Please help me decide about extending syntax for jmespath

I am in process of starting new project extending jmespath with more syntax. Currently now I work on basic jmespath and extend it to support math operation `+` `-` `*` `/` `%` with antlr. I got the antlr file from https://github.com/burtcorp/jmespath-java

I am now stuck on design decision and wish that you could kindly help me with some suggestion

- Should I support bitwise operation with `&&` `||` `^` ?
- Is it acceptable to use `&&` and `||` as bitwise operator?
- `1 || 2` will return `3` for instance
- And still wonder is it really necessary, especially xor operator `^`
- But if I include this `^` operator, it also support boolean `xor` in addition to `&&` and `||`

- Should I bring back root node `$` from jsonpath?

- Should I bring back `**` operator from jsonpath?

- Should I support ternary `condition ? true : false` operator ?

- Should I support `??` and `?!` operator ?
- And remove support on `&&` `||` for null check in the same manner of js
- It might be used as bitwise operator above instead
- One difference is it will not treat `false` as `null`. Only `null` and empty
- I would like to add support to backtracing to parent node with `@..` syntax
- `nth number of dots - 1` will backtrack to nth parent
- `$.me.obj..` is equal to `$.me`
- `$.me.obj...` is equal to `$`
- Is there any better syntax for this ?

- I would like to add support to index value with `#` symbol
- For array, `#` would be index number `0,1,2,...`
- For object, `#` would be string `"{key}"`
- What should I do for deep reference ?
- `#` for current level, `##` for previous level ?
- `$.me.obj[0].#` return `0`
- `$.me.obj[0].##` return `"obj"`
- `$.me.obj[0].###` return `"me"`
- `#` for current level, `..#` for previous level ?
- `$.me.obj[0].#` return `0`
- `$.me.obj[0]..#` return `"obj"`
- `$.me.obj[0]...#` return `"me"`
- `#` for current level, `##` will be fullpath as array?
- `$.me.obj[0].#` return `0`
- `$.me.obj[0].##` return `["me","obj",0]`
- What should I do for slice and query? `#` will be index of sliced iteration or actual index?

- I would like to support object projection key by expression #64

- Any other idea overall? Any other things you don't satisfied with jmespath?