[Haskell-cafe] Replace data constructors via meta programming

[Vilem-Benjamin Liepelt]

Hi David,

I don't think this is well-typed. GHC seems to infer `Proposition a -> Bool -> Bool` (by majority vote?) but obviously then complains about the cases `id` and `not`.

I believe that there is a way to do this with dependent types, but not sure whether this is possible in Haskell.

Best,

Vilem

> On 2018-02-15, at 13:51, David Fox <dsf at seereason.com> wrote:
> 
> You actually can pattern match on constructor only:
> 
> magic = \case
>     Var {} -> id
>     Not  {}-> not
>     And {} -> (&&)
>     Or {} -> (||)
>     If {} -> (==>)
>     Iff {} -> (==)
> 
> On Sun, Feb 11, 2018 at 6:30 PM, Vilem-Benjamin Liepelt <vl81 at kent.ac.uk <mailto:vl81 at kent.ac.uk>> wrote:
> Hi,
> 
> I am looking for a solution to get rid of this silly boilerplate:
> 
> eval :: Ord var => Map var Bool -> Proposition var -> Bool
> eval ctx prop = evalP $ fmap (ctx Map.!) prop
>   where
>     evalP = \case
>         Var b -> b
>         Not q -> not $ evalP q
>         And p q -> evalP p && evalP q
>         Or p q -> evalP p || evalP q
>         If p q -> evalP p ==> evalP q
>         Iff p q -> evalP p == evalP q
> 
> What I would like to do in essence is to replace the data constructors like so:
> 
> -- Not valid Haskell!! Can't pattern match on constructor only...
> magic = \case
>     Var -> id
>     Not -> not
>     And -> (&&)
>     Or -> (||)
>     If -> (==>)
>     Iff -> (==)
> 
> compile = transformAST magic $ fmap (\case 'P' -> False; 'Q' -> True)
> 
> >>> compile (Iff (Not (And (Var 'P') (Var 'Q'))) (Or (Not (Var 'P')) (Not (Var 'Q'))))
>             ((==) (not ((&&) (id True) (id False))) ((||) (not (id True)) (not (id False))))
> 
> Note how the compiled expression exactly mirrors the AST, so there should be some meta programming technique for this.
> 
> Does anyone have an idea how I can achieve this?
> 
> The full source code is here: https://gist.github.com/vimuel/7dcb8a9f1d2b7b72f020d66ec4157d7b <https://gist.github.com/vimuel/7dcb8a9f1d2b7b72f020d66ec4157d7b>
> 
> I am happy to take any other comments relating to my code...
> 
> Best,
> 
> Vilem
> 
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