chore: replace check_membership with compute_merkle_root

[TomAFrench]

Related to noir-lang/acvm#66

I've also inlined the testing for merkle trees into pwg.rs. A lot of the merkle logic is unnecessary imo as it's related to constructing a merkle tree rather than just proving against an existing one. I'm then planning on removing this in a later PR.

[vezenovm]

A lot of the merkle logic is unnecessary imo as it's related to constructing a merkle tree rather than just proving against an existing one. I'm then planning on removing this in a later PR.

Yeah it is only related to constructing a merkle tree and is really only useful for tests. We should be careful about removing things that we may have to potentially bring back. If we ever implement any sparse merkle tree functions or natively enable merkle trees of different arity we will want to expand upon these merkle tree classes

[TomAFrench]

We should be careful about removing things that we may have to potentially bring back.

I'm of the opinion that that's best left to git to handle. If we need a merkle tree implementation then we can fish it back from the git history, otherwise we need to do all the work to maintain this code all while never using it.

These tests don't feel particularly useful to me as the vast majority of the complexity is actually in the testing code (the merkle tree implementation to construct the tree rather than the function which is verifying it).

[vezenovm]

These tests don't feel particularly useful to me as the vast majority of the complexity is actually in the testing code (the merkle tree implementation to construct the tree rather than the function which is verifying it).

For the basic interop tests I agree. But the tests that use compute_merkle_root are useful. I also have used them to update inputs to our nargo integration tests that use merkle trees.

[vezenovm]

I'm of the opinion that that's best left to git to handle. If we need a merkle tree implementation then we can fish it back from the git history, otherwise we need to do all the work to maintain this code all while never using it.

The dead code can be removed in a separate PR