Oleg,

Let me try to understand what you're saying here:

(1) Church encoding was discovered and investigated in an untyped setting. I understand your tightness criterion to mean surjectivity, the absence of which means having to deal with junk.

(2) Church didn't give an encoding for pattern-matching to match with construction. Boehm and Berarducci did. So properly speaking, tail and pred for Church-encoded lists and nats are trial-and-error affairs. But the point is they need not be if we use B-B encoding, which looks _exactly_ the same, except one gets a citation link to a systematic procedure.

So it looks like you're trying to set the record straight on who actually did what.


-- Kim-Ee


On Tue, Sep 18, 2012 at 3:27 PM, <oleg@okmij.org> wrote:

There has been a recent discussion of ``Church encoding'' of lists and
the comparison with Scott encoding.

I'd like to point out that what is often called Church encoding is
actually Boehm-Berarducci encoding. That is, often seen

> newtype ChurchList a =
>     CL { cataCL :: forall r. (a -> r -> r) -> r -> r }

(in http://community.haskell.org/%7Ewren/list-extras/Data/List/Church.hs )

is _not_ Church encoding. First of all, Church encoding is not typed
and it is not tight. The following article explains the other
difference between the encodings

        http://okmij.org/ftp/tagless-final/course/Boehm-Berarducci.html

Boehm-Berarducci encoding is very insightful and influential. The
authors truly deserve credit.

P.S. It is actually possible to write zip function using Boehm-Berarducci
encoding:
        http://okmij.org/ftp/ftp/Algorithms.html#zip-folds