Help with understanding Taproot tree expression

[punk.zink]

As far as I know, to describe Script Tree with Script Path 1:

Code:

<Key1> OP_CHECKSIG <Key2> OP_CHECKSIGADD OP_2 OP_NUMEQUAL

and Script Path 2:

Code:

<Key3> OP_CHECKSIG 

I have to use Taproot expression: tr(InternalKey,{multi_a(2,Key1,Key2),pk(Key3)}), so that the descriptor can be imported into Bitcoin core with private key disabled.

However, for example, if I want to change script path 2 as

Code:

OP_10 OP_CHECKSEQUENCEVERIFY OP_DROP <Key3> OP_CHECKSIG

I don't know what kind of expression to use?

tr(InternalKey,{sortedmulti_a(2,Key1,Key2),???)})

[achow101]

Descriptors cannot describe all arbitrary scripts, only a subset with specific properties that make them analyzable. You must use Miniscript for those scripts.

The miniscript that you want is probably something like

Code:

and_v(v:pk(key3),older(10))

and that would make a script of

Code:

<key3> OP_CHECKSIGVERIFY 10 OP_CHECKSEQUENCEVERIFY

[punk.zink]

Descriptors cannot describe all arbitrary scripts, only a subset with specific properties that make them analyzable. You must use Miniscript for those scripts.

The miniscript that you want is probably something like

Code:

and_v(v:pk(key3),older(10))

and that would make a script of

Code:

<key3> OP_CHECKSIGVERIFY 10 OP_CHECKSEQUENCEVERIFY

Thank you for the explanation. Now I know that because tree expressions in Taproot output have limitations, then to describe certain arbitrary scripts I have to use Miniscript, so that valid descriptors can be generated.

With your explanation, I succeeded in importing the descriptor: tr(InternalKey,{sortedmulti_a(2,Key1,Key2),and_v(v:pk(key3),older(10))}) , and successfully created a transaction with the multisig 2-of-2 script path spend (through the GUI or using a console with walletcreatefundedpsbt option), but still have no luck in creating transactions with and_v(v:pk(key3),older(10)) script path spend.

[achow101]

Not all Miniscript can be signed yet. I think we haven't implemented everything that's needed to pass in the information required to sign for both kinds of timelocks as well as hashlocks.

[punk.zink]

Not all Miniscript can be signed yet. I think we haven't implemented everything that's needed to pass in the information required to sign for both kinds of timelocks as well as hashlocks.

Ah, I see. I thought there is something wrong with the variables that I used when building the transaction with walletcreatefundedpsbt, because for every change in the variables and arguments that I used, the results are the same, where the psbt cannot be signed with (Key3) descriptor.