> Could you suggest how else we could gain the advantages of op_eval
> without it?   How can I secure my wallet under whatever scheme I like—
> create a trust that requires multiparty signoff— and securely have
> senders pay into it without expecting them all to handle some rare and
> complicated procedure for sending to me?

Yes - by the burdensome address ;) - which I am not sure I consider that much 
of a trouble, for practical uses... Anyway, it could just be added to the URI 
scheme and then it would still only be a click away.

> but it
> seems to me that there is a serious misunderstanding that there is a
> bijection between hash160s and public keys, and one between ECC
> private keys and spendable transactions, and that this bijection is
> desirable or even essential to bitcoin.

So far we had by the standard transactions a nice bijection, I do however, 
share your concern for other and more rich scripting... And here we need to 
make some choices! 
Do we want to keep this notion of transactions between addresses or do we want 
to start unfold the richness of the scripting - I am not sure we actually gain 
that much from OP_EVAL and the extra scripting. And what bothers me is that you 
then cannot define a set of data (be that key, scripts or whatever) from which 
you can obtain all possible txes send to you. If I e.g. looses this argument 
and want to donate a beer to each of you and Gavin, that I want you to drink 
together. I would make a "both of two" btc-addresses script transaction using 
OP_EVAL. And post it.
You would then not be able to know that you actually got a beer unless I told 
you so in a mail.

This means that we move from a setup where transactions needs not only to be 
asked for but also they need to be announced by the sender. I don't like 
this... 

Further, if you make a uint160 from a OP_EVAL script and post this as a bitcoin 
address - the user should then know that this was a special address - otherwise 
he would be sending money nowhere. I agree that this could be encoded into the 
bitcoin address using e.g. a 2... instead of a 3..., but as you mention 
yourself this is only the start of the OP_EVAL uses and hence you would need a 
whole series of strange numbering to define what script a specific address was 
referring to. 

At least it challenges my esthetics...

Cheers,

M
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