[Haskell-cafe] Announcing Djinn, version 2004-12-11, a coding wizard

[Lennart Augustsson]

Howdy, y'all!

I've written a small program that takes a (Haskell) type
and gives you back a function of that type if one exists.
It's kind of fun, so I thought I'd share it.

It's probably best explained with a sample session.

   calvin% djinn
   Welcome to Djinn version 2005-12-11.
   Type :h to get help.
# Djinn is interactive if not given any arguments.
# Let's see if it can find the identity function.
   Djinn> f ? a->a
   f :: a -> a
   f x1 = x1
# Yes, that was easy.  Let's try some tuple munging.
   Djinn> sel ? ((a,b),(c,d)) -> (b,c)
   sel :: ((a, b), (c, d)) -> (b, c)
   sel ((_, v5), (v6, _)) = (v5, v6)

# We can ask for the impossible, but then we get what we
# deserve.
   Djinn> cast ? a->b
   -- cast cannot be realized.

# OK, let's be bold and try some functions that are tricky to write:
# return, bind, and callCC in the continuation monad
   Djinn> type C a = (a -> r) -> r
   Djinn> returnC ? a -> C a
   returnC :: a -> C a
   returnC x1 x2 = x2 x1

   Djinn> bindC ? C a -> (a -> C b) -> C b
   bindC :: C a -> (a -> C b) -> C b
   bindC x1 x2 x3 = x1 (\ c15 -> x2 c15 (\ c17 -> x3 c17))

   Djinn> callCC ? ((a -> C b) -> C a) -> C a
   callCC :: ((a -> C b) -> C a) -> C a
   callCC x1 x2 = x1 (\ c15 _ -> x2 c15) (\ c11 -> x2 c11)
# Well, poor Djinn has a sweaty brow after deducing the code
# for callCC so we had better quit.
   Djinn> :q
   Bye.


To play with Djinn do a
   darcs get http://darcs.augustsson.net/Darcs/Djinn
or get
   http://darcs.augustsson.net/Darcs/Djinn/Djinn.tar.gz
Then just type make.  (You need a Haskell 98 implementation and
some libraries.)  And then start djinn.

For the curious, Djinn uses a decision procedure for intuitionistic
propositional calculus due to Roy Dyckhoff.  It's a variation of
Gentzen's LJ system.  This means that (in theory) Djinn will always
find a function if one exists, and if one doesn't exist Djinn will
terminate telling you so.

This is the very first version, so expect bugs. :)

Share and enjoy.

     -- Lennart