Re: Simplifying casts and beta-reduction

Sorry to jump in mid-conversation, but since I read about people doing exactly this a few days ago, I thought this might be useful. See the paper Michael D. Adams http://www.informatik.uni-trier.de/%7Eley/pers/hd/a/Adams:Michael_D=.html, Andrew Farmer http://www.informatik.uni-trier.de/%7Eley/pers/hd/f/Farmer:Andrew.html, José Pedro Magalhães: Optimizing SYB is easy! PEPM 2014 http://www.informatik.uni-trier.de/%7Eley/db/conf/pepm/pepm2014.html#AdamsFM...: 71-82 http://www.ittc.ku.edu/csdl/fpg/files/Adams-13-OSIE.pdf where they use Hermit http://www.ittc.ku.edu/csdl/fpg/software/hermit.html http://hackage.haskell.org/package/hermit to do exactly this transformation [and a fair bit more]. Jacques On 2014-05-07 11:18 PM, Conal Elliott wrote:

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 mailto:conal@conal.net> 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 mailto:simonpj@microsoft.com> 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//

//

I hope that's useful.

Simon

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

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