Refactor variable traits in r1cs-std.

r1cs-std/src/alloc.rs

@@ -1,141 +1,72 @@
 use crate::Vec;
 use algebra::Field;
 use core::borrow::Borrow;
-use r1cs_core::{ConstraintSystem, SynthesisError};
+use r1cs_core::{Namespace, SynthesisError};
 
-pub trait AllocGadget<V, ConstraintF: Field>
+#[derive(Eq, PartialEq, Ord, PartialOrd, Debug, Copy, Clone)]
+pub enum AllocationMode {
+    Constant = 0,
+    Input = 1,
+    Witness = 2,
+}
+
+impl AllocationMode {
+    // Outputs the maximum according to the relation `Constant < Input < Witness`.
+    pub fn max(&self, other: Self) -> Self {
+        use AllocationMode::*;
+        match (self, other) {
+            (Constant, _) => other,
+            (Input, Constant) => *self,
+            (Input, _) => other,
+            (Witness, _) => *self,
+        }
+    }
+}
+
+pub trait AllocVar<V, F: Field>
 where
     Self: Sized,
     V: ?Sized,
 {
-    fn alloc_constant<T, CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        t: T,
-    ) -> Result<Self, SynthesisError>
-    where
-        T: Borrow<V>;
+    fn new_variable<T: Borrow<V>>(
+        cs: impl Into<Namespace<F>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+        mode: AllocationMode,
+    ) -> Result<Self, SynthesisError>;
 
-    fn alloc<F, T, CS: ConstraintSystem<ConstraintF>>(cs: CS, f: F) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<V>;
-
-    fn alloc_checked<F, T, CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<V>,
-    {
-        Self::alloc(cs, f)
+    fn new_constant(
+        cs: impl Into<Namespace<F>>,
+        t: impl Borrow<V>,
+    ) -> Result<Self, SynthesisError> {
+        Self::new_variable(cs, || Ok(t), AllocationMode::Constant)
     }
 
-    fn alloc_input<F, T, CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<V>;
+    fn new_input<T: Borrow<V>>(
+        cs: impl Into<Namespace<F>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+    ) -> Result<Self, SynthesisError> {
+        Self::new_variable(cs, f, AllocationMode::Input)
+    }
 
-    fn alloc_input_checked<F, T, CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<V>,
-    {
-        Self::alloc_input(cs, f)
+    fn new_witness<T: Borrow<V>>(
+        cs: impl Into<Namespace<F>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+    ) -> Result<Self, SynthesisError> {
+        Self::new_variable(cs, f, AllocationMode::Witness)
     }
 }
 
-impl<I, ConstraintF: Field, A: AllocGadget<I, ConstraintF>> AllocGadget<[I], ConstraintF>
-    for Vec<A>
-{
-    #[inline]
-    fn alloc_constant<T, CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        t: T,
-    ) -> Result<Self, SynthesisError>
-    where
-        T: Borrow<[I]>,
-    {
+impl<I, F: Field, A: AllocVar<I, F>> AllocVar<[I], F> for Vec<A> {
+    fn new_variable<T: Borrow<[I]>>(
+        cs: impl Into<Namespace<F>>,
+        f: impl FnOnce() -> Result<T, SynthesisError>,
+        mode: AllocationMode,
+    ) -> Result<Self, SynthesisError> {
+        let ns = cs.into();
+        let cs = ns.cs();
         let mut vec = Vec::new();
-        for (i, value) in t.borrow().iter().enumerate() {
-            vec.push(A::alloc_constant(cs.ns(|| format!("value_{}", i)), value)?);
-        }
-        Ok(vec)
-    }
-
-    fn alloc<F, T, CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<[I]>,
-    {
-        let mut vec = Vec::new();
-        for (i, value) in f()?.borrow().iter().enumerate() {
-            vec.push(A::alloc(&mut cs.ns(|| format!("value_{}", i)), || {
-                Ok(value)
-            })?);
-        }
-        Ok(vec)
-    }
-
-    fn alloc_input<F, T, CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<[I]>,
-    {
-        let mut vec = Vec::new();
-        for (i, value) in f()?.borrow().iter().enumerate() {
-            vec.push(A::alloc_input(
-                &mut cs.ns(|| format!("value_{}", i)),
-                || Ok(value),
-            )?);
-        }
-        Ok(vec)
-    }
-
-    fn alloc_checked<F, T, CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<[I]>,
-    {
-        let mut vec = Vec::new();
-        for (i, value) in f()?.borrow().iter().enumerate() {
-            vec.push(A::alloc_checked(
-                &mut cs.ns(|| format!("value_{}", i)),
-                || Ok(value),
-            )?);
-        }
-        Ok(vec)
-    }
-
-    fn alloc_input_checked<F, T, CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        f: F,
-    ) -> Result<Self, SynthesisError>
-    where
-        F: FnOnce() -> Result<T, SynthesisError>,
-        T: Borrow<[I]>,
-    {
-        let mut vec = Vec::new();
-        for (i, value) in f()?.borrow().iter().enumerate() {
-            vec.push(A::alloc_input_checked(
-                &mut cs.ns(|| format!("value_{}", i)),
-                || Ok(value),
-            )?);
+        for value in f()?.borrow().iter() {
+            vec.push(A::new_variable(cs.clone(), || Ok(value), mode)?);
         }
         Ok(vec)
     }

r1cs-std/src/eq.rs

@@ -1,142 +1,131 @@
-use crate::prelude::*;
+use crate::{prelude::*, Vec};
 use algebra::Field;
-use r1cs_core::{ConstraintSystem, SynthesisError};
+use r1cs_core::SynthesisError;
 
-/// If `condition == 1`, then enforces that `self` and `other` are equal;
-/// otherwise, it doesn't enforce anything.
-pub trait ConditionalEqGadget<ConstraintF: Field>: Eq {
-    fn conditional_enforce_equal<CS: ConstraintSystem<ConstraintF>>(
-        &self,
-        cs: CS,
-        other: &Self,
-        condition: &Boolean,
-    ) -> Result<(), SynthesisError>;
+pub trait EqGadget<F: Field> {
+    /// Output a `Boolean` value representing whether `self.value() == other.value()`.
+    fn is_eq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>;
 
-    fn cost() -> usize;
+    /// Output a `Boolean` value representing whether `self.value() != other.value()`.
+    fn is_neq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError> {
+        Ok(self.is_eq(other)?.not())
     }
-impl<T: ConditionalEqGadget<ConstraintF>, ConstraintF: Field> ConditionalEqGadget<ConstraintF>
-    for [T]
-{
-    fn conditional_enforce_equal<CS: ConstraintSystem<ConstraintF>>(
+
+    /// If `should_enforce == true`, enforce that `self` and `other` are equal; else,
+    /// enforce a vacuously true statement.
+    fn conditional_enforce_equal(
         &self,
-        mut cs: CS,
         other: &Self,
-        condition: &Boolean,
+        should_enforce: &Boolean<F>,
     ) -> Result<(), SynthesisError> {
-        for (i, (a, b)) in self.iter().zip(other.iter()).enumerate() {
-            let mut cs = cs.ns(|| format!("Iteration {}", i));
-            a.conditional_enforce_equal(&mut cs, b, condition)?;
+        self.is_eq(&other)?
+            .conditional_enforce_equal(&Boolean::constant(true), should_enforce)
+    }
+
+    /// Enforce that `self` and `other` are equal.
+    fn enforce_equal(&self, other: &Self) -> Result<(), SynthesisError> {
+        self.conditional_enforce_equal(other, &Boolean::constant(true))
+    }
+
+    /// If `should_enforce == true`, enforce that `self` and `other` are not equal; else,
+    /// enforce a vacuously true statement.
+    fn conditional_enforce_not_equal(
+        &self,
+        other: &Self,
+        should_enforce: &Boolean<F>,
+    ) -> Result<(), SynthesisError> {
+        self.is_neq(&other)?
+            .conditional_enforce_equal(&Boolean::constant(true), should_enforce)
+    }
+
+    /// Enforce that `self` and `other` are not equal.
+    fn enforce_not_equal(&self, other: &Self) -> Result<(), SynthesisError> {
+        self.conditional_enforce_not_equal(other, &Boolean::constant(true))
+    }
+}
+
+impl<T: EqGadget<F> + R1CSVar<F>, F: Field> EqGadget<F> for [T] {
+    fn is_eq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError> {
+        assert_eq!(self.len(), other.len());
+        assert!(!self.is_empty());
+        let mut results = Vec::with_capacity(self.len());
+        for (a, b) in self.iter().zip(other) {
+            results.push(a.is_eq(b)?);
+        }
+        Boolean::kary_and(&results)
+    }
+
+    fn conditional_enforce_equal(
+        &self,
+        other: &Self,
+        condition: &Boolean<F>,
+    ) -> Result<(), SynthesisError> {
+        assert_eq!(self.len(), other.len());
+        for (a, b) in self.iter().zip(other) {
+            a.conditional_enforce_equal(b, condition)?;
         }
         Ok(())
     }
 
-    fn cost() -> usize {
-        unimplemented!()
-    }
-}
-
-pub trait EqGadget<ConstraintF: Field>: Eq
-where
-    Self: ConditionalEqGadget<ConstraintF>,
-{
-    fn enforce_equal<CS: ConstraintSystem<ConstraintF>>(
+    fn conditional_enforce_not_equal(
         &self,
-        cs: CS,
         other: &Self,
+        should_enforce: &Boolean<F>,
     ) -> Result<(), SynthesisError> {
-        self.conditional_enforce_equal(cs, other, &Boolean::constant(true))
-    }
-
-    fn cost() -> usize {
-        <Self as ConditionalEqGadget<ConstraintF>>::cost()
+        assert_eq!(self.len(), other.len());
+        let some_are_different = self.is_neq(other)?;
+        if let Some(cs) = some_are_different.cs().or(should_enforce.cs()) {
+            cs.enforce_constraint(
+                some_are_different.lc(),
+                should_enforce.lc(),
+                should_enforce.lc(),
+            )
+        } else {
+            // `some_are_different` and `should_enforce` are both constants
+            assert!(some_are_different.value().unwrap());
+            Ok(())
         }
     }
-
-impl<T: EqGadget<ConstraintF>, ConstraintF: Field> EqGadget<ConstraintF> for [T] {}
-
-pub trait NEqGadget<ConstraintF: Field>: Eq {
-    fn enforce_not_equal<CS: ConstraintSystem<ConstraintF>>(
-        &self,
-        cs: CS,
-        other: &Self,
-    ) -> Result<(), SynthesisError>;
-
-    fn cost() -> usize;
 }
 
 pub trait OrEqualsGadget<ConstraintF: Field>
 where
     Self: Sized,
 {
-    fn enforce_equal_or<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        cond: &Boolean,
-        var: &Self,
+    /// If `should_enforce == true`, enforce that `self` equals
+    /// (a) `first` (if `cond` is `true`)
+    /// (b) `second` (if `cond` is `false`)
+    fn conditional_enforce_equal_or(
+        &self,
+        cond: &Boolean<ConstraintF>,
         first: &Self,
         second: &Self,
+        should_enforce: &Boolean<ConstraintF>,
     ) -> Result<(), SynthesisError>;
 
-    fn cost() -> usize;
-}
-
-impl<ConstraintF: Field, T: Sized + ConditionalOrEqualsGadget<ConstraintF>>
-    OrEqualsGadget<ConstraintF> for T
-{
-    fn enforce_equal_or<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        cond: &Boolean,
-        var: &Self,
+    fn enforce_equal_or(
+        &self,
+        cond: &Boolean<ConstraintF>,
         first: &Self,
         second: &Self,
     ) -> Result<(), SynthesisError> {
-        Self::conditional_enforce_equal_or(cs, cond, var, first, second, &Boolean::Constant(true))
-    }
-
-    fn cost() -> usize {
-        <Self as ConditionalOrEqualsGadget<ConstraintF>>::cost()
+        self.conditional_enforce_equal_or(cond, first, second, &Boolean::Constant(true))
     }
 }
 
-pub trait ConditionalOrEqualsGadget<ConstraintF: Field>
+impl<ConstraintF, T> OrEqualsGadget<ConstraintF> for T
 where
-    Self: Sized,
-{
-    fn conditional_enforce_equal_or<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        cond: &Boolean,
-        var: &Self,
-        first: &Self,
-        second: &Self,
-        should_enforce: &Boolean,
-    ) -> Result<(), SynthesisError>;
-
-    fn cost() -> usize;
-}
-
-impl<
     ConstraintF: Field,
-        T: Sized + ConditionalEqGadget<ConstraintF> + CondSelectGadget<ConstraintF>,
-    > ConditionalOrEqualsGadget<ConstraintF> for T
+    T: Sized + EqGadget<ConstraintF> + CondSelectGadget<ConstraintF>,
 {
-    fn conditional_enforce_equal_or<CS: ConstraintSystem<ConstraintF>>(
-        mut cs: CS,
-        cond: &Boolean,
-        var: &Self,
+    fn conditional_enforce_equal_or(
+        &self,
+        cond: &Boolean<ConstraintF>,
         first: &Self,
         second: &Self,
-        should_enforce: &Boolean,
+        should_enforce: &Boolean<ConstraintF>,
     ) -> Result<(), SynthesisError> {
-        let match_opt = Self::conditionally_select(
-            &mut cs.ns(|| "conditional_select_in_or"),
-            cond,
-            first,
-            second,
-        )?;
-        var.conditional_enforce_equal(&mut cs.ns(|| "equals_in_or"), &match_opt, should_enforce)
-    }
-
-    fn cost() -> usize {
-        <Self as ConditionalEqGadget<ConstraintF>>::cost()
-            + <Self as CondSelectGadget<ConstraintF>>::cost()
+        let match_opt = cond.select(first, second)?;
+        self.conditional_enforce_equal(&match_opt, should_enforce)
     }
 }

r1cs-std/src/lib.rs

@@ -20,21 +20,16 @@ extern crate algebra;
 #[macro_use]
 extern crate derivative;
 
-/// used by test_constraint_system
-#[cfg(not(feature = "std"))]
-macro_rules! println {
-    () => {};
-    ($($arg: tt)*) => {};
-}
+#[macro_use]
+pub mod macros;
 
 #[cfg(not(feature = "std"))]
-use ralloc::{collections::BTreeMap, string::String, vec::Vec};
+use ralloc::vec::Vec;
 
 #[cfg(feature = "std")]
-use std::{collections::BTreeMap, string::String, vec::Vec};
+use std::vec::Vec;
 
-pub mod test_constraint_counter;
-pub mod test_constraint_system;
+use algebra::prelude::Field;
 
 pub mod bits;
 pub use self::bits::*;
@@ -48,6 +43,9 @@ mod instantiated;
 #[cfg(feature = "bls12_377")]
 pub use instantiated::bls12_377;
 
+#[cfg(feature = "ed_on_bn254")]
+pub use instantiated::ed_on_bn254;
+
 #[cfg(feature = "ed_on_bls12_377")]
 pub use instantiated::ed_on_bls12_377;
 
@@ -60,8 +58,8 @@ pub use instantiated::ed_on_mnt4_753;
 #[cfg(feature = "ed_on_cp6_782")]
 pub use instantiated::ed_on_cp6_782;
 
-#[cfg(feature = "ed_on_bn254")]
-pub use instantiated::ed_on_bn254;
+#[cfg(feature = "ed_on_bw6_761")]
+pub use instantiated::ed_on_bw6_761;
 
 #[cfg(feature = "ed_on_bls12_381")]
 pub use instantiated::ed_on_bls12_381;
@@ -89,20 +87,70 @@ pub mod prelude {
         alloc::*,
         bits::{boolean::Boolean, uint32::UInt32, uint8::UInt8, ToBitsGadget, ToBytesGadget},
         eq::*,
-        fields::{fp::FpGadget, FieldGadget, ToConstraintFieldGadget},
-        groups::GroupGadget,
+        fields::{FieldOpsBounds, FieldVar},
+        groups::{CurveVar, GroupOpsBounds},
         instantiated::*,
-        pairing::PairingGadget,
+        pairing::PairingVar,
         select::*,
+        R1CSVar,
     };
 }
 
+pub trait R1CSVar<F: Field> {
+    type Value: core::fmt::Debug + Eq + Clone;
+
+    /// Returns the underlying `ConstraintSystemRef`.
+    fn cs(&self) -> Option<r1cs_core::ConstraintSystemRef<F>>;
+
+    /// Returns `true` if `self` is a circuit-generation-time constant.
+    fn is_constant(&self) -> bool {
+        self.cs()
+            .map_or(true, |cs| cs == r1cs_core::ConstraintSystemRef::None)
+    }
+
+    /// Returns the value that is assigned to `self` in the underlying
+    /// `ConstraintSystem`.
+    fn value(&self) -> Result<Self::Value, r1cs_core::SynthesisError>;
+}
+
+impl<F: Field, T: R1CSVar<F>> R1CSVar<F> for [T] {
+    type Value = Vec<T::Value>;
+
+    fn cs(&self) -> Option<r1cs_core::ConstraintSystemRef<F>> {
+        let mut result = None;
+        for var in self {
+            result = var.cs().or(result);
+        }
+        result
+    }
+
+    fn value(&self) -> Result<Self::Value, r1cs_core::SynthesisError> {
+        let mut result = Vec::new();
+        for var in self {
+            result.push(var.value()?);
+        }
+        Ok(result)
+    }
+}
+
+impl<'a, F: Field, T: 'a + R1CSVar<F>> R1CSVar<F> for &'a T {
+    type Value = T::Value;
+
+    fn cs(&self) -> Option<r1cs_core::ConstraintSystemRef<F>> {
+        (*self).cs()
+    }
+
+    fn value(&self) -> Result<Self::Value, r1cs_core::SynthesisError> {
+        (*self).value()
+    }
+}
+
 pub trait Assignment<T> {
     fn get(self) -> Result<T, r1cs_core::SynthesisError>;
 }
 
 impl<T> Assignment<T> for Option<T> {
     fn get(self) -> Result<T, r1cs_core::SynthesisError> {
-        self.ok_or_else(|| r1cs_core::SynthesisError::AssignmentMissing)
+        self.ok_or(r1cs_core::SynthesisError::AssignmentMissing)
     }
 }

r1cs-std/src/macros.rs

@@ -0,0 +1,135 @@
+// Implements AddAssign on Self by deferring to an implementation on &Self
+#[macro_export]
+macro_rules! impl_ops {
+    (
+        $type: ty,
+        $native: ty,
+        $trait: ident,
+        $fn: ident,
+        $assign_trait: ident,
+        $assign_fn: ident,
+        $impl: expr,
+        $constant_impl: expr,
+        $($args:tt)*
+    ) => {
+        impl_bounded_ops!($type, $native, $trait, $fn, $assign_trait, $assign_fn, $impl, $constant_impl, ($($args)+), );
+    };
+}
+
+macro_rules! impl_bounded_ops {
+    (
+        $type: ty,
+        $native: ty,
+        $trait: ident,
+        $fn: ident,
+        $assign_trait: ident,
+        $assign_fn: ident,
+        $impl: expr,
+        $constant_impl: expr,
+        ($($params:tt)+),
+        $($bounds:tt)*
+    ) => {
+        impl<'a, $($params)+> core::ops::$trait<&'a $type> for &'a $type
+        where
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: Self) -> Self::Output {
+                $impl(self, other)
+            }
+        }
+
+        impl<'a, $($params)+> core::ops::$trait<$type> for &'a $type
+        where
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: $type) -> Self::Output {
+                core::ops::$trait::$fn(self, &other)
+            }
+        }
+
+        impl<'a, $($params)+> core::ops::$trait<&'a $type> for $type
+        where
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: &'a $type) -> Self::Output {
+                core::ops::$trait::$fn(&self, other)
+            }
+        }
+
+        impl<$($params)+> core::ops::$trait<$type> for $type
+        where
+
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: $type) -> Self::Output {
+                core::ops::$trait::$fn(&self, &other)
+            }
+        }
+
+        impl<$($params)+> core::ops::$assign_trait<$type> for $type
+        where
+
+            $($bounds)*
+        {
+            fn $assign_fn(&mut self, other: $type) {
+                let result = core::ops::$trait::$fn(&*self, &other);
+                *self = result
+            }
+        }
+
+        impl<'a, $($params)+> core::ops::$assign_trait<&'a $type> for $type
+        where
+
+            $($bounds)*
+        {
+            fn $assign_fn(&mut self, other: &'a $type) {
+                let result = core::ops::$trait::$fn(&*self, other);
+                *self = result
+            }
+        }
+
+        impl<'a, $($params)+> core::ops::$trait<$native> for &'a $type
+        where
+
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: $native) -> Self::Output {
+                $constant_impl(self, other)
+            }
+        }
+
+        impl<$($params)+> core::ops::$trait<$native> for $type
+        where
+
+            $($bounds)*
+        {
+            type Output = $type;
+
+            fn $fn(self, other: $native) -> Self::Output {
+                core::ops::$trait::$fn(&self, other)
+            }
+        }
+
+        impl<$($params)+> core::ops::$assign_trait<$native> for $type
+        where
+
+            $($bounds)*
+        {
+
+            fn $assign_fn(&mut self, other: $native) {
+                let result = core::ops::$trait::$fn(&*self, other);
+                *self = result
+            }
+        }
+    }
+}

r1cs-std/src/select.rs

@@ -1,20 +1,17 @@
 use crate::prelude::*;
 use algebra::Field;
-use r1cs_core::{ConstraintSystem, SynthesisError};
+use r1cs_core::SynthesisError;
 
 /// If condition is `true`, return `true_value`; else, select `false_value`.
 pub trait CondSelectGadget<ConstraintF: Field>
 where
     Self: Sized,
 {
-    fn conditionally_select<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        cond: &Boolean,
+    fn conditionally_select(
+        cond: &Boolean<ConstraintF>,
         true_value: &Self,
         false_value: &Self,
     ) -> Result<Self, SynthesisError>;
-
-    fn cost() -> usize;
 }
 
 /// Uses two bits to perform a lookup into a table
@@ -23,13 +20,10 @@ where
     Self: Sized,
 {
     type TableConstant;
-    fn two_bit_lookup<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        bits: &[Boolean],
+    fn two_bit_lookup(
+        bits: &[Boolean<ConstraintF>],
         constants: &[Self::TableConstant],
     ) -> Result<Self, SynthesisError>;
-
-    fn cost() -> usize;
 }
 
 /// Uses three bits to perform a lookup into a table, where the last bit
@@ -39,12 +33,9 @@ where
     Self: Sized,
 {
     type TableConstant;
-    fn three_bit_cond_neg_lookup<CS: ConstraintSystem<ConstraintF>>(
-        cs: CS,
-        bits: &[Boolean],
-        b0b1: &Boolean,
+    fn three_bit_cond_neg_lookup(
+        bits: &[Boolean<ConstraintF>],
+        b0b1: &Boolean<ConstraintF>,
         constants: &[Self::TableConstant],
     ) -> Result<Self, SynthesisError>;
-
-    fn cost() -> usize;
 }