# Native vs Non-Native Computation

ECLAIR aims to unify and simplify the development of ZK applications by providing a circuit language that can target a myriad of zero knowledge proof systems. In doing so ECLAIR treats each ZK proof system as its own computational environment. Much as Rust source code can be compiled to executables for Linux, MacOS, or Windows, a circuit written in ECLAIR can target implementations of Groth16, Plonk-like proving systems, or any other proving backend for which an appropriate plugin exists.

In this framework it is useful to distinguish between "native" and "non-native" computational environments. "Native computation" is the everyday sort of computation that simply concerns itself with executing instructions on computer hardware; it produces no ZKP to attest to the computation's correctness. This is what computers do natively.

In ECLAIR, native computation is treated on an equal footing with other computational environments that do produce ZKPs of a computation's correctness. These are collectively referred to as "non-native computation." A proving system such as Groth16 is a non-native computational environment which provides a proof of correctness for any computation that can be represented as an arithmetic circuit. Likewise there are a variety of "Plonk-like" proving systems that achieve the same goal of performing a computation and providing a succinct argument of its correctness.

Given the variety of non-native computational environments and the current rate of innovation in ZK proving systems, it is desirable to describe circuits in a proving system agnostic representation like ECLAIR. The main advantages of doing so are:

• Agility: A circuit described in ECLAIR can target any proving system via plugins. Thus a developer can quickly switch the proving system used in their ZK app according to their needs. When the next hot new ZK proving system is discovered, a new plugin allows existing ECLAIR circuits to target that proving system.
• Correctness: Computation described in ECLAIR is performed the same way in all computational environments, native or non-native. This gives developers confidence that computations performed within a ZK proving system match their native version.

## The COM Abstraction

As explained above, a computation described in ECLAIR can be carried out in various native or non-native computational environments. The computational environment is specified by choosing a type COM, short for "compiler."

We think of COM as a compiler that takes instructions written in ECLAIR and translates them to instructions for the target computational environment. In the case of native computation, COM would compile ECLAIR circuits to machine code for manipulating computer hardware. In the case of non-native computation, COM would compile ECLAIR circuits to a constraint representation such as R1CS for ZK proof generation.

For example, consider a trait Add that consists of a single function fn add for adding like types. Ordinarily, the signature of this function would be

#![allow(unused)]
fn main() {
fn add(lhs: Self, rhs: Self) -> Self
}

But in ECLAIR, we include a generic type COM to define a trait Add<COM> for addition in an arbitrary computational environment. The signature of fn add becomes

#![allow(unused)]
fn main() {
fn add(lhs: Self, rhs: Self, compiler: &mut COM) -> Self
}

In an ECLAIR circuit we may see a line like

#![allow(unused)]
fn main() {
output = add(lhs, rhs, &mut compiler);
}

In the case of non-native computation, this results in a constraint being added to enforce output = lhs + rhs in whatever constraint system is appropriate to that computational environment. A circuit described using the Add<COM> trait can be compiled to any proving system that has a type implementing Add<COM>.

### The Native Compiler Default COM = ()

In native computation there is no correctness proof and therefore no constraints for the compiler to generate. In this case ECLAIR hands off compilation to the Rust compiler to produce machine code. The native equivalent of an unsatisfied circuit is a computation that produces a runtime error. ECLAIR uses the unit type COM = () to represent the native compiler.

ECLAIR traits generally use the native compiler by default, such as Add<COM = ()>. This means that unless a ZK proving system is chosen by specifying some other type for COM, the computation will be carried out natively. When implementing ECLAIR traits for the native compiler, we still need to include the compiler argument in function signatures. For native-only computation this looks like

#![allow(unused)]
fn main() {
output = add(lhs, rhs, &mut ());
}