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

On 2018-02-15, at 14:16, Vilem-Benjamin Liepelt <vl81@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@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@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

I am happy to take any other comments relating to my code...

Best,

Vilem

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