At 3:36 AM -0600 10/5/10, Luke Palmer wrote:
On Mon, Oct 4, 2010 at 9:04 PM, Dean Herington
<heringtonla...@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
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