[Haskell-cafe] Replace data constructors via meta programming

[Vilem-Benjamin Liepelt]

PS: I meant cases `Var {}` and `Not {}`.

> On 2018-02-15, at 14:16, Vilem-Benjamin Liepelt <vl81 at kent.ac.uk> wrote:
> 
> 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 <mailto: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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