Simplifying casts and beta-reduction

[Conal Elliott]

Thanks, Simon. I'll keep poking around.


On Thu, May 8, 2014 at 12:54 AM, Simon Peyton Jones
<simonpj at microsoft.com>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 at gmail.com [mailto:conal.elliott at gmail.com] *On
> Behalf Of *Conal Elliott
> *Sent:* 08 May 2014 04:19
> *To:* Simon Peyton Jones
> *Cc:* ghc-devs at 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 <conal at 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 <simonpj at 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/
> <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 at haskell.org] *On Behalf Of *Conal
> Elliott
> *Sent:* 07 May 2014 04:50
> *To:* ghc-devs at 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 $dEncodable1 of _
> >           D:Encodable tpl_B2 _ ->
> >             \ (g :: a8 -> b) (eta :: Encode a8) -> tpl_B2 (g (tpl_B3
> eta))
> >     )
> >  `cast` (forall a8 b.
> >          <Encodable a8>_R
> >          -> <Encodable b>_R
> >          -> <a8 -> b>_R
> >          -> Sub (Sym (TFCo:R:Encode(->)[0] <a8>_N <b>_N))
> >          :: (forall a8 b. (Encodable a8, Encodable b) =>
> >              (a8 -> b) -> Encode a8 -> Encode b)
> >               ~#
> >             (forall a8 b. (Encodable a8, Encodable b) =>
> >              (a8 -> b) -> Encode (a8 -> b))))
>
> I can imagine pushing the `cast` down through the type lambdas while
> stripping off `forall` coercions, then pushing the remaining `cast` through
> the dictionary arguments, while stripping off the outer `<Encodable t>_R
> ->` coercion wrappers, and then pushing the cast into the `case`
> alternatives and the lambda body, leaving something like
>
> >  (\ (@ a8) (@ b)
> >     ($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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