diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..866fb9b
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,511 @@
+extern crate pairing;
+
+use pairing::{Engine, Field};
+use std::ops::{Add, Sub};
+use std::fmt;
+use std::error::Error;
+
+/// This represents a linear combination of some variables, with coefficients
+/// in the scalar field of a pairing-friendly elliptic curve group.
+pub struct LinearCombination<T, E: Engine>(Vec<(T, E::Fr)>);
+
+impl<T, E: Engine> AsRef<[(T, E::Fr)]> for LinearCombination<T, E> {
+    fn as_ref(&self) -> &[(T, E::Fr)] {
+        &self.0
+    }
+}
+
+impl<T, E: Engine> LinearCombination<T, E> {
+    pub fn zero() -> LinearCombination<T, E> {
+        LinearCombination(vec![])
+    }
+}
+
+impl<T, E: Engine> Add<(E::Fr, T)> for LinearCombination<T, E> {
+    type Output = LinearCombination<T, E>;
+
+    fn add(mut self, (coeff, var): (E::Fr, T)) -> LinearCombination<T, E> {
+        self.0.push((var, coeff));
+
+        self
+    }
+}
+
+impl<T, E: Engine> Sub<(E::Fr, T)> for LinearCombination<T, E> {
+    type Output = LinearCombination<T, E>;
+
+    fn sub(self, (mut coeff, var): (E::Fr, T)) -> LinearCombination<T, E> {
+        coeff.negate();
+
+        self + (coeff, var)
+    }
+}
+
+impl<T, E: Engine> Add<T> for LinearCombination<T, E> {
+    type Output = LinearCombination<T, E>;
+
+    fn add(self, other: T) -> LinearCombination<T, E> {
+        self + (E::Fr::one(), other)
+    }
+}
+
+impl<T, E: Engine> Sub<T> for LinearCombination<T, E> {
+    type Output = LinearCombination<T, E>;
+
+    fn sub(self, other: T) -> LinearCombination<T, E> {
+        self - (E::Fr::one(), other)
+    }
+}
+
+#[test]
+fn test_lc() {
+    use pairing::bls12_381::{Bls12, Fr};
+
+    let a = LinearCombination::<usize, Bls12>::zero() + 0usize + 1usize + 2usize - 3usize;
+
+    let mut negone = Fr::one();
+    negone.negate();
+
+    assert_eq!(a.0, vec![(0usize, Fr::one()), (1usize, Fr::one()), (2usize, Fr::one()), (3usize, negone)]);
+}
+
+/// This is an error that could occur during circuit synthesis contexts,
+/// such as CRS generation, proving or verification.
+#[derive(Debug)]
+pub enum SynthesisError {
+    AssignmentMissing
+}
+
+impl Error for SynthesisError {
+    fn description(&self) -> &str {
+        match *self {
+            SynthesisError::AssignmentMissing => "an assignment for a variable could not be computed"
+        }
+    }
+}
+
+impl fmt::Display for SynthesisError {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        write!(f, "{}", self.description())
+    }
+}
+
+pub trait ConstraintSystem<E: Engine>: Sized {
+    type Variable: Sized + Copy + Clone;
+
+    /// Represents the type of the "root" of this constraint system
+    /// so that nested namespaces can minimize indirection.
+    type Root: ConstraintSystem<E, Variable=Self::Variable>;
+
+    /// Return the "one" input variable
+    fn one(&self) -> Self::Variable;
+
+    /// Allocate a private variable in the constraint system. The provided function is used to
+    /// determine the assignment of the variable. The given `annotation` function is invoked
+    /// in testing contexts in order to derive a unique name for this variable in the current
+    /// namespace.
+    fn alloc<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>;
+
+    /// Enforce that `A` * `B` = `C`. The `annotation` function is invoked in testing contexts
+    /// in order to derive a unique name for the constraint in the current namespace.
+    fn enforce<A, AR>(
+        &mut self,
+        annotation: A,
+        a: LinearCombination<Self::Variable, E>,
+        b: LinearCombination<Self::Variable, E>,
+        c: LinearCombination<Self::Variable, E>
+    )
+        where A: FnOnce() -> AR, AR: Into<String>;
+
+    /// Create a new (sub)namespace and enter into it. Not intended
+    /// for downstream use; use `namespace` instead.
+    fn push_namespace<NR, N>(&mut self, name_fn: N)
+        where NR: Into<String>, N: FnOnce() -> NR;
+
+    /// Exit out of the existing namespace. Not intended for
+    /// downstream use; use `namespace` instead.
+    fn pop_namespace(&mut self);
+
+    /// Gets the "root" constraint system, bypassing the namespacing.
+    /// Not intended for downstream use; use `namespace` instead.
+    fn get_root(&mut self) -> &mut Self::Root;
+
+    /// Begin a namespace for this constraint system.
+    fn namespace<'a, NR, N>(
+        &'a mut self,
+        name_fn: N
+    ) -> Namespace<'a, E, Self::Root>
+        where NR: Into<String>, N: FnOnce() -> NR
+    {
+        self.get_root().push_namespace(name_fn);
+
+        Namespace(self.get_root(), PhantomData)
+    }
+}
+
+pub trait PublicConstraintSystem<E: Engine>: ConstraintSystem<E>
+{
+    /// Represents the type of the "root" of this constraint system
+    /// so that nested namespaces can minimize indirection.
+    type PublicRoot: PublicConstraintSystem<E, Variable=Self::Variable>;
+
+    /// Allocate a public variable in the constraint system. The provided function is used to
+    /// determine the assignment of the variable.
+    fn alloc_input<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>;
+
+    /// Gets the "root" constraint system, bypassing the namespacing.
+    /// Not intended for downstream use; use `namespace` instead.
+    fn get_public_root(&mut self) -> &mut Self::PublicRoot;
+
+    /// Begin a namespace for this constraint system.
+    fn namespace_public<'a, NR, N>(
+        &'a mut self,
+        name_fn: N
+    ) -> Namespace<'a, E, Self::PublicRoot>
+        where NR: Into<String>, N: FnOnce() -> NR
+    {
+        self.get_root().push_namespace(name_fn);
+
+        Namespace(self.get_public_root(), PhantomData)
+    }
+}
+
+use std::marker::PhantomData;
+
+/// This is a "namespaced" constraint system which borrows a constraint system (pushing
+/// a namespace context) and, when dropped, pops out of the namespace context.
+pub struct Namespace<'a, E: Engine, CS: ConstraintSystem<E> + 'a>(&'a mut CS, PhantomData<E>);
+
+impl<'cs, E: Engine, CS: PublicConstraintSystem<E>> PublicConstraintSystem<E> for Namespace<'cs, E, CS> {
+    type PublicRoot = CS::PublicRoot;
+
+    fn alloc_input<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+    {
+        self.0.alloc_input(annotation, f)
+    }
+
+    fn get_public_root(&mut self) -> &mut Self::PublicRoot
+    {
+        self.0.get_public_root()
+    }
+}
+
+impl<'cs, E: Engine, CS: ConstraintSystem<E>> ConstraintSystem<E> for Namespace<'cs, E, CS> {
+    type Variable = CS::Variable;
+    type Root = CS::Root;
+
+    fn one(&self) -> Self::Variable {
+        self.0.one()
+    }
+
+    fn alloc<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+    {
+        self.0.alloc(annotation, f)
+    }
+
+    fn enforce<A, AR>(
+        &mut self,
+        annotation: A,
+        a: LinearCombination<Self::Variable, E>,
+        b: LinearCombination<Self::Variable, E>,
+        c: LinearCombination<Self::Variable, E>
+    )
+        where A: FnOnce() -> AR, AR: Into<String>
+    {
+        self.0.enforce(annotation, a, b, c)
+    }
+
+    // Downstream users who use `namespace` will never interact with these
+    // functions and they will never be invoked because the namespace is
+    // never a root constraint system.
+
+    fn push_namespace<NR, N>(&mut self, _: N)
+        where NR: Into<String>, N: FnOnce() -> NR
+    {
+        panic!("only the root's push_namespace should be called");
+    }
+
+    fn pop_namespace(&mut self)
+    {
+        panic!("only the root's pop_namespace should be called");
+    }
+
+    fn get_root(&mut self) -> &mut Self::Root
+    {
+        self.0.get_root()
+    }
+}
+
+impl<'a, E: Engine, CS: ConstraintSystem<E>> Drop for Namespace<'a, E, CS> {
+    fn drop(&mut self) {
+        self.get_root().pop_namespace()
+    }
+}
+
+/// Convenience implementation of PublicConstraintSystem<E> for mutable references to
+/// public constraint systems.
+impl<'cs, E: Engine, CS: PublicConstraintSystem<E>> PublicConstraintSystem<E> for &'cs mut CS {
+    type PublicRoot = CS::PublicRoot;
+
+    fn alloc_input<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+    {
+        (**self).alloc_input(annotation, f)
+    }
+
+    fn get_public_root(&mut self) -> &mut Self::PublicRoot
+    {
+        (**self).get_public_root()
+    }
+}
+
+/// Convenience implementation of ConstraintSystem<E> for mutable references to
+/// constraint systems.
+impl<'cs, E: Engine, CS: ConstraintSystem<E>> ConstraintSystem<E> for &'cs mut CS {
+    type Variable = CS::Variable;
+    type Root = CS::Root;
+
+    fn one(&self) -> Self::Variable {
+        (**self).one()
+    }
+
+    fn alloc<F, A, AR>(
+        &mut self,
+        annotation: A,
+        f: F
+    ) -> Result<Self::Variable, SynthesisError>
+        where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+    {
+        (**self).alloc(annotation, f)
+    }
+
+    fn enforce<A, AR>(
+        &mut self,
+        annotation: A,
+        a: LinearCombination<Self::Variable, E>,
+        b: LinearCombination<Self::Variable, E>,
+        c: LinearCombination<Self::Variable, E>
+    )
+        where A: FnOnce() -> AR, AR: Into<String>
+    {
+        (**self).enforce(annotation, a, b, c)
+    }
+
+    fn push_namespace<NR, N>(&mut self, name_fn: N)
+        where NR: Into<String>, N: FnOnce() -> NR
+    {
+        (**self).push_namespace(name_fn)
+    }
+
+    fn pop_namespace(&mut self)
+    {
+        (**self).pop_namespace()
+    }
+
+    fn get_root(&mut self) -> &mut Self::Root
+    {
+        (**self).get_root()
+    }
+}
+
+#[test]
+fn test_cs() {
+    use pairing::bls12_381::{Bls12, Fr};
+
+    #[derive(PartialEq, Copy, Clone)]
+    enum Var {
+        Input(usize),
+        Aux(usize)
+    }
+
+    struct MySillyConstraintSystem<E: Engine> {
+        inputs: Vec<(E::Fr, String)>,
+        aux: Vec<(E::Fr, String)>,
+        constraints: Vec<(LinearCombination<Var, E>, LinearCombination<Var, E>, LinearCombination<Var, E>, String)>,
+        current_namespace: Vec<String>
+    }
+
+    fn compute_path(ns: &[String], this: String) -> String {
+        let mut name = String::new();
+
+        let mut needs_separation = false;
+        for ns in ns.iter().chain(Some(&this).into_iter())
+        {
+            if needs_separation {
+                name += "/";
+            }
+
+            name += ns;
+            needs_separation = true;
+        }
+
+        name
+    }
+
+    impl<E: Engine> PublicConstraintSystem<E> for MySillyConstraintSystem<E> {
+        type PublicRoot = Self;
+
+        fn alloc_input<F, A, AR>(
+            &mut self,
+            annotation: A,
+            f: F
+        ) -> Result<Self::Variable, SynthesisError>
+            where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+        {
+            let index = self.inputs.len();
+            let path = compute_path(&self.current_namespace, annotation().into());
+            self.inputs.push((f()?, path));
+
+            Ok(Var::Input(index))
+        }
+
+        fn get_public_root(&mut self) -> &mut Self::PublicRoot
+        {
+            self
+        }
+    }
+
+    impl<E: Engine> ConstraintSystem<E> for MySillyConstraintSystem<E> {
+        type Variable = Var;
+        type Root = Self;
+
+        fn one(&self) -> Self::Variable {
+            Var::Input(0)
+        }
+
+        fn alloc<F, A, AR>(
+            &mut self,
+            annotation: A,
+            f: F
+        ) -> Result<Self::Variable, SynthesisError>
+            where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>
+        {
+            let index = self.aux.len();
+            let path = compute_path(&self.current_namespace, annotation().into());
+            self.aux.push((f()?, path));
+
+            Ok(Var::Aux(index))
+        }
+
+        fn enforce<A, AR>(
+            &mut self,
+            annotation: A,
+            a: LinearCombination<Self::Variable, E>,
+            b: LinearCombination<Self::Variable, E>,
+            c: LinearCombination<Self::Variable, E>
+        )
+            where A: FnOnce() -> AR, AR: Into<String>
+        {
+            let path = compute_path(&self.current_namespace, annotation().into());
+
+            self.constraints.push((a, b, c, path));
+        }
+
+        fn push_namespace<NR, N>(&mut self, name_fn: N)
+        where NR: Into<String>, N: FnOnce() -> NR
+        {
+            self.current_namespace.push(name_fn().into());
+        }
+
+        fn pop_namespace(&mut self)
+        {
+            self.current_namespace.pop();
+        }
+
+        fn get_root(&mut self) -> &mut Self::Root
+        {
+            self
+        }
+    }
+
+    fn do_stuff_with_pcs<E: Engine, CS: PublicConstraintSystem<E>>(mut cs: CS, one_more: bool)
+    {
+        cs.alloc_input(|| "something", || Ok(E::Fr::zero())).unwrap();
+
+        if one_more {
+            do_stuff_with_pcs(cs.namespace_public(|| "cool namespace"), false);
+        }
+    }
+
+    let mut cs = MySillyConstraintSystem::<Bls12> {
+        inputs: vec![(Fr::one(), "ONE".into())],
+        aux: vec![],
+        constraints: vec![],
+        current_namespace: vec![]
+    };
+    cs.alloc(|| "something", || Ok(Fr::zero())).unwrap();
+    assert_eq!(cs.inputs, vec![(Fr::one(), "ONE".into())]);
+    assert_eq!(cs.aux, vec![(Fr::zero(), "something".into())]);
+    {
+        let mut cs = cs.namespace(|| "woohoo");
+
+        cs.alloc(|| "whatever", || Ok(Fr::one())).unwrap();
+        cs.alloc(|| "you", || Ok(Fr::zero())).unwrap();
+        cs.alloc(|| "say", || Ok(Fr::one())).unwrap();
+
+        {
+            let mut cs = cs.namespace(|| "hehe");
+
+            let v1 = cs.alloc(|| "hehe, indeed", || Ok(Fr::one())).unwrap();
+            let v2 = cs.alloc_input(|| "works lol", || Ok(Fr::zero())).unwrap();
+
+            let one = cs.one();
+
+            cs.enforce(
+                || "great constraint",
+                LinearCombination::zero() + v1,
+                LinearCombination::zero() + one,
+                LinearCombination::zero() + v2
+            );
+        }
+    }
+    assert_eq!(cs.aux, vec![
+        (Fr::zero(), "something".into()),
+        (Fr::one(), "woohoo/whatever".into()),
+        (Fr::zero(), "woohoo/you".into()),
+        (Fr::one(), "woohoo/say".into()),
+        (Fr::one(), "woohoo/hehe/hehe, indeed".into()),
+    ]);
+    assert_eq!(cs.inputs, vec![
+        (Fr::one(), "ONE".into()),
+        (Fr::zero(), "woohoo/hehe/works lol".into()),
+    ]);
+    assert!(cs.constraints.len() == 1);
+    assert!((cs.constraints[0].0).0 == vec![(Var::Aux(4), Fr::one())]);
+    assert!((cs.constraints[0].1).0 == vec![(Var::Input(0), Fr::one())]);
+    assert!((cs.constraints[0].2).0 == vec![(Var::Input(1), Fr::one())]);
+    assert!(cs.constraints[0].3 == "woohoo/hehe/great constraint");
+
+    do_stuff_with_pcs(cs.namespace(|| "namey"), true);
+
+    assert_eq!(cs.inputs, vec![
+        (Fr::one(), "ONE".into()),
+        (Fr::zero(), "woohoo/hehe/works lol".into()),
+        (Fr::zero(), "namey/something".into()),
+        (Fr::zero(), "namey/cool namespace/something".into()),
+    ]);
+}