There is no need for a BIP draft.  "Turing complete" is just a fancy,
executive-impressing term for "it can run any computer program", or put
even more simply, "it can loop"

Furthermore, the specification of such a language is trivial.  It is the
economics of validation that is the complex piece.  Proving whether or not
a program will halt as expected - The Halting Problem - is near impossible
for most complex programs.  As a result, your proof is... running the
program.  That produces enormous validation consequences and costs for
generic-execution scripts when applied to a decentralized network of
validation P2P nodes.

If you need that capability, it is just as easy to use a normal C/C++/etc.
computer language, with your preferred algorithm libraries and development
tools.

See https://github.com/jgarzik/moxiebox for a working example of provable
execution.



On Thu, Dec 10, 2015 at 9:35 AM, Luke Durback via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> Hello Bitcoin-Dev,
>
> I hope this isn't out of line, but I joined the mailing list to try to
> start a discussion on adding opcodes to make Script Turing Pseudo-Complete
> as Wright suggested is possible.
>
> ---
>
> In line with Wright's suggestion, I propose adding a return stack
> alongside the, already existing, control stack.
>
> The principle opcodes (excluding conditional versions of call and
> return_from) needed are
>
> OP_DEFINITION_START FunctionName:  The code that follows is the definition
> of a new function to be named TransactionSenderAddress.FunctionName.  If
> this function name is already taken, the transaction is marked invalid.
> Within the transaction, the function can be called simply as FunctionName.
>
> OP_DEFINITION_END:  This ends a function definition
>
> OP_FUNCTION_NAME FunctionName:  Gives the current transaction the name
> FunctionName (this is necessary to build recursive functions)
>
> ---
>
> OP_CALL Namespace.FunctionName Value TransactionFee:  This marks the
> transaction as valid.  It also pushes the current execution location onto
> the return stack, debits the calling transaction by the TransactionFee and
> Value, and creates a new transaction specified by Namespace.FunctionName
> with both stacks continued from before (this may be dangerous, but I see no
> way around it) with the specified value.
>
> OP_RETURN_FROM_CALL_AND_CONTINUE:  This pops the top value off the return
> stack and continues from the specified location with both stacks in tact.
>
> ---
>
> It would also be useful if a transaction can create another transaction
> arbitrarily, so to prepare for that, I additionally propose
>
> OP_NAMESPACE:  Pushes the current namespace onto the control stack
>
> This, combined with the ability to make new transactions arbitrarily would
> allow a function to pay its creator.
>
>
>
> I understand that this isn't all that is needed, but I think it's a
> start.  I hope this proposal has met you all well,
>
> Luke Durback
>
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>
>