Re: Simplifying casts and beta-reduction

Thanks, Simon. I'll keep poking around. On Thu, May 8, 2014 at 12:54 AM, Simon Peyton Jones wrote:

Yes, that’s right: simplCast is the guy. I can’t explain why it’s not working for you, though

Simon

*From:* conal.elliott@gmail.com [mailto:conal.elliott@gmail.com] *On Behalf Of *Conal Elliott *Sent:* 08 May 2014 04:19 *To:* Simon Peyton Jones *Cc:* ghc-devs@haskell.org *Subject:* Re: Simplifying casts and beta-reduction

I'm still sorting through how to optimize these almost-beta-redexes in the form `((\ x -> u) |> co) v`, shifting coercions to enable beta-reduction (as described in section 3.1 of "Evidence normalization"). Is it done by `simplCast` (with help from `simplCoercion`), as called indirectly from `simplifyExpr` in `SimplCore`? I think I'm now calling `simplifyExpr` from HERMIT but I'm not getting the cast-shifting I'm looking for.

-- Conal

On Wed, May 7, 2014 at 1:02 PM, Conal Elliott wrote:

Very useful, indeed! Exactly what I was looking for. Thanks, Simon. Now I've read the evidence normalization and the deferred types paper, and I have a much better understanding of what's going on.

-- Conal

On Wed, May 7, 2014 at 1:28 AM, Simon Peyton Jones wrote:

Absolutely. There’s a whole module that does this: OptCoercion. If you want to see what programs look like without coercion optimisation, try –fno-opt-coercion.

The rules are described in our paper *Evidence normalization in System FC: http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/ http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/*

I hope that’s useful.

Simon

*From:* ghc-devs [mailto:ghc-devs-bounces@haskell.org] *On Behalf Of *Conal Elliott *Sent:* 07 May 2014 04:50 *To:* ghc-devs@haskell.org *Subject:* Simplifying casts and beta-reduction

I'm looking for tools to help simplify Core terms that involve casts. In particular, I want to beta-reduce when the function is wrapped with a cast. Do the GHC sources have such utility functions?

Here is an example of a lambda expression with a cast. In context, it's applied to two type arguments and two dictionary arguments and returns a function of one more argument. (The function `(-->)` is defined as `(f --> h) g = h . g . f`.)

...

((\ (@ a8) (@ b) ($dEncodable :: Encodable a8) ($dEncodable1 :: Encodable b) -> case $dEncodable of _ D:Encodable _ tpl_B3 -> case $dEncodable1 of _ D:Encodable tpl_B2 _ -> \ (g :: a8 -> b) (eta :: Encode a8) -> tpl_B2 (g (tpl_B3 eta)) ) `cast` (forall a8 b. <Encodable a8>_R -> <Encodable b>_R -> b>_R -> Sub (Sym (TFCo:R:Encode(->)[0] <a8>_N <b>_N)) :: (forall a8 b. (Encodable a8, Encodable b) => (a8 -> b) -> Encode a8 -> Encode b) ~# (forall a8 b. (Encodable a8, Encodable b) => (a8 -> b) -> Encode (a8 -> b))))

I can imagine pushing the `cast` down through the type lambdas while stripping off `forall` coercions, then pushing the remaining `cast` through the dictionary arguments, while stripping off the outer `<Encodable t>_R ->` coercion wrappers, and then pushing the cast into the `case` alternatives and the lambda body, leaving something like

...

(\ (@ a8) (@ b) ($dEncodable :: Encodable a8) ($dEncodable1 :: Encodable b) -> case $dEncodable of _ D:Encodable _ tpl_B3 -> case $dEncodable1 of _ D:Encodable tpl_B2 _ -> \ (g :: a8 -> b) -> (\ (eta :: Encode a8) -> tpl_B2 (g (tpl_B3 eta))) `cast` (Sub (Sym (TFCo:R:Encode(->)[0] <a8>_N <b>_N)) :: (Encode a8 -> Encode b) ~# (Encode (a8 -> b))))

Now, given type, dictionary, and function arguments, I think we could beta-reduce.

Before I try implementing these transformations, does something like them already exist in GHC?

Thanks, -- Conal