instance Monad m => Monad (SName m) where
return = SN . return
m >>= f = SN $ unSN m >>= unSN . f
instance MonadIO m => MonadIO (SName m) where
liftIO = SN . liftIO
-- Call-by-name
instance MonadIO m => EDSL (SName m) where
int = return
add x y = do a <- x
b <- y
liftIO $ putStrLn "Adding"
return (a + b)
sub x y = do a <- x
b <- y
liftIO $ putStrLn "Subtracting"
return (a - b)
lam f = return f
app x y = x >>= ($ y)
-- Tests
runName :: SName m a -> m a
runName x = unSN x
-- The addition (x `add` x) is performed twice because y is bound
-- to a computation, and y is evaluated twice
t0SN = runName t >>= print
{-
Adding
Adding
Adding
40
-}
-- A more elaborate example
t1 :: EDSL exp => exp Int
t1 = (lam $ \x -> let_ (x `add` x)
$ \y -> lam $ \z ->
z `add` (z `add` (y `add` y))) `app` (int 10 `sub` int 5)
`app` (int 20 `sub` int 10)
t1SN = runName t1 >>= print
{-
*CB> t1SN
Subtracting
Subtracting
Subtracting
Subtracting
Adding
Subtracting
Subtracting
Adding
Adding
Adding
Adding
40
-}
-- A better example
t2 :: EDSL exp => exp Int
t2 = (lam $ \z -> lam $ \x -> let_ (x `add` x)
$ \y -> y `add` y) `app` (int 100 `sub` int 10)
`app` (int 5 `add` int 5)
-- The result of subtraction was not needed, and so it was not performed
-- OTH, (int 5 `add` int 5) was computed four times
t2SN = runName t2 >>= print
{-
*CB> t2SN
Adding
Adding
Adding
Adding
Adding
Adding
Adding
40
-}
-- Call-by-value
newtype SValue m a = SV { unSV :: m a }
-- Could be automatically derived by GHC.
instance Monad m => Monad (SValue m) where
return = SV . return
m >>= f = SV $ unSV m >>= unSV . f
instance MonadIO m => MonadIO (SValue m) where
liftIO = SV . liftIO
-- We reuse most of EDSL (SName) except for lam
vn :: SValue m x -> SName m x
vn = SN . unSV
nv :: SName m x -> SValue m x
nv = SV . unSN
instance MonadIO m => EDSL (SValue m) where
int = nv . int
add x y = nv $ add (vn x) (vn y)
sub x y = nv $ sub (vn x) (vn y)
-- Easier to write it rather than to change the label and then
-- invoke SName's app
app x y = x >>= ($ y)
-- This is the only difference between CBN and CBV:
-- lam first evaluates its argument, no matter what
-- This is the definition of CBV after all
-- lam f = return (\x -> (f . return) =<< x)
-- or, in the pointless notation suggested by Jacques Carette
lam f = return (f . return =<<)
runValue :: SValue m a -> m a
runValue x = unSV x
-- We now evaluate the previously written tests t, t1, t2
-- under the new interpretation
t0SV = runValue t >>= print
{-
*CB> t0SV
Adding
Adding
40
-}
t1SV = runValue t1 >>= print
{-
*CB> t1SV
Subtracting
Adding
Subtracting
Adding
Adding
Adding
40
-}
-- Although the result of subs-traction was not needed, it was still performed
-- OTH, (int 5 `add` int 5) was computed only once
t2SV = runValue t2 >>= print
{-
*CB> t2SV
Subtracting
Adding
Adding
Adding
40
-}
-- Call-by-need
share :: MonadIO m => m a -> m (m a)
share m = do
r <- liftIO $ newIORef (False,m)
let ac = do
(f,m) <- liftIO $ readIORef r
if f then m
else do
v <- m
liftIO $ writeIORef r (True,return v)
return v
return ac
newtype SLazy m a = SL { unSL :: m a }
-- Could be automatically derived by GHC.
instance Monad m => Monad (SLazy m) where
return = SL . return
m >>= f = SL $ unSL m >>= unSL . f
instance MonadIO m => MonadIO (SLazy m) where
liftIO = SL . liftIO
ln :: SLazy m x -> SName m x
ln = SN . unSL
nl :: SName m x -> SLazy m x
nl = SL . unSN
-- We reuse most of EDSL (SName) except for lam
instance MonadIO m => EDSL (SLazy m) where
int = nl . int
add x y = nl $ add (ln x) (ln y)
sub x y = nl $ sub (ln x) (ln y)
-- Easier to write it rather than change the label and then
-- invoke SName's app
app x y = x >>= ($ y)
-- This is the only difference between CBN and CBNeed
-- lam shares its argument, no matter what
-- This is the definition of CBNeed after all
-- lam f = return (\x -> f =<< share x)
-- Or, in the pointless notation
lam f = return ((f =<<) . share)
runLazy :: SLazy m a -> m a
runLazy x = unSL x
-- We now evaluate the previously written tests t, t1, t2
-- under the new interpretation
-- Here, Lazy is just as efficient as CBV
t0SL = runLazy t >>= print
{-
*CB> t0SL
Adding
Adding
40
-}
-- Ditto
t1SL = runLazy t1 >>= print
{-
*CB> t1SL
Subtracting
Subtracting
Adding
Adding
Adding
Adding
40
-}
-- Now, Lazy is better than both CBN and CBV: subtraction was not needed,
-- and it was not performed.
-- All other expressions were needed, and evaluated once.
t2SL = runLazy t2 >>= print
{-
*CB> t2SL
Adding
Adding
Adding
40
-}