Using AST to Generate Default Data for Array Fields in React Hook Form

Hello smart people!

I have an interesting problem.
I generate a schema then I walk through its AST to generate a form I also use

react-hook-form

react-hook-form

to handle validation based on the generated schema.
Now, I have example of array fields in my schema.
I have an

Add

Add

button in that case so I can add more items to that array in the form.

react-hook-form

react-hook-form

provides a hook that gives as an

append

append

method to do that.
Now,

append

append

should take in the shape of the item of the array.
At this point I have an

AST

AST

that represents the correct shape.
I know that I could use

Arbitrary

Arbitrary

(https://effect.website/docs/schema/arbitrary/) to generate example data from a schema. Is there a way I could use the AST to do the same? Eg.: turning the AST back into the relevant Schema then use that?
Also, is there a way to generate data using a schema where the values are defaulted to undefined or empty string?