[Haskell-cafe] Lambda-case / lambda-if

[Dean Herington & Elizabeth Lacey]

At 3:36 AM -0600 10/5/10, Luke Palmer wrote:
>On Mon, Oct 4, 2010 at 9:04 PM, Dean Herington
><heringtonlacey at mindspring.com> wrote:
>>  With respect to "datatype destructing" functions, the Prelude has:
>>
>>  maybe :: b -> (a -> b) -> Maybe a -> b
>>  either :: (a -> c) -> (b -> c) -> Either a b -> c
>>
>>  which suggests the following signatures for the analogues for Bool and list
>>  types:
>>
>>  bool :: a -> a -> Bool -> a
>>  list :: b -> (a -> [a] -> b) -> [a] -> b
>
>This suggestion is not so clear to me.  Maybe and Either are both
>non-recursive, so the Church and Scott encodings coincide.  You've
>written the Scott encoding of list.  The Church encoding should look
>familiar:
>
>     list :: b -> (a -> b -> b) -> [a] -> b
>
>Intuitively, a Scott encoding peels off one layer of datatype, whereas
>a Church encoding flattens down a whole recursive structure.  Church
>encodings are more powerful -- you can do more without requiring a
>fixed point operator.
>
>Just to be clear, I am not arguing anything other than "maybe" and
>"either" don't readily generalize to "list" because of list's
>recursiveness.
>
>Luke

Thanks, Luke, for pointing out the Church vs. Scott encoding issue. 
I agree with your conclusion (and feel better about the lack of the 
version of "list" I had suggested).

Dean