ichistmeinname / free-theorems Goto Github PK

While a -> a and (a -> b) -> [a] -> [b] have their relation variables reduced into functions, that's not the case for (forall x. a x -> a x) and (a -> b) -> f a -> f b, so we don't end up without a equal/inequal theorem.

The problem is that unfoldFormula simply returns return . Predicate . IsMember x y $ rel for RelConsFunVar (with #3) and RelTypeConsApp. I'm not sufficiently familiar with free theorem derivation to know what they should return instead though.

Currently, it prints type instantiations like this:

forall t1,t2 in TYPES, R in REL(t1,t2).
 forall p :: t1 -> Bool.
  forall q :: t2 -> Bool.
   (forall (x, y) in R. p x = q y)
   ==> (forall (z, v) in lift{[]}(R).
         (f_{t1} p z, f_{t2} q v) in lift{[]}(R))

but these days, Haskell has “Proper” syntax for this:

forall t1,t2 in TYPES, R in REL(t1,t2).
 forall p :: t1 -> Bool.
  forall q :: t2 -> Bool.
   (forall (x, y) in R. p x = q y)
   ==> (forall (z, v) in lift{[]}(R).
         (f @t1 p z, f @t2 q v) in lift{[]}(R))

and I think this library should use it.

• Building with newer GHC: #2
• Exposing support for higher-ranked types: #3
• Handling incomplete pattern matches
• New hackage release
• Potentially upstream into ghci

There's 30-40 incomplete patterns laying around. For some of them it's obvious what to do, but in general I've been mostly doing throwError or documenting with error, depending on what's already there. Hardly ideal but still better than Non-exhaustive patterns in function foo, which is what we currently get for (intentionally or not) unsupported operations.

I wanted to port just #3 to @nomeata's version to get one last useful/releasable step before the big merge/jump, but it required also porting the work getting haskell-src-exts to build for newer ghc, so meh.

I do wonder if it makes sense for free-theorems to keep living as a standalone thing that has its own mini haskell AST types in addition to the ones in haskell-src-exts (which is now in life support). Would it be more at home in ghci under :i or so? Maybe it could be a google summer of code or haskell foundation project.
After all, the compiler already has everything in scope, and squeezing every bit of reasoning based on types alone is textbook haskell. I'm not sure if the theorems could also be useful for automatically obtaining rewrite rules or if that always needs human curation.

cc @ichistmeinname @nomeata