feat(noir): added distinct keyword

[joss-aztec]

Related issue(s)

Resolves # 1183

Description

Summary of changes

Added distinct keyword for preventing repetitions of witness indices in the program's abi.

fn main(x : pub Field, y : pub Field) -> pub [Field; 4] {
    let a = 1;
    let b = 1;
    [x + 1, y, a, b]
}

Compiles to:

{
  //...
  "abi": {
    //...
    "param_witnesses": { "x": [1], "y": [2] },
    "return_witnesses": [3, 2, 4, 4]
  }
}

EXPR [ (1, _1) (-1, _3) 1 ]
EXPR [ (-1, _4) 1 ]

Whereas

fn main(x : pub Field, y : pub Field) -> distinct pub [Field; 4] {
    let a = 1;
    let b = 1;
    [x + 1, y, a, b]
}

compiles to:

{
  //...
  "abi": {
    //...
    "param_witnesses": { "x": [1], "y": [2] },
    //...
    "return_witnesses": [3, 4, 5, 6]
  }
}

EXPR [ (1, _1) (-1, _3) 1 ]
EXPR [ (1, _2) (-1, _4) 0 ]
EXPR [ (-1, _5) 1 ]
EXPR [ (1, _5) (-1, _6) 0 ]

Key behaviours:

• witness 2 no longer appears in both the input and output
• witness 3 is unchanged because it was already unique
• the last 2 elements of the return are now also unique
• the above changes required the addition of two extra constraints

Dependency additions / changes

Test additions / changes

Checklist

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt with default settings.
• I have linked this PR to the issue(s) that it resolves.
• I have reviewed the changes on GitHub, line by line.
• I have ensured all changes are covered in the description.

Documentation needs

• This PR requires documentation updates when merged.

• what the keyword does

• when it can be used (only on main or contract entry points, i.e. similar to pub return)

• keyword ordering (distinct first, pub second)

• motivation/use case (see Add distinct keyword to make public return values be assigned to distinct witnesses #1183)

Additional context

[jfecher]

Looks like there were some typos introduced by this PR as well

[jfecher]

LGTM