Simplifying casts and beta-reduction

[Conal Elliott]

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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