ark_relations/r1cs/constraint_system.rs
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#[cfg(feature = "std")]
use crate::r1cs::ConstraintTrace;
use crate::r1cs::{LcIndex, LinearCombination, Matrix, SynthesisError, Variable};
use ark_ff::Field;
use ark_std::{
any::{Any, TypeId},
boxed::Box,
cell::{Ref, RefCell, RefMut},
collections::BTreeMap,
format,
rc::Rc,
string::String,
vec,
vec::Vec,
};
/// Computations are expressed in terms of rank-1 constraint systems (R1CS).
/// The `generate_constraints` method is called to generate constraints for
/// both CRS generation and for proving.
// TODO: Think: should we replace this with just a closure?
pub trait ConstraintSynthesizer<F: Field> {
/// Drives generation of new constraints inside `cs`.
fn generate_constraints(self, cs: ConstraintSystemRef<F>) -> crate::r1cs::Result<()>;
}
/// An Rank-One `ConstraintSystem`. Enforces constraints of the form
/// `⟨a_i, z⟩ ⋅ ⟨b_i, z⟩ = ⟨c_i, z⟩`, where `a_i`, `b_i`, and `c_i` are linear
/// combinations over variables, and `z` is the concrete assignment to these
/// variables.
#[derive(Debug, Clone)]
pub struct ConstraintSystem<F: Field> {
/// The mode in which the constraint system is operating. `self` can either
/// be in setup mode (i.e., `self.mode == SynthesisMode::Setup`) or in
/// proving mode (i.e., `self.mode == SynthesisMode::Prove`). If we are
/// in proving mode, then we have the additional option of whether or
/// not to construct the A, B, and C matrices of the constraint system
/// (see below).
pub mode: SynthesisMode,
/// The number of variables that are "public inputs" to the constraint
/// system.
pub num_instance_variables: usize,
/// The number of variables that are "private inputs" to the constraint
/// system.
pub num_witness_variables: usize,
/// The number of constraints in the constraint system.
pub num_constraints: usize,
/// The number of linear combinations
pub num_linear_combinations: usize,
/// The parameter we aim to minimize in this constraint system (either the
/// number of constraints or their total weight).
pub optimization_goal: OptimizationGoal,
/// Assignments to the public input variables. This is empty if `self.mode
/// == SynthesisMode::Setup`.
pub instance_assignment: Vec<F>,
/// Assignments to the private input variables. This is empty if `self.mode
/// == SynthesisMode::Setup`.
pub witness_assignment: Vec<F>,
/// Map for gadgets to cache computation results.
pub cache_map: Rc<RefCell<BTreeMap<TypeId, Box<dyn Any>>>>,
lc_map: BTreeMap<LcIndex, LinearCombination<F>>,
#[cfg(feature = "std")]
constraint_traces: Vec<Option<ConstraintTrace>>,
a_constraints: Vec<LcIndex>,
b_constraints: Vec<LcIndex>,
c_constraints: Vec<LcIndex>,
lc_assignment_cache: Rc<RefCell<BTreeMap<LcIndex, F>>>,
}
impl<F: Field> Default for ConstraintSystem<F> {
fn default() -> Self {
Self::new()
}
}
/// Defines the mode of operation of a `ConstraintSystem`.
#[derive(Copy, Clone, Debug, Eq, PartialEq, Ord, PartialOrd)]
pub enum SynthesisMode {
/// Indicate to the `ConstraintSystem` that it should only generate
/// constraint matrices and not populate the variable assignments.
Setup,
/// Indicate to the `ConstraintSystem` that it populate the variable
/// assignments. If additionally `construct_matrices == true`, then generate
/// the matrices as in the `Setup` case.
Prove {
/// If `construct_matrices == true`, then generate
/// the matrices as in the `Setup` case.
construct_matrices: bool,
},
}
/// Defines the parameter to optimize for a `ConstraintSystem`.
#[derive(Copy, Clone, Debug, Eq, PartialEq, Ord, PartialOrd)]
pub enum OptimizationGoal {
/// Make no attempt to optimize.
None,
/// Minimize the number of constraints.
Constraints,
/// Minimize the total weight of the constraints (the number of nonzero
/// entries across all constraints).
Weight,
}
impl<F: Field> ConstraintSystem<F> {
#[inline]
fn make_row(&self, l: &LinearCombination<F>) -> Vec<(F, usize)> {
let num_input = self.num_instance_variables;
l.0.iter()
.filter_map(|(coeff, var)| {
if coeff.is_zero() {
None
} else {
Some((
*coeff,
var.get_index_unchecked(num_input).expect("no symbolic LCs"),
))
}
})
.collect()
}
/// Construct an empty `ConstraintSystem`.
pub fn new() -> Self {
Self {
num_instance_variables: 1,
num_witness_variables: 0,
num_constraints: 0,
num_linear_combinations: 0,
a_constraints: Vec::new(),
b_constraints: Vec::new(),
c_constraints: Vec::new(),
instance_assignment: vec![F::one()],
witness_assignment: Vec::new(),
cache_map: Rc::new(RefCell::new(BTreeMap::new())),
#[cfg(feature = "std")]
constraint_traces: Vec::new(),
lc_map: BTreeMap::new(),
lc_assignment_cache: Rc::new(RefCell::new(BTreeMap::new())),
mode: SynthesisMode::Prove {
construct_matrices: true,
},
optimization_goal: OptimizationGoal::Constraints,
}
}
/// Create a new `ConstraintSystemRef<F>`.
pub fn new_ref() -> ConstraintSystemRef<F> {
ConstraintSystemRef::new(Self::new())
}
/// Set `self.mode` to `mode`.
pub fn set_mode(&mut self, mode: SynthesisMode) {
self.mode = mode;
}
/// Check whether `self.mode == SynthesisMode::Setup`.
pub fn is_in_setup_mode(&self) -> bool {
self.mode == SynthesisMode::Setup
}
/// Check whether this constraint system aims to optimize weight,
/// number of constraints, or neither.
pub fn optimization_goal(&self) -> OptimizationGoal {
self.optimization_goal
}
/// Specify whether this constraint system should aim to optimize weight,
/// number of constraints, or neither.
pub fn set_optimization_goal(&mut self, goal: OptimizationGoal) {
// `set_optimization_goal` should only be executed before any constraint or value is created.
assert_eq!(self.num_instance_variables, 1);
assert_eq!(self.num_witness_variables, 0);
assert_eq!(self.num_constraints, 0);
assert_eq!(self.num_linear_combinations, 0);
self.optimization_goal = goal;
}
/// Check whether or not `self` will construct matrices.
pub fn should_construct_matrices(&self) -> bool {
match self.mode {
SynthesisMode::Setup => true,
SynthesisMode::Prove { construct_matrices } => construct_matrices,
}
}
/// Return a variable representing the constant "zero" inside the constraint
/// system.
#[inline]
pub fn zero() -> Variable {
Variable::Zero
}
/// Return a variable representing the constant "one" inside the constraint
/// system.
#[inline]
pub fn one() -> Variable {
Variable::One
}
/// Obtain a variable representing a new public instance input.
#[inline]
pub fn new_input_variable<Func>(&mut self, f: Func) -> crate::r1cs::Result<Variable>
where
Func: FnOnce() -> crate::r1cs::Result<F>,
{
let index = self.num_instance_variables;
self.num_instance_variables += 1;
if !self.is_in_setup_mode() {
self.instance_assignment.push(f()?);
}
Ok(Variable::Instance(index))
}
/// Obtain a variable representing a new private witness input.
#[inline]
pub fn new_witness_variable<Func>(&mut self, f: Func) -> crate::r1cs::Result<Variable>
where
Func: FnOnce() -> crate::r1cs::Result<F>,
{
let index = self.num_witness_variables;
self.num_witness_variables += 1;
if !self.is_in_setup_mode() {
self.witness_assignment.push(f()?);
}
Ok(Variable::Witness(index))
}
/// Obtain a variable representing a linear combination.
#[inline]
pub fn new_lc(&mut self, lc: LinearCombination<F>) -> crate::r1cs::Result<Variable> {
let index = LcIndex(self.num_linear_combinations);
let var = Variable::SymbolicLc(index);
self.lc_map.insert(index, lc);
self.num_linear_combinations += 1;
Ok(var)
}
/// Enforce a R1CS constraint with the name `name`.
#[inline]
pub fn enforce_constraint(
&mut self,
a: LinearCombination<F>,
b: LinearCombination<F>,
c: LinearCombination<F>,
) -> crate::r1cs::Result<()> {
if self.should_construct_matrices() {
let a_index = self.new_lc(a)?.get_lc_index().unwrap();
let b_index = self.new_lc(b)?.get_lc_index().unwrap();
let c_index = self.new_lc(c)?.get_lc_index().unwrap();
self.a_constraints.push(a_index);
self.b_constraints.push(b_index);
self.c_constraints.push(c_index);
}
self.num_constraints += 1;
#[cfg(feature = "std")]
{
let trace = ConstraintTrace::capture();
self.constraint_traces.push(trace);
}
Ok(())
}
/// Count the number of times each LC is used within other LCs in the
/// constraint system
fn lc_num_times_used(&self, count_sinks: bool) -> Vec<usize> {
let mut num_times_used = vec![0; self.lc_map.len()];
// Iterate over every lc in constraint system
for (index, lc) in self.lc_map.iter() {
num_times_used[index.0] += count_sinks as usize;
// Increment the counter for each lc that this lc has a direct dependency on.
for &(_, var) in lc.iter() {
if var.is_lc() {
let lc_index = var.get_lc_index().expect("should be lc");
num_times_used[lc_index.0] += 1;
}
}
}
num_times_used
}
/// Transform the map of linear combinations.
/// Specifically, allow the creation of additional witness assignments.
///
/// This method is used as a subroutine of `inline_all_lcs` and `outline_lcs`.
///
/// The transformer function is given a references of this constraint system (&self),
/// number of times used, and a mutable reference of the linear combination to be transformed.
/// (&ConstraintSystem<F>, usize, &mut LinearCombination<F>)
///
/// The transformer function returns the number of new witness variables needed
/// and a vector of new witness assignments (if not in the setup mode).
/// (usize, Option<Vec<F>>)
pub fn transform_lc_map(
&mut self,
transformer: &mut dyn FnMut(
&ConstraintSystem<F>,
usize,
&mut LinearCombination<F>,
) -> (usize, Option<Vec<F>>),
) {
// `transformed_lc_map` stores the transformed linear combinations.
let mut transformed_lc_map = BTreeMap::<_, LinearCombination<F>>::new();
let mut num_times_used = self.lc_num_times_used(false);
// This loop goes through all the LCs in the map, starting from
// the early ones. The transformer function is applied to the
// inlined LC, where new witness variables can be created.
for (&index, lc) in &self.lc_map {
let mut transformed_lc = LinearCombination::new();
// Inline the LC, unwrapping symbolic LCs that may constitute it,
// and updating them according to transformations in prior iterations.
for &(coeff, var) in lc.iter() {
if var.is_lc() {
let lc_index = var.get_lc_index().expect("should be lc");
// If `var` is a `SymbolicLc`, fetch the corresponding
// inlined LC, and substitute it in.
//
// We have the guarantee that `lc_index` must exist in
// `new_lc_map` since a LC can only depend on other
// LCs with lower indices, which we have transformed.
//
let lc = transformed_lc_map
.get(&lc_index)
.expect("should be inlined");
transformed_lc.extend((lc * coeff).0.into_iter());
// Delete linear combinations that are no longer used.
//
// Deletion is safe for both outlining and inlining:
// * Inlining: the LC is substituted directly into all use sites, and so once it
// is fully inlined, it is redundant.
//
// * Outlining: the LC is associated with a new variable `w`, and a new
// constraint of the form `lc_data * 1 = w`, where `lc_data` is the actual
// data in the linear combination. Furthermore, we replace its entry in
// `new_lc_map` with `(1, w)`. Once `w` is fully inlined, then we can delete
// the entry from `new_lc_map`
//
num_times_used[lc_index.0] -= 1;
if num_times_used[lc_index.0] == 0 {
// This lc is not used any more, so remove it.
transformed_lc_map.remove(&lc_index);
}
} else {
// Otherwise, it's a concrete variable and so we
// substitute it in directly.
transformed_lc.push((coeff, var));
}
}
transformed_lc.compactify();
// Call the transformer function.
let (num_new_witness_variables, new_witness_assignments) =
transformer(&self, num_times_used[index.0], &mut transformed_lc);
// Insert the transformed LC.
transformed_lc_map.insert(index, transformed_lc);
// Update the witness counter.
self.num_witness_variables += num_new_witness_variables;
// Supply additional witness assignments if not in the
// setup mode and if new witness variables are created.
if !self.is_in_setup_mode() && num_new_witness_variables > 0 {
assert!(new_witness_assignments.is_some());
if let Some(new_witness_assignments) = new_witness_assignments {
assert_eq!(new_witness_assignments.len(), num_new_witness_variables);
self.witness_assignment
.extend_from_slice(&new_witness_assignments);
}
}
}
// Replace the LC map.
self.lc_map = transformed_lc_map;
}
/// Naively inlines symbolic linear combinations into the linear
/// combinations that use them.
///
/// Useful for standard pairing-based SNARKs where addition gates are cheap.
/// For example, in the SNARKs such as [\[Groth16\]](https://eprint.iacr.org/2016/260) and
/// [\[Groth-Maller17\]](https://eprint.iacr.org/2017/540), addition gates
/// do not contribute to the size of the multi-scalar multiplication, which
/// is the dominating cost.
pub fn inline_all_lcs(&mut self) {
// Only inline when a matrix representing R1CS is needed.
if !self.should_construct_matrices() {
return;
}
// A dummy closure is used, which means that
// - it does not modify the inlined LC.
// - it does not add new witness variables.
self.transform_lc_map(&mut |_, _, _| (0, None));
}
/// If a `SymbolicLc` is used in more than one location and has sufficient
/// length, this method makes a new variable for that `SymbolicLc`, adds
/// a constraint ensuring the equality of the variable and the linear
/// combination, and then uses that variable in every location the
/// `SymbolicLc` is used.
///
/// Useful for SNARKs like [\[Marlin\]](https://eprint.iacr.org/2019/1047) or
/// [\[Fractal\]](https://eprint.iacr.org/2019/1076), where addition gates
/// are not cheap.
fn outline_lcs(&mut self) {
// Only inline when a matrix representing R1CS is needed.
if !self.should_construct_matrices() {
return;
}
// Store information about new witness variables created
// for outlining. New constraints will be added after the
// transformation of the LC map.
let mut new_witness_linear_combinations = Vec::new();
let mut new_witness_indices = Vec::new();
// It goes through all the LCs in the map, starting from
// the early ones, and decides whether or not to dedicate a witness
// variable for this LC.
//
// If true, the LC is replaced with 1 * this witness variable.
// Otherwise, the LC is inlined.
//
// Each iteration first updates the LC according to outlinings in prior
// iterations, and then sees if it should be outlined, and if so adds
// the outlining to the map.
//
self.transform_lc_map(&mut |cs, num_times_used, inlined_lc| {
let mut should_dedicate_a_witness_variable = false;
let mut new_witness_index = None;
let mut new_witness_assignment = Vec::new();
// Check if it is worthwhile to dedicate a witness variable.
let this_used_times = num_times_used + 1;
let this_len = inlined_lc.len();
// Cost with no outlining = `lc_len * number of usages`
// Cost with outlining is one constraint for `(lc_len) * 1 = {new variable}` and
// using that single new variable in each of the prior usages.
// This has total cost `number_of_usages + lc_len + 2`
if this_used_times * this_len > this_used_times + 2 + this_len {
should_dedicate_a_witness_variable = true;
}
// If it is worthwhile to dedicate a witness variable,
if should_dedicate_a_witness_variable {
// Add a new witness (the value of the linear combination).
// This part follows the same logic of `new_witness_variable`.
let witness_index = cs.num_witness_variables;
new_witness_index = Some(witness_index);
// Compute the witness assignment.
if !cs.is_in_setup_mode() {
let mut acc = F::zero();
for (coeff, var) in inlined_lc.iter() {
acc += *coeff * &cs.assigned_value(*var).unwrap();
}
new_witness_assignment.push(acc);
}
// Add a new constraint for this new witness.
new_witness_linear_combinations.push(inlined_lc.clone());
new_witness_indices.push(witness_index);
// Replace the linear combination with (1 * this new witness).
*inlined_lc = LinearCombination::from(Variable::Witness(witness_index));
}
// Otherwise, the LC remains unchanged.
// Return information about new witness variables.
if new_witness_index.is_some() {
(1, Some(new_witness_assignment))
} else {
(0, None)
}
});
// Add the constraints for the newly added witness variables.
for (new_witness_linear_combination, new_witness_variable) in
new_witness_linear_combinations
.iter()
.zip(new_witness_indices.iter())
{
// Add a new constraint
self.enforce_constraint(
new_witness_linear_combination.clone(),
LinearCombination::from(Self::one()),
LinearCombination::from(Variable::Witness(*new_witness_variable)),
)
.unwrap();
}
}
/// Finalize the constraint system (either by outlining or inlining,
/// if an optimization goal is set).
pub fn finalize(&mut self) {
match self.optimization_goal {
OptimizationGoal::None => self.inline_all_lcs(),
OptimizationGoal::Constraints => self.inline_all_lcs(),
OptimizationGoal::Weight => self.outline_lcs(),
};
}
/// This step must be called after constraint generation has completed, and
/// after all symbolic LCs have been inlined into the places that they
/// are used.
pub fn to_matrices(&self) -> Option<ConstraintMatrices<F>> {
if let SynthesisMode::Prove {
construct_matrices: false,
} = self.mode
{
None
} else {
let a: Vec<_> = self
.a_constraints
.iter()
.map(|index| self.make_row(self.lc_map.get(index).unwrap()))
.collect();
let b: Vec<_> = self
.b_constraints
.iter()
.map(|index| self.make_row(self.lc_map.get(index).unwrap()))
.collect();
let c: Vec<_> = self
.c_constraints
.iter()
.map(|index| self.make_row(self.lc_map.get(index).unwrap()))
.collect();
let a_num_non_zero: usize = a.iter().map(|lc| lc.len()).sum();
let b_num_non_zero: usize = b.iter().map(|lc| lc.len()).sum();
let c_num_non_zero: usize = c.iter().map(|lc| lc.len()).sum();
let matrices = ConstraintMatrices {
num_instance_variables: self.num_instance_variables,
num_witness_variables: self.num_witness_variables,
num_constraints: self.num_constraints,
a_num_non_zero,
b_num_non_zero,
c_num_non_zero,
a,
b,
c,
};
Some(matrices)
}
}
fn eval_lc(&self, lc: LcIndex) -> Option<F> {
let lc = self.lc_map.get(&lc)?;
let mut acc = F::zero();
for (coeff, var) in lc.iter() {
acc += *coeff * self.assigned_value(*var)?;
}
Some(acc)
}
/// If `self` is satisfied, outputs `Ok(true)`.
/// If `self` is unsatisfied, outputs `Ok(false)`.
/// If `self.is_in_setup_mode()`, outputs `Err(())`.
pub fn is_satisfied(&self) -> crate::r1cs::Result<bool> {
self.which_is_unsatisfied().map(|s| s.is_none())
}
/// If `self` is satisfied, outputs `Ok(None)`.
/// If `self` is unsatisfied, outputs `Some(i)`, where `i` is the index of
/// the first unsatisfied constraint. If `self.is_in_setup_mode()`, outputs
/// `Err(())`.
pub fn which_is_unsatisfied(&self) -> crate::r1cs::Result<Option<String>> {
if self.is_in_setup_mode() {
Err(SynthesisError::AssignmentMissing)
} else {
for i in 0..self.num_constraints {
let a = self
.eval_lc(self.a_constraints[i])
.ok_or(SynthesisError::AssignmentMissing)?;
let b = self
.eval_lc(self.b_constraints[i])
.ok_or(SynthesisError::AssignmentMissing)?;
let c = self
.eval_lc(self.c_constraints[i])
.ok_or(SynthesisError::AssignmentMissing)?;
if a * b != c {
let trace;
#[cfg(feature = "std")]
{
trace = self.constraint_traces[i].as_ref().map_or_else(
|| {
eprintln!("Constraint trace requires enabling `ConstraintLayer`");
format!("{}", i)
},
|t| format!("{}", t),
);
}
#[cfg(not(feature = "std"))]
{
trace = format!("{}", i);
}
return Ok(Some(trace));
}
}
Ok(None)
}
}
/// Obtain the assignment corresponding to the `Variable` `v`.
pub fn assigned_value(&self, v: Variable) -> Option<F> {
match v {
Variable::One => Some(F::one()),
Variable::Zero => Some(F::zero()),
Variable::Witness(idx) => self.witness_assignment.get(idx).copied(),
Variable::Instance(idx) => self.instance_assignment.get(idx).copied(),
Variable::SymbolicLc(idx) => {
let value = self.lc_assignment_cache.borrow().get(&idx).copied();
if value.is_some() {
value
} else {
let value = self.eval_lc(idx)?;
self.lc_assignment_cache.borrow_mut().insert(idx, value);
Some(value)
}
},
}
}
}
/// The A, B and C matrices of a Rank-One `ConstraintSystem`.
/// Also contains metadata on the structure of the constraint system
/// and the matrices.
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct ConstraintMatrices<F: Field> {
/// The number of variables that are "public instances" to the constraint
/// system.
pub num_instance_variables: usize,
/// The number of variables that are "private witnesses" to the constraint
/// system.
pub num_witness_variables: usize,
/// The number of constraints in the constraint system.
pub num_constraints: usize,
/// The number of non_zero entries in the A matrix.
pub a_num_non_zero: usize,
/// The number of non_zero entries in the B matrix.
pub b_num_non_zero: usize,
/// The number of non_zero entries in the C matrix.
pub c_num_non_zero: usize,
/// The A constraint matrix. This is empty when
/// `self.mode == SynthesisMode::Prove { construct_matrices = false }`.
pub a: Matrix<F>,
/// The B constraint matrix. This is empty when
/// `self.mode == SynthesisMode::Prove { construct_matrices = false }`.
pub b: Matrix<F>,
/// The C constraint matrix. This is empty when
/// `self.mode == SynthesisMode::Prove { construct_matrices = false }`.
pub c: Matrix<F>,
}
/// A shared reference to a constraint system that can be stored in high level
/// variables.
#[derive(Debug, Clone)]
pub enum ConstraintSystemRef<F: Field> {
/// Represents the case where we *don't* need to allocate variables or
/// enforce constraints. Encountered when operating over constant
/// values.
None,
/// Represents the case where we *do* allocate variables or enforce
/// constraints.
CS(Rc<RefCell<ConstraintSystem<F>>>),
}
impl<F: Field> PartialEq for ConstraintSystemRef<F> {
fn eq(&self, other: &Self) -> bool {
match (self, other) {
(Self::None, Self::None) => true,
(..) => false,
}
}
}
impl<F: Field> Eq for ConstraintSystemRef<F> {}
/// A namespaced `ConstraintSystemRef`.
#[derive(Debug, Clone)]
pub struct Namespace<F: Field> {
inner: ConstraintSystemRef<F>,
id: Option<tracing::Id>,
}
impl<F: Field> From<ConstraintSystemRef<F>> for Namespace<F> {
fn from(other: ConstraintSystemRef<F>) -> Self {
Self {
inner: other,
id: None,
}
}
}
impl<F: Field> Namespace<F> {
/// Construct a new `Namespace`.
pub fn new(inner: ConstraintSystemRef<F>, id: Option<tracing::Id>) -> Self {
Self { inner, id }
}
/// Obtain the inner `ConstraintSystemRef<F>`.
pub fn cs(&self) -> ConstraintSystemRef<F> {
self.inner.clone()
}
/// Manually leave the namespace.
pub fn leave_namespace(self) {
drop(self)
}
}
impl<F: Field> Drop for Namespace<F> {
fn drop(&mut self) {
if let Some(id) = self.id.as_ref() {
tracing::dispatcher::get_default(|dispatch| dispatch.exit(id))
}
let _ = self.inner;
}
}
impl<F: Field> ConstraintSystemRef<F> {
/// Returns `self` if `!self.is_none()`, otherwise returns `other`.
pub fn or(self, other: Self) -> Self {
match self {
ConstraintSystemRef::None => other,
_ => self,
}
}
/// Returns `true` is `self == ConstraintSystemRef::None`.
pub fn is_none(&self) -> bool {
matches!(self, ConstraintSystemRef::None)
}
/// Construct a `ConstraintSystemRef` from a `ConstraintSystem`.
#[inline]
pub fn new(inner: ConstraintSystem<F>) -> Self {
Self::CS(Rc::new(RefCell::new(inner)))
}
fn inner(&self) -> Option<&Rc<RefCell<ConstraintSystem<F>>>> {
match self {
Self::CS(a) => Some(a),
Self::None => None,
}
}
/// Consumes self to return the inner `ConstraintSystem<F>`. Returns
/// `None` if `Self::CS` is `None` or if any other references to
/// `Self::CS` exist.
pub fn into_inner(self) -> Option<ConstraintSystem<F>> {
match self {
Self::CS(a) => Rc::try_unwrap(a).ok().map(|s| s.into_inner()),
Self::None => None,
}
}
/// Obtain an immutable reference to the underlying `ConstraintSystem`.
///
/// # Panics
/// This method panics if `self` is already mutably borrowed.
#[inline]
pub fn borrow(&self) -> Option<Ref<'_, ConstraintSystem<F>>> {
self.inner().map(|cs| cs.borrow())
}
/// Obtain a mutable reference to the underlying `ConstraintSystem`.
///
/// # Panics
/// This method panics if `self` is already mutably borrowed.
#[inline]
pub fn borrow_mut(&self) -> Option<RefMut<'_, ConstraintSystem<F>>> {
self.inner().map(|cs| cs.borrow_mut())
}
/// Set `self.mode` to `mode`.
pub fn set_mode(&self, mode: SynthesisMode) {
self.inner().map_or((), |cs| cs.borrow_mut().set_mode(mode))
}
/// Check whether `self.mode == SynthesisMode::Setup`.
#[inline]
pub fn is_in_setup_mode(&self) -> bool {
self.inner()
.map_or(false, |cs| cs.borrow().is_in_setup_mode())
}
/// Returns the number of constraints.
#[inline]
pub fn num_constraints(&self) -> usize {
self.inner().map_or(0, |cs| cs.borrow().num_constraints)
}
/// Returns the number of instance variables.
#[inline]
pub fn num_instance_variables(&self) -> usize {
self.inner()
.map_or(0, |cs| cs.borrow().num_instance_variables)
}
/// Returns the number of witness variables.
#[inline]
pub fn num_witness_variables(&self) -> usize {
self.inner()
.map_or(0, |cs| cs.borrow().num_witness_variables)
}
/// Check whether this constraint system aims to optimize weight,
/// number of constraints, or neither.
#[inline]
pub fn optimization_goal(&self) -> OptimizationGoal {
self.inner().map_or(OptimizationGoal::Constraints, |cs| {
cs.borrow().optimization_goal()
})
}
/// Specify whether this constraint system should aim to optimize weight,
/// number of constraints, or neither.
#[inline]
pub fn set_optimization_goal(&self, goal: OptimizationGoal) {
self.inner()
.map_or((), |cs| cs.borrow_mut().set_optimization_goal(goal))
}
/// Check whether or not `self` will construct matrices.
#[inline]
pub fn should_construct_matrices(&self) -> bool {
self.inner()
.map_or(false, |cs| cs.borrow().should_construct_matrices())
}
/// Obtain a variable representing a new public instance input.
#[inline]
pub fn new_input_variable<Func>(&self, f: Func) -> crate::r1cs::Result<Variable>
where
Func: FnOnce() -> crate::r1cs::Result<F>,
{
self.inner()
.ok_or(SynthesisError::MissingCS)
.and_then(|cs| {
if !self.is_in_setup_mode() {
// This is needed to avoid double-borrows, because `f`
// might itself mutably borrow `cs` (eg: `f = || g.value()`).
let value = f();
cs.borrow_mut().new_input_variable(|| value)
} else {
cs.borrow_mut().new_input_variable(f)
}
})
}
/// Obtain a variable representing a new private witness input.
#[inline]
pub fn new_witness_variable<Func>(&self, f: Func) -> crate::r1cs::Result<Variable>
where
Func: FnOnce() -> crate::r1cs::Result<F>,
{
self.inner()
.ok_or(SynthesisError::MissingCS)
.and_then(|cs| {
if !self.is_in_setup_mode() {
// This is needed to avoid double-borrows, because `f`
// might itself mutably borrow `cs` (eg: `f = || g.value()`).
let value = f();
cs.borrow_mut().new_witness_variable(|| value)
} else {
cs.borrow_mut().new_witness_variable(f)
}
})
}
/// Obtain a variable representing a linear combination.
#[inline]
pub fn new_lc(&self, lc: LinearCombination<F>) -> crate::r1cs::Result<Variable> {
self.inner()
.ok_or(SynthesisError::MissingCS)
.and_then(|cs| cs.borrow_mut().new_lc(lc))
}
/// Enforce a R1CS constraint with the name `name`.
#[inline]
pub fn enforce_constraint(
&self,
a: LinearCombination<F>,
b: LinearCombination<F>,
c: LinearCombination<F>,
) -> crate::r1cs::Result<()> {
self.inner()
.ok_or(SynthesisError::MissingCS)
.and_then(|cs| cs.borrow_mut().enforce_constraint(a, b, c))
}
/// Naively inlines symbolic linear combinations into the linear
/// combinations that use them.
///
/// Useful for standard pairing-based SNARKs where addition gates are cheap.
/// For example, in the SNARKs such as [\[Groth16\]](https://eprint.iacr.org/2016/260) and
/// [\[Groth-Maller17\]](https://eprint.iacr.org/2017/540), addition gates
/// do not contribute to the size of the multi-scalar multiplication, which
/// is the dominating cost.
pub fn inline_all_lcs(&self) {
if let Some(cs) = self.inner() {
cs.borrow_mut().inline_all_lcs()
}
}
/// Finalize the constraint system (either by outlining or inlining,
/// if an optimization goal is set).
pub fn finalize(&self) {
if let Some(cs) = self.inner() {
cs.borrow_mut().finalize()
}
}
/// This step must be called after constraint generation has completed, and
/// after all symbolic LCs have been inlined into the places that they
/// are used.
#[inline]
pub fn to_matrices(&self) -> Option<ConstraintMatrices<F>> {
self.inner().and_then(|cs| cs.borrow().to_matrices())
}
/// If `self` is satisfied, outputs `Ok(true)`.
/// If `self` is unsatisfied, outputs `Ok(false)`.
/// If `self.is_in_setup_mode()` or if `self == None`, outputs `Err(())`.
pub fn is_satisfied(&self) -> crate::r1cs::Result<bool> {
self.inner()
.map_or(Err(SynthesisError::AssignmentMissing), |cs| {
cs.borrow().is_satisfied()
})
}
/// If `self` is satisfied, outputs `Ok(None)`.
/// If `self` is unsatisfied, outputs `Some(i)`, where `i` is the index of
/// the first unsatisfied constraint.
/// If `self.is_in_setup_mode()` or `self == None`, outputs `Err(())`.
pub fn which_is_unsatisfied(&self) -> crate::r1cs::Result<Option<String>> {
self.inner()
.map_or(Err(SynthesisError::AssignmentMissing), |cs| {
cs.borrow().which_is_unsatisfied()
})
}
/// Obtain the assignment corresponding to the `Variable` `v`.
pub fn assigned_value(&self, v: Variable) -> Option<F> {
self.inner().and_then(|cs| cs.borrow().assigned_value(v))
}
/// Get trace information about all constraints in the system
pub fn constraint_names(&self) -> Option<Vec<String>> {
#[cfg(feature = "std")]
{
self.inner().and_then(|cs| {
cs.borrow()
.constraint_traces
.iter()
.map(|trace| {
let mut constraint_path = String::new();
let mut prev_module_path = "";
let mut prefixes = ark_std::collections::BTreeSet::new();
for step in trace.as_ref()?.path() {
let module_path = if prev_module_path == step.module_path {
prefixes.insert(step.module_path.to_string());
String::new()
} else {
let mut parts = step
.module_path
.split("::")
.filter(|&part| part != "r1cs_std" && part != "constraints");
let mut path_so_far = String::new();
for part in parts.by_ref() {
if path_so_far.is_empty() {
path_so_far += part;
} else {
path_so_far += &["::", part].join("");
}
if prefixes.contains(&path_so_far) {
continue;
} else {
prefixes.insert(path_so_far.clone());
break;
}
}
parts.collect::<Vec<_>>().join("::") + "::"
};
prev_module_path = step.module_path;
constraint_path += &["/", &module_path, step.name].join("");
}
Some(constraint_path)
})
.collect::<Option<Vec<_>>>()
})
}
#[cfg(not(feature = "std"))]
{
None
}
}
}
#[cfg(test)]
mod tests {
use crate::r1cs::*;
use ark_ff::One;
use ark_test_curves::bls12_381::Fr;
#[test]
fn matrix_generation() -> crate::r1cs::Result<()> {
let cs = ConstraintSystem::<Fr>::new_ref();
let two = Fr::one() + Fr::one();
let a = cs.new_input_variable(|| Ok(Fr::one()))?;
let b = cs.new_witness_variable(|| Ok(Fr::one()))?;
let c = cs.new_witness_variable(|| Ok(two))?;
cs.enforce_constraint(lc!() + a, lc!() + (two, b), lc!() + c)?;
let d = cs.new_lc(lc!() + a + b)?;
cs.enforce_constraint(lc!() + a, lc!() + d, lc!() + d)?;
let e = cs.new_lc(lc!() + d + d)?;
cs.enforce_constraint(lc!() + Variable::One, lc!() + e, lc!() + e)?;
cs.inline_all_lcs();
let matrices = cs.to_matrices().unwrap();
assert_eq!(matrices.a[0], vec![(Fr::one(), 1)]);
assert_eq!(matrices.b[0], vec![(two, 2)]);
assert_eq!(matrices.c[0], vec![(Fr::one(), 3)]);
assert_eq!(matrices.a[1], vec![(Fr::one(), 1)]);
assert_eq!(matrices.b[1], vec![(Fr::one(), 1), (Fr::one(), 2)]);
assert_eq!(matrices.c[1], vec![(Fr::one(), 1), (Fr::one(), 2)]);
assert_eq!(matrices.a[2], vec![(Fr::one(), 0)]);
assert_eq!(matrices.b[2], vec![(two, 1), (two, 2)]);
assert_eq!(matrices.c[2], vec![(two, 1), (two, 2)]);
Ok(())
}
#[test]
fn matrix_generation_outlined() -> crate::r1cs::Result<()> {
let cs = ConstraintSystem::<Fr>::new_ref();
cs.set_optimization_goal(OptimizationGoal::Weight);
let two = Fr::one() + Fr::one();
let a = cs.new_input_variable(|| Ok(Fr::one()))?;
let b = cs.new_witness_variable(|| Ok(Fr::one()))?;
let c = cs.new_witness_variable(|| Ok(two))?;
cs.enforce_constraint(lc!() + a, lc!() + (two, b), lc!() + c)?;
let d = cs.new_lc(lc!() + a + b)?;
cs.enforce_constraint(lc!() + a, lc!() + d, lc!() + d)?;
let e = cs.new_lc(lc!() + d + d)?;
cs.enforce_constraint(lc!() + Variable::One, lc!() + e, lc!() + e)?;
cs.finalize();
assert!(cs.is_satisfied().unwrap());
let matrices = cs.to_matrices().unwrap();
assert_eq!(matrices.a[0], vec![(Fr::one(), 1)]);
assert_eq!(matrices.b[0], vec![(two, 2)]);
assert_eq!(matrices.c[0], vec![(Fr::one(), 3)]);
assert_eq!(matrices.a[1], vec![(Fr::one(), 1)]);
// Notice here how the variable allocated for d is outlined
// compared to the example in previous test case.
// We are optimising for weight: there are less non-zero elements.
assert_eq!(matrices.b[1], vec![(Fr::one(), 4)]);
assert_eq!(matrices.c[1], vec![(Fr::one(), 4)]);
assert_eq!(matrices.a[2], vec![(Fr::one(), 0)]);
assert_eq!(matrices.b[2], vec![(two, 4)]);
assert_eq!(matrices.c[2], vec![(two, 4)]);
Ok(())
}
/// Example meant to follow as closely as possible the excellent R1CS
/// write-up by [Vitalik Buterin](https://vitalik.eth.limo/general/2016/12/10/qap.html)
/// and demonstrate how to construct such matrices in arkworks.
#[test]
fn matrix_generation_example() -> crate::r1cs::Result<()> {
let cs = ConstraintSystem::<Fr>::new_ref();
// helper definitions
let three = Fr::from(3u8);
let five = Fr::from(5u8);
let nine = Fr::from(9u8);
// There will be six variables in the system, in the order governed by adding
// them to the constraint system (Note that the CS is initialised with
// `Variable::One` in the first position implicitly).
// Note also that the all public variables will always be placed before all witnesses
//
// Variable::One
// Variable::Instance(35)
// Variable::Witness(3) ( == x )
// Variable::Witness(9) ( == sym_1 )
// Variable::Witness(27) ( == y )
// Variable::Witness(30) ( == sym_2 )
// let one = Variable::One; // public input, implicitly defined
let out = cs.new_input_variable(|| Ok(nine * three + three + five))?; // public input
let x = cs.new_witness_variable(|| Ok(three))?; // explicit witness
let sym_1 = cs.new_witness_variable(|| Ok(nine))?; // intermediate witness variable
let y = cs.new_witness_variable(|| Ok(nine * three))?; // intermediate witness variable
let sym_2 = cs.new_witness_variable(|| Ok(nine * three + three))?; // intermediate witness variable
cs.enforce_constraint(lc!() + x, lc!() + x, lc!() + sym_1)?;
cs.enforce_constraint(lc!() + sym_1, lc!() + x, lc!() + y)?;
cs.enforce_constraint(lc!() + y + x, lc!() + Variable::One, lc!() + sym_2)?;
cs.enforce_constraint(
lc!() + sym_2 + (five, Variable::One),
lc!() + Variable::One,
lc!() + out,
)?;
cs.finalize();
assert!(cs.is_satisfied().unwrap());
let matrices = cs.to_matrices().unwrap();
// There are four gates(constraints), each generating a row.
// Resulting matrices:
// (Note how 2nd & 3rd columns are swapped compared to the online example.
// This results from an implementation detail of placing all Variable::Instances(_) first.
//
// A
// [0, 0, 1, 0, 0, 0]
// [0, 0, 0, 1, 0, 0]
// [0, 0, 1, 0, 1, 0]
// [5, 0, 0, 0, 0, 1]
// B
// [0, 0, 1, 0, 0, 0]
// [0, 0, 1, 0, 0, 0]
// [1, 0, 0, 0, 0, 0]
// [1, 0, 0, 0, 0, 0]
// C
// [0, 0, 0, 1, 0, 0]
// [0, 0, 0, 0, 1, 0]
// [0, 0, 0, 0, 0, 1]
// [0, 1, 0, 0, 0, 0]
assert_eq!(matrices.a[0], vec![(Fr::one(), 2)]);
assert_eq!(matrices.b[0], vec![(Fr::one(), 2)]);
assert_eq!(matrices.c[0], vec![(Fr::one(), 3)]);
assert_eq!(matrices.a[1], vec![(Fr::one(), 3)]);
assert_eq!(matrices.b[1], vec![(Fr::one(), 2)]);
assert_eq!(matrices.c[1], vec![(Fr::one(), 4)]);
assert_eq!(matrices.a[2], vec![(Fr::one(), 2), (Fr::one(), 4)]);
assert_eq!(matrices.b[2], vec![(Fr::one(), 0)]);
assert_eq!(matrices.c[2], vec![(Fr::one(), 5)]);
assert_eq!(matrices.a[3], vec![(five, 0), (Fr::one(), 5)]);
assert_eq!(matrices.b[3], vec![(Fr::one(), 0)]);
assert_eq!(matrices.c[3], vec![(Fr::one(), 1)]);
Ok(())
}
}