[Haskell-cafe] Simple GADT parser for the eval example

[Greg Buchholz]

    Thanks to everyone who replied (especially Dimitrios Vytiniotis and
Joost Visser).  I now know the standard way to write the GADT parser.
But I'm still curious if anyone has comments pertaining to the version
using type classes.  It seems so close to doing what we want, and it is
pretty straightforward to implement.  The best way I can think to
describe it would be to say it uses the type system to find what it
should parse next, and dies of a pattern match failure if something
unexpected shows up, instead of checking to see if we can assemble a
type safe tree from pre-parsed parts (does that make any sense?).

    I'm curious if there could be a small change to the type system to
make the fully general "my_read" possible, or if it suffers from an
incurable defect. 

Thanks, 
Greg Buchholz 

> {-# OPTIONS -fglasgow-exts #-}  
> 
> main = print test
> 
> test :: Int                             
> test = eval.my_read.read $
>             "(EIf (EIsZ (ELit 0))          " ++
>             "     (EInc (ELit 1))          " ++
>             "     (EFst (EPair (ELit 42)   " ++
>             "                  (ELit 43))))"
> 
> class MyRead a where
>     my_read :: Expr -> Term a 
> 
> instance MyRead Int where
>     my_read (ELit a)    = Lit a
>     my_read (EInc a)    = Inc (my_read a)    
>     my_read (EIf p t e) = If  (my_read p) (my_read t) (my_read e)
>     my_read (EFst a)    = Fst (my_read a :: Term (Int,Int))
>     my_read (ESnd a)    = Snd (my_read a :: Term (Int,Int))
> 
> instance MyRead Bool where
>     my_read (EIsZ a)    = IsZ (my_read a)
>     my_read (EIf p t e) = If  (my_read p) (my_read t) (my_read e)
>     my_read (EFst a)    = Fst (my_read a :: Term (Bool,Bool))
>     my_read (ESnd a)    = Snd (my_read a :: Term (Bool,Bool))
>     
> instance (MyRead a, MyRead x) => MyRead (a,x) where
>     my_read (EPair a b) = Pair (my_read a) (my_read b)
>     my_read (EIf p t e) = If   (my_read p) (my_read t) (my_read e)
> 
> data Expr = ELit Int
>           | EInc Expr
>           | EIsZ Expr 
>           | EPair Expr Expr
>           | EIf Expr Expr Expr
>           | EFst Expr
>           | ESnd Expr
>             deriving (Read,Show)
> 
> data Term a where
>     Lit  :: Int -> Term Int
>     Inc  :: Term Int -> Term Int
>     IsZ  :: Term Int -> Term Bool
>     If   :: Term Bool -> Term a -> Term a -> Term a
>     Pair :: Term a -> Term b -> Term (a,b)
>     Fst  :: Term (a,b) -> Term a
>     Snd  :: Term (a,b) -> Term b 
>   
> eval :: Term a -> a
> eval (Lit i)    = i
> eval (Inc t)    = eval t + 1
> eval (IsZ t)    = eval t == 0
> eval (If b t e) = if eval b then eval t else eval e
> eval (Pair a b) = (eval a, eval b)
> eval (Fst t)    = fst (eval t)
> eval (Snd t)    = snd (eval t)