Good morning Jorge,

> OP_CAT was removed. If I remember correctly, some speculated that perhaps it was removed because it could allow covenants.I don't remember any technical concern about the OP besides enabling covenants.Before it was a common opinion that covenants shouldn't be enabled in bitcoin because, despite having good use case, there are some nasty attacks that are enabled with them too. These days it seems the opinion of the benefits being worth the dangers is quite generalized. Which is quite understandable given that more use cases have been thought since then.

I think the more accurate reason for why it was removed is because the following SCRIPT of N size would lead to 2^N memory usage:

    OP_1 OP_DUP OP_CAT OP_DUP OP_CAT OP_DUP OP_CAT OP_DUP OP_CAT OP_DUP OP_CAT OP_DUP OP_CAT ...

In particular it was removed at about the same time as `OP_MUL`, which has similar behavior (consider that multiplying two 32-bit numbers results in a 64-bit number, similar to `OP_CAT`ting a vector to itself).

`OP_CAT` was removed long before covenants were even expressed as a possibility.

Covenants were first expressed as a possibility, I believe, during discussions around P2SH.
Basically, at the time, the problem was this:

* Some receivers wanted to use k-of-n multisignature for improved security.
* The only way to implement this, pre-P2SH, was by putting in the `scriptPubKey` all the public keys.
* The sender is the one paying for the size of the `scriptPubKey`.
* It was considered unfair that the sender is paying for the security of the receiver.

Thus, `OP_EVAL` and the P2SH concept was conceived.
Instead of the `scriptPubKey` containing the k-of-n multisignature, you create a separate script containing the public keys, then hash it, and the `scriptPubKey` would contain the hash of the script.
By symmetry with the P2PKH template:

    OP_DUP OP_HASH160 <hash160(pubkey)> OP_EQUALVERIFY OP_CHECKSIG

The P2SH template would be:

    OP_DUP OP_HASH160 <hash160(redeemScript)> OP_EQUALVERIFY OP_EVAL

`OP_EVAL` would take the stack top vector and treat it as a Bitcoin SCRIPT.

It was then pointed out that `OP_EVAL` could be used to create recursive SCRIPTs by quining using `OP_CAT`.
`OP_CAT` was already disabled by then, but people were talking about re-enabling it somehow by restricting the output size of `OP_CAT` to limit the O(2^N) behavior.

Thus, since then, `OP_CAT` has been associated with ***recursive*** covenants (and people are now reluctant to re-enable it even with a limit on its output size, because recursive covenants).
In particular, `OP_CAT` in combination with `OP_CHECKSIGFROMSTACK` and `OP_CHECKSIG`, you could get a deferred `OP_EVAL` and then use `OP_CAT` too to quine.

Because of those concerns, the modern P2SH is now "just a template" with an implicit `OP_EVAL` of the `redeemScript`, but without any `OP_EVAL` being actually enabled.

(`OP_EVAL` cannot replace an `OP_NOP` in a softfork, but it is helpful to remember that P2SH was pretty much what codified the difference between softfork and hardfork, and the community at the time was small enough (or so it seemed) that a hardfork might not have been disruptive.)

> Re-enabling OP_CAT with the exact same OP would be a hardfork, but creating a new OP_CAT2 that does the same would be a softfork.

If you are willing to work in Taproot the same OP-code can be enabled in a softfork by using a new Tapscript version.

If you worry about quantum-computing-break, a new SegWit version (which is more limited than Tapscript versions, unfortunately) can also be used, creating a new P2WSHv2 (or whatever version) that enables these opcodes.

> As far a I know, this is the covenants proposal that has been implemented for the longest time, if that's to be used as a selection criteria.And as always, this is not incompatible with deploying other convenant proposals later.

No, it was `OP_EVAL`, not `OP_CAT`.
In particular if `OP_EVAL` was allowed in the `redeemScript` then it would enable covenants as well.
It was just pointed out that `OP_CAT` enables recursive covenenats in combination with `OP_EVAL`-in-`redeemScript`.

In particular, in combination with `OP_CAT`, `OP_EVAL` not only allows recursive covenants, but also recursion *within* a SCRIPT i.e. unbounded SCRIPT execution.
Thus, `OP_EVAL` is simply not going to fly, at all.

> Personally I find the simplicity proposal the best one among all the covenant proposals by far, including this one.But I understand that despite the name, the proposal is harder to review and test than other proposals, for it wouldn't simply add covenants, but a complete new scripting language that is better in many senses.Speedy covenants, on the other hand, is much simpler and has been implemented for longer, so in principle, it should be easier to deploy in a speedy manner.
>
> What are the main arguments against speedy covenants (aka op_cat2) and against deploying simplicity in bitcoin respectively?
> Sorry if this was discussed before.

`OP_CAT`, by itself, does not implement any covenants --- instead, it creates recursive covenants when combined with almost all covenant opcodes.

Regards,
ZmnSCPxj