Proposal to modify chiquito step definition

Current state

Currently a step is defined the following way:

ctx.step_type_def(step1, |ctx| {
    // define internal signals
    let c = ctx.internal("c")
    // ...
    
    // define internal constraints
    ctx.constr(eq(a + b, c));
    // ...
    
    // define transition constraints
    ctx.transition(eq(b, a.next()));
    // ...
    
    // witness generation or assignation
    ctx.wg(move |ctx, (a_value, b_value)| {
        ctx.assign(a, a_value.field());
        // ...
    });
});

Note that in this example "a" and "b" are forward signals declared outside the step type.

Problem

We have observed that new developers have problems differentiation the assignation from the setup in Chiquito, and some times try to use the setup expressions for the assignation.

Proposed solution

We would make setup inside a new lambda, that is at the same level of witness assignation, so it is clear due to scope that one cannot access the constraints from the assignation. Also, perhaps, rename "wg" to assign, that is more clear.

Example:

ctx.step_type_def(step1, |ctx| {
    // define internal signals
    let c = ctx.internal("c")
    // ...
    
    ctx.setup(move |ctx| {
        // define internal constraints
        ctx.constr(eq(a + b, c));
        // ...
    
        // define transition constraints
        ctx.transition(eq(b, a.next()));
        // ...
    });
    
    
    // witness generation or assignation
    ctx.assign(move |ctx, (a_value, b_value)| {
        ctx.assign(a, a_value.field());
        // ...
    });
});

Alternatives

Perhaps there are better keywords than "setup" and "assign"?

Perhaps it is better to separate the setup in internal and transition? Like here:

ctx.step_type_def(step1, |ctx| {
    // define internal signals
    let c = ctx.internal("c")
    // ...
    
    ctx.setup_internal(move |ctx| {
        // define internal constraints
        ctx.constr(eq(a + b, c));
        // ...
    });

    ctx.setup_transition(move |ctx| {
        // define transition constraints
        ctx.constr(eq(b, a.next()));
        // ...
    });
    
    
    // witness generation or assignation
    ctx.assign(move |ctx, (a_value, b_value)| {
        ctx.assign(a, a_value.field());
        // ...
    });
});