Expose array lookups to SnarkyJS

[joseandro]

No description provided.

[dannywillems]

(note - DRAFT)

For more context, lookups from plookup are fixed lookup tables, i.e they are the same for all circuits, and we can not therefore make tables at runtime and perform lookups in it.
The RFC Extended lookup tables describes, in particular, the concept of runtime tables.

The Rust code already implements the runtime table feature, but it is not exposed to Caml/Snarky/SnarkyJS.
In SnarkyJS, the developer should be able to define arrays at runtime, and perform lookups in it. The suggested syntax would be the same than accessing the element at the index i of the array arr, i.e. arr[i].
Tests can be found here and can help to drive the finish the epic. The final SnarkyJS implementation is described in this task and this task.

Regarding the implementation of runtime tables:

• the setup has to be prepared for the presence of runtime tables using RuntimeTableCfg. Currently, commit ca0b9e53d15e3ab5db6fb8c20617979cbf74215e, the constraint system structure defined here tracks the runtime tables in its definition in the LookupConstraintSystem and the builder correctly uses the information (see here). However, on the Caml side, nothing is tracked (see here). This should be implemented and it is relatd to this task.
• At proving time, the prover can use RuntimeTable to specify the actual tables. This is related to this task.

The important files are:

• runtime_tables. It contains the runtime tables description (i.e. a list of id's and the lengths of each table that will be defined at runtime) which must be given in the setup phase and it describes the RuntimeTable structure that the prover must give.
• plonk_dlog_proof.ml which defines the interface for the Plonk prover. The function create and its derivative should take as arguments a runtime table value.
• plonk_constraint_system should track the runtime tables specification.

[dannywillems]

List of PR's, in order:

• Bump up ocaml-gen to 0.1.5 o1-labs/proof-systems#1113
• Remove "indexed" runtime table configuration #13532
• Bump up ocaml-gen to 0.1.5 #13545
• Expose runtime table types to ocaml o1-labs/proof-systems#1112
• Expose lookup tables types ocaml o1-labs/proof-systems#1114
• Expose runtime table spec types ocaml o1-labs/proof-systems#1115
• Run prettier on bindings.js o1-labs/o1js-bindings#69
• Update snarkyjs-bindings o1-labs/o1js#1019
• Extract WasmVecVec to use it later o1-labs/o1js-bindings#70
• Define wasm lookup tables o1-labs/o1js-bindings#71
• Define wasm runtime table cfg o1-labs/o1js-bindings#73

Wasm/JS definitions and converters between Wasm/jsoo

• [develop] Define wasm runtime table o1-labs/o1js-bindings#74
• Define converters js wasm runtime table o1-labs/o1js-bindings#75
• bindings.js: remove duplicated definition o1-labs/o1js-bindings#76
• Define converters runtime table cfg js o1-labs/o1js-bindings#77
• Converters lookup table js o1-labs/o1js-bindings#78

Prover index creation: runtime table cfgs

• [develop] Bindings - add runtime table cfg to prover index creation o1-labs/o1js-bindings#79
• [develop] Bindings - add runtime table cfg to prover index creation o1-labs/o1js#1020
• [develop] Bindings - add runtime table cfg to prover index creation #13549

Prover index creation: lookup tables - #13089 and #13468

• Add lookup table to prover index creation o1-labs/o1js-bindings#82
• [develop] Bindings - add lookup table to prover index creation o1-labs/o1js#1027
• [develop] Bindings - add lookup table to prover index creation #13565

Prover: runtime tables - #13090

• [develop] Bindings - pass runtime tables to proof creation o1-labs/o1js-bindings#85
• [develop] Bindings - pass runtime table parameter to proof creation o1-labs/o1js#1031
• [develop] Bindings - pass runtime table parameter to proof creation #13593

Constraint system creation

• Track runtime table cfg: Plonk_constraint_system: runtime table cfg + runtime table to prover #13605.
• Interface to register runtime table cfg while creating the cs: TODO
• Write an OCaml test to replicate https://github.com/o1-labs/proof-systems/blob/master/kimchi/src/tests/lookup.rs#L128

MISC

• Runtime table test: randomize queries and negative tests o1-labs/proof-systems#1127
• MISC: add link to related issue on GitHub o1-labs/proof-systems#1126