Re: [Haskell-cafe] Replace data constructors via meta programming

15 Feb 2018

      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  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 mailto:vl81@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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