At the middleware we were defining some types that actually are dependant on the
backend no matter how we define them in the middleware.
For example, we were hardcoding the `Hash` and `Value` types and their related
behaviour (eg. `.to_fields()`) to be based on the length of 4 field elements,
but that's not a choice of the middleware, and in fact this is determined by the
backend itself. On the same time, those types and related methods do not belong
to the backend, since conceptually they are part of the middleware reasoning.
The intention of this PR is not to prematurely abstract the library, but to
avoid inconsistencies where a type or parameter is defined in the middleware to
have certain carachteristic and later in the backend it gets used differently.
The idea is that those types and parameters (eg. lengths) have a single source
of truth in the code; and in the case of the "base types" (hash, value, etc)
this is determined by the backend being used under the hood, not by a choice of
the middleware parameters.
The idea with this approach, is that the frontend & middleware should not need
to import the proving library used by the backend (eg. plonky2, plonky3, etc).
As mentioned earlier, the `Hash` and `Value` types are types belonging at the
middleware, and is the middleware who reasons about them, but depending on the
backend being used, the `Hash` and `Value` types will have different sizes. So
it's the backend being used who actually defines their nature under the hood.
For example with a plonky2 backend, these types will have a length of 4 field
elements, whereas with a plonky3 backend they will have a length of 8 field
eleements.
Note that his approach does not introduce new traits or abstract code, just
makes use of rust features to define 'base types' that are being used in the
middleware.
* Print pods from SignedPodBuilder
* Add additional print to test printing SignedPodBuilder
* Mock-prove and print MainPod
* Implement ToFields for custom predicates and dependencies
* Test: print serialization of a recursive batch
* Rearrange serialization of CustomPredicate so args_len is always in the same position
* Serialize predicates with first entry nonzero to avoid collision with padding
* Off by one error in ethdos test BatchSelf(2)
* cargo fmt
* not a typo
* Typos, trying again
* Experiment with statement & op enums
* Clean-up & fixes
* More clean-up
* Add argument length checks
* More clean-up
* Place statement and operation logic in submodules
