Add Selector for gate API polynomials

`Selector` will introduce a fail-safe type that can be used to build
custom constraints.

It will replace any composer argument that takes the circuit
description/selector polynomials.

README.md

@@ -38,36 +38,37 @@ impl Circuit for TestCircuit {
     ) -> Result<(), Error> {
         let a = composer.append_witness(self.a);
         let b = composer.append_witness(self.b);
+
         // Make first constraint a + b = c
+        let selector = Selector::new()
+            .left(1)
+            .right(1)
+            .public(-self.c);
+
         composer.append_gate(
             a,
             b,
             composer.constant_zero(),
             composer.constant_zero(),
-            BlsScalar::zero(),
-            BlsScalar::one(),
-            BlsScalar::one(),
-            BlsScalar::zero(),
-            BlsScalar::zero(),
-            BlsScalar::zero(),
-            Some(-self.c),
+            selector,
         );
+
         // Check that a and b are in range
         composer.component_range(a, 1 << 6);
         composer.component_range(b, 1 << 5);
+
         // Make second constraint a * b = d
+        let selector = Selector::new()
+            .multiplication(1)
+            .output(1)
+            .public(-self.d);
+
         composer.append_gate(
             a,
             b,
             composer.constant_zero(),
             composer.constant_zero(),
-            BlsScalar::one(),
-            BlsScalar::zero(),
-            BlsScalar::zero(),
-            BlsScalar::one(),
-            BlsScalar::zero(),
-            BlsScalar::zero(),
-            Some(-self.d),
+            selector,
         );
 
         let e = composer.append_witness(self.e);

src/circuit.rs

@@ -155,36 +155,37 @@ impl VerifierData {
 ///         let zero = composer.constant_zero();
 ///         let a = composer.append_witness(self.a);
 ///         let b = composer.append_witness(self.b);
+///
 ///         // Make first constraint a + b = c
+///         let selector = Selector::new()
+///             .left(1)
+///             .right(1)
+///             .public(-self.c);
+///
 ///         composer.append_gate(
 ///             a,
 ///             b,
 ///             zero,
 ///             zero,
-///             BlsScalar::zero(),
-///             BlsScalar::one(),
-///             BlsScalar::one(),
-///             BlsScalar::zero(),
-///             BlsScalar::zero(),
-///             BlsScalar::zero(),
-///             Some(-self.c),
+///             selector,
 ///         );
+///
 ///         // Check that a and b are in range
 ///         composer.component_range(a, 1 << 6);
 ///         composer.component_range(b, 1 << 5);
+///
 ///         // Make second constraint a * b = d
+///         let selector = Selector::new()
+///             .multiplication(1)
+///             .output(1)
+///             .public(-self.d);
+///
 ///         composer.append_gate(
 ///             a,
 ///             b,
 ///             zero,
 ///             zero,
-///             BlsScalar::one(),
-///             BlsScalar::zero(),
-///             BlsScalar::zero(),
-///             BlsScalar::one(),
-///             BlsScalar::zero(),
-///             BlsScalar::zero(),
-///             Some(-self.d),
+///             selector,
 ///         );
 ///
 ///         let e = composer.append_witness(self.e);
@@ -359,7 +360,7 @@ where
 #[cfg(test)]
 mod tests {
     use super::*;
-    use crate::constraint_system::TurboComposer;
+    use crate::constraint_system::{Selector, TurboComposer};
     use crate::proof_system::ProverKey;
 
     type Result<T> = std::result::Result<T, TestError>;
@@ -406,36 +407,30 @@ mod tests {
         ) -> std::result::Result<(), Error> {
             let a = composer.append_witness(self.a);
             let b = composer.append_witness(self.b);
+
             // Make first constraint a + b = c
+            let selector = Selector::new().left(1).right(1).public(-self.c);
             composer.append_gate(
                 a,
                 b,
                 composer.constant_zero(),
                 composer.constant_zero(),
-                BlsScalar::zero(),
-                BlsScalar::one(),
-                BlsScalar::one(),
-                BlsScalar::zero(),
-                BlsScalar::zero(),
-                BlsScalar::zero(),
-                Some(-self.c),
+                selector,
             );
+
             // Check that a and b are in range
             composer.component_range(a, 1 << 6);
             composer.component_range(b, 1 << 5);
+
             // Make second constraint a * b = d
+            let selector =
+                Selector::new().multiplication(1).output(1).public(-self.d);
             composer.append_gate(
                 a,
                 b,
                 composer.constant_zero(),
                 composer.constant_zero(),
-                BlsScalar::one(),
-                BlsScalar::zero(),
-                BlsScalar::zero(),
-                BlsScalar::one(),
-                BlsScalar::zero(),
-                BlsScalar::zero(),
-                Some(-self.d),
+                selector,
             );
 
             let e = composer.append_witness(self.e);

src/constraint_system.rs

@@ -13,6 +13,7 @@ pub(crate) mod composer;
 pub(crate) mod ecc;
 pub(crate) mod logic;
 pub(crate) mod range;
+pub(crate) mod selector;
 pub(crate) mod witness;
 
 pub(crate) use witness::WireData;
@@ -26,4 +27,5 @@ pub(crate) mod helper;
 
 pub use composer::TurboComposer;
 pub use ecc::WitnessPoint;
+pub use selector::{Selector, SelectorRepr};
 pub use witness::Witness;