Allow virtual targets to be routed (#84)

As in plonky1. The semantics of virtual targets in plonky1 were rather weird, but I think it's somewhat better here, since we already separate `generate_copy` and `assert_equal` methods. Users now make more of an explicit choice -- they can use a `VirtualTarget` for the witness generation only using `generate_copy`, or they can involve it in copy constraints.

src/circuit_builder.rs

@@ -36,7 +36,7 @@ pub struct CircuitBuilder<F: Extendable<D>, const D: usize> {
     /// The next available index for a public input.
     public_input_index: usize,
 
-    /// The next available index for a VirtualAdviceTarget.
+    /// The next available index for a `VirtualTarget`.
     virtual_target_index: usize,
 
     copy_constraints: Vec<(Target, Target)>,
@@ -77,22 +77,18 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         (0..n).map(|_i| self.add_public_input()).collect()
     }
 
-    /// Adds a new "virtual" advice target. This is not an actual wire in the witness, but just a
-    /// target that help facilitate witness generation. In particular, a generator can assign a
-    /// values to a virtual target, which can then be copied to other (virtual or concrete) targets
-    /// via `generate_copy`. When we generate the final witness (a grid of wire values), these
-    /// virtual targets will go away.
-    ///
-    /// Since virtual targets are not part of the actual permutation argument, they cannot be used
-    /// with `assert_equal`.
-    pub fn add_virtual_advice_target(&mut self) -> Target {
+    /// Adds a new "virtual" target. This is not an actual wire in the witness, but just a target
+    /// that help facilitate witness generation. In particular, a generator can assign a values to a
+    /// virtual target, which can then be copied to other (virtual or concrete) targets. When we
+    /// generate the final witness (a grid of wire values), these virtual targets will go away.
+    pub fn add_virtual_target(&mut self) -> Target {
         let index = self.virtual_target_index;
         self.virtual_target_index += 1;
-        Target::VirtualAdviceTarget { index }
+        Target::VirtualTarget { index }
     }
 
-    pub fn add_virtual_advice_targets(&mut self, n: usize) -> Vec<Target> {
-        (0..n).map(|_i| self.add_virtual_advice_target()).collect()
+    pub fn add_virtual_targets(&mut self, n: usize) -> Vec<Target> {
+        (0..n).map(|_i| self.add_virtual_target()).collect()
     }
 
     pub fn add_gate_no_constants(&mut self, gate_type: GateRef<F, D>) -> usize {
@@ -368,7 +364,11 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         }
 
         for index in 0..self.public_input_index {
-            target_partitions.add_partition(Target::PublicInput { index })
+            target_partitions.add_partition(Target::PublicInput { index });
+        }
+
+        for index in 0..self.virtual_target_index {
+            target_partitions.add_partition(Target::VirtualTarget { index });
         }
 
         for &(a, b) in &self.copy_constraints {

src/gadgets/split_join.rs

@@ -9,14 +9,14 @@ use crate::wire::Wire;
 use crate::witness::PartialWitness;
 
 impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
-    /// Split the given integer into a list of virtual advice targets, where each one represents a
-    /// bit of the integer, with little-endian ordering.
+    /// Split the given integer into a list of virtual targets, where each one represents a bit of
+    /// the integer, with little-endian ordering.
     ///
     /// Note that this only handles witness generation; it does not enforce that the decomposition
     /// is correct. The output should be treated as a "purported" decomposition which must be
     /// enforced elsewhere.
     pub(crate) fn split_le_virtual(&mut self, integer: Target, num_bits: usize) -> Vec<Target> {
-        let bit_targets = self.add_virtual_advice_targets(num_bits);
+        let bit_targets = self.add_virtual_targets(num_bits);
         self.add_generator(SplitGenerator {
             integer,
             bits: bit_targets.clone(),

src/permutation_argument.rs

@@ -57,7 +57,7 @@ impl TargetPartitions {
     }
 
     pub fn to_wire_partitions(&self) -> WirePartitions {
-        // Here we just drop all CircuitInputs, leaving all GateInputs.
+        // Here we keep just the Wire targets, filtering out everything else.
         let mut partitions = Vec::new();
         let mut indices = HashMap::new();
 

src/target.rs

@@ -8,7 +8,10 @@ use crate::wire::Wire;
 pub enum Target {
     Wire(Wire),
     PublicInput { index: usize },
-    VirtualAdviceTarget { index: usize },
+    /// A target that doesn't have any inherent location in the witness (but it can be copied to
+    /// another target that does). This is useful for representing intermediate values in witness
+    /// generation.
+    VirtualTarget { index: usize },
 }
 
 impl Target {
@@ -20,7 +23,7 @@ impl Target {
         match self {
             Target::Wire(wire) => wire.is_routable(config),
             Target::PublicInput { .. } => true,
-            Target::VirtualAdviceTarget { .. } => false,
+            Target::VirtualTarget { .. } => true,
         }
     }
 

src/witness.rs

@@ -30,7 +30,7 @@ impl<F: Field> Witness<F> {
         F: Extendable<D>,
     {
         for &(a, b) in copy_constraints {
-            // TODO: Take care of public inputs once they land.
+            // TODO: Take care of public inputs once they land, and virtual targets.
             if let (
                 Target::Wire(Wire {
                     gate: a_gate,