simplify GroupType trait parameters

2024-11-25 13:53:29 +03:00 · 2020-06-01 17:52:33 -07:00 · 2020-06-01 17:52:33 -07:00 · 8852c17857
commit 8852c17857
parent 5db9b043dc
23 changed files with 180 additions and 336 deletions
--- a/Cargo.lock
+++ b/Cargo.lock
@ -99,13 +99,14 @@ checksum = "cf1de2fe8c75bc145a2f577add951f8134889b4795d47466a54a5c846d691693"

 [[package]]
 name = "blake2"
-version = "0.7.1"
+version = "0.8.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "73b77e29dbd0115e43938be2d5128ecf81c0353e00acaa65339a1242586951d9"
+checksum = "94cb07b0da6a73955f8fb85d24c466778e70cda767a568229b104f0264089330"
 dependencies = [
- "byte-tools 0.2.0",
+ "byte-tools",
 "crypto-mac",
- "digest 0.7.6",
+ "digest",
+ "opaque-debug",
 ]

 [[package]]
@ -115,9 +116,9 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c0940dc441f31689269e10ac70eb1002a3a1d3ad1390e030043662eb7fe4688b"
 dependencies = [
 "block-padding",
- "byte-tools 0.3.1",
+ "byte-tools",
 "byteorder",
- "generic-array 0.12.3",
+ "generic-array",
 ]

 [[package]]
@ -126,15 +127,9 @@ version = "0.1.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "fa79dedbb091f449f1f39e53edf88d5dbe95f895dae6135a8d7b881fb5af73f5"
 dependencies = [
- "byte-tools 0.3.1",
+ "byte-tools",
 ]

-[[package]]
-name = "byte-tools"
-version = "0.2.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "560c32574a12a89ecd91f5e742165893f86e3ab98d21f8ea548658eb9eef5f40"
-
 [[package]]
 name = "byte-tools"
 version = "0.3.1"
@ -208,12 +203,6 @@ dependencies = [
 "winapi",
 ]

-[[package]]
-name = "constant_time_eq"
-version = "0.1.5"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "245097e9a4535ee1e3e3931fcfcd55a796a44c643e8596ff6566d68f09b87bbc"
-
 [[package]]
 name = "crossbeam-deque"
 version = "0.7.3"
@ -263,32 +252,23 @@ dependencies = [

 [[package]]
 name = "crypto-mac"
-version = "0.5.2"
+version = "0.7.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0999b4ff4d3446d4ddb19a63e9e00c1876e75cd7000d20e57a693b4b3f08d958"
+checksum = "4434400df11d95d556bac068ddfedd482915eb18fe8bea89bc80b6e4b1c179e5"
 dependencies = [
- "constant_time_eq",
- "generic-array 0.9.0",
+ "generic-array",
+ "subtle",
 ]

 [[package]]
 name = "derivative"
-version = "1.0.4"
+version = "2.1.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3c6d883546668a3e2011b6a716a7330b82eabb0151b138217f632c8243e17135"
+checksum = "cb582b60359da160a9477ee80f15c8d784c477e69c217ef2cdd4169c24ea380f"
 dependencies = [
- "proc-macro2 0.4.30",
- "quote 0.6.13",
- "syn 0.15.44",
-]
-
-[[package]]
-name = "digest"
-version = "0.7.6"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "03b072242a8cbaf9c145665af9d250c59af3b958f83ed6824e13533cf76d5b90"
-dependencies = [
- "generic-array 0.9.0",
+ "proc-macro2 1.0.9",
+ "quote 1.0.3",
+ "syn 1.0.16",
 ]

 [[package]]
@ -297,7 +277,7 @@ version = "0.8.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "f3d0c8c8752312f9713efd397ff63acb9f85585afbf179282e720e7704954dd5"
 dependencies = [
- "generic-array 0.12.3",
+ "generic-array",
 ]

 [[package]]
@ -363,15 +343,6 @@ version = "0.1.29"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "1b980f2816d6ee8673b6517b52cb0e808a180efc92e5c19d02cdda79066703ef"

-[[package]]
-name = "generic-array"
-version = "0.9.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ef25c5683767570c2bbd7deba372926a55eaae9982d7726ee2a1050239d45b9d"
-dependencies = [
- "typenum",
-]
-
 [[package]]
 name = "generic-array"
 version = "0.12.3"
@ -522,6 +493,7 @@ dependencies = [
 "pest-ast",
 "pest_derive",
 "rand",
+ "rand_xorshift",
 "sha2",
 "snarkos-algorithms",
 "snarkos-curves",
@ -922,7 +894,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "f7d94d0bede923b3cea61f3f1ff57ff8cdfd77b400fb8f9998949e0cf04163df"
 dependencies = [
 "block-buffer",
- "digest 0.8.1",
+ "digest",
 "fake-simd",
 "opaque-debug",
 ]
@ -934,7 +906,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "27044adfd2e1f077f649f59deb9490d3941d674002f7d062870a60ebe9bd47a0"
 dependencies = [
 "block-buffer",
- "digest 0.8.1",
+ "digest",
 "fake-simd",
 "opaque-debug",
 ]
@ -966,8 +938,9 @@ version = "0.8.0"
 dependencies = [
 "blake2",
 "derivative",
- "digest 0.7.6",
+ "digest",
 "rand",
+ "rand_chacha",
 "rayon",
 "sha2",
 "smallvec",
@ -993,10 +966,10 @@ name = "snarkos-errors"
 version = "0.8.0"
 dependencies = [
 "bincode",
- "failure",
 "hex",
 "jsonrpc-core",
 "rocksdb",
+ "thiserror",
 ]

 [[package]]
@ -1004,7 +977,7 @@ name = "snarkos-gadgets"
 version = "0.8.0"
 dependencies = [
 "derivative",
- "digest 0.7.6",
+ "digest",
 "snarkos-algorithms",
 "snarkos-curves",
 "snarkos-errors",
@ -1017,7 +990,6 @@ name = "snarkos-models"
 version = "0.8.0"
 dependencies = [
 "derivative",
- "failure",
 "rand",
 "rand_xorshift",
 "smallvec",
@ -1066,6 +1038,12 @@ dependencies = [
 "syn 1.0.16",
 ]

+[[package]]
+name = "subtle"
+version = "1.0.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2d67a5a62ba6e01cb2192ff309324cb4875d0c451d55fe2319433abe7a05a8ee"
+
 [[package]]
 name = "syn"
 version = "0.15.44"
--- a/compiler/src/compiler.rs
+++ b/compiler/src/compiler.rs
@ -18,18 +18,16 @@ use sha2::{Digest, Sha256};
 use std::{fs, marker::PhantomData, path::PathBuf};

 #[derive(Clone)]
-pub struct Compiler<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> {
+pub struct Compiler<F: Field + PrimeField, G: GroupType<F>> {
    package_name: String,
    main_file_path: PathBuf,
    program: Program<F>,
    program_inputs: Vec<Option<InputValue<F>>>,
-    output: Option<ConstrainedValue<NativeF, F, GType>>,
+    output: Option<ConstrainedValue<F, G>>,
    _engine: PhantomData<F>,
 }

-impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
-    Compiler<NativeF, F, GType>
-{
+impl<F: Field + PrimeField, G: GroupType<F>> Compiler<F, G> {
    pub fn init(package_name: String, main_file_path: PathBuf) -> Result<Self, CompilerError> {
        let mut program = Self {
            package_name,
@ -66,7 +64,7 @@ impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
    pub fn compile_constraints<CS: ConstraintSystem<F>>(
        self,
        cs: &mut CS,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, CompilerError> {
+    ) -> Result<ConstrainedValue<F, G>, CompilerError> {
        generate_constraints(cs, self.program, self.program_inputs)
    }

@ -109,16 +107,13 @@ impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
    }
 }

-impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> ConstraintSynthesizer<F>
-    for Compiler<NativeF, F, GType>
-{
+impl<F: Field + PrimeField, G: GroupType<F>> ConstraintSynthesizer<F> for Compiler<F, G> {
    fn generate_constraints<CS: ConstraintSystem<F>>(
        self,
        cs: &mut CS,
    ) -> Result<(), SynthesisError> {
        let _result =
-            generate_constraints::<NativeF, _, GType, _>(cs, self.program, self.program_inputs)
-                .unwrap();
+            generate_constraints::<_, G, _>(cs, self.program, self.program_inputs).unwrap();

        // Write results to file or something

--- a/compiler/src/constraints/boolean.rs
+++ b/compiler/src/constraints/boolean.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn bool_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        input_value: Option<InputValue<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, BooleanError> {
+    ) -> Result<ConstrainedValue<F, G>, BooleanError> {
        // Check that the input value is the correct type
        let bool_value = match input_value {
            Some(input) => {
@ -56,13 +50,13 @@ impl<
        Ok(ConstrainedValue::Boolean(number))
    }

-    pub(crate) fn get_boolean_constant(bool: Boolean) -> ConstrainedValue<NativeF, F, GType> {
+    pub(crate) fn get_boolean_constant(bool: Boolean) -> ConstrainedValue<F, G> {
        ConstrainedValue::Boolean(bool)
    }

    pub(crate) fn evaluate_not(
-        value: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, BooleanError> {
+        value: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, BooleanError> {
        match value {
            ConstrainedValue::Boolean(boolean) => Ok(ConstrainedValue::Boolean(boolean.not())),
            value => Err(BooleanError::CannotEvaluate(format!("!{}", value))),
@ -72,9 +66,9 @@ impl<
    pub(crate) fn enforce_or(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, BooleanError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, BooleanError> {
        match (left, right) {
            (ConstrainedValue::Boolean(left_bool), ConstrainedValue::Boolean(right_bool)) => Ok(
                ConstrainedValue::Boolean(Boolean::or(cs, &left_bool, &right_bool)?),
@ -89,9 +83,9 @@ impl<
    pub(crate) fn enforce_and(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, BooleanError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, BooleanError> {
        match (left, right) {
            (ConstrainedValue::Boolean(left_bool), ConstrainedValue::Boolean(right_bool)) => Ok(
                ConstrainedValue::Boolean(Boolean::and(cs, &left_bool, &right_bool)?),
@ -103,7 +97,7 @@ impl<
        }
    }

-    pub(crate) fn boolean_eq(left: Boolean, right: Boolean) -> ConstrainedValue<NativeF, F, GType> {
+    pub(crate) fn boolean_eq(left: Boolean, right: Boolean) -> ConstrainedValue<F, G> {
        ConstrainedValue::Boolean(Boolean::Constant(left.eq(&right)))
    }

--- a/compiler/src/constraints/expression.rs
+++ b/compiler/src/constraints/expression.rs
@ -19,13 +19,7 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    /// Enforce a variable expression by getting the resolved value
    pub(crate) fn evaluate_identifier(
        &mut self,
@ -33,7 +27,7 @@ impl<
        function_scope: String,
        expected_types: &Vec<Type<F>>,
        unresolved_identifier: Identifier<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        // Evaluate the identifier name in the current function scope
        let variable_name = new_scope(function_scope, unresolved_identifier.to_string());
        let identifier_name = new_scope(file_scope, unresolved_identifier.to_string());
@ -59,9 +53,9 @@ impl<
    fn enforce_add_expression(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Integer(num_1), ConstrainedValue::Integer(num_2)) => {
                Ok(Self::enforce_integer_add(cs, num_1, num_2)?)
@ -90,9 +84,9 @@ impl<
    fn enforce_sub_expression(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Integer(num_1), ConstrainedValue::Integer(num_2)) => {
                Ok(Self::enforce_integer_sub(cs, num_1, num_2)?)
@ -121,9 +115,9 @@ impl<
    fn enforce_mul_expression(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Integer(num_1), ConstrainedValue::Integer(num_2)) => {
                Ok(Self::enforce_integer_mul(cs, num_1, num_2)?)
@ -151,9 +145,9 @@ impl<
    fn enforce_div_expression(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Integer(num_1), ConstrainedValue::Integer(num_2)) => {
                Ok(Self::enforce_integer_div(cs, num_1, num_2)?)
@ -180,9 +174,9 @@ impl<
    fn enforce_pow_expression(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Integer(num_1), ConstrainedValue::Integer(num_2)) => {
                Ok(Self::enforce_integer_pow(cs, num_1, num_2)?)
@ -211,9 +205,9 @@ impl<
    /// Evaluate Boolean operations
    fn evaluate_eq_expression(
        &mut self,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            (ConstrainedValue::Boolean(bool_1), ConstrainedValue::Boolean(bool_2)) => {
                Ok(Self::boolean_eq(bool_1, bool_2))
@ -244,9 +238,9 @@ impl<

    fn evaluate_geq_expression(
        &mut self,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            // (ResolvedValue::FieldElement(fe_1), ResolvedValue::FieldElement(fe_2)) => {
            //     Self::field_geq(fe_1, fe_2)
@ -268,9 +262,9 @@ impl<

    fn evaluate_gt_expression(
        &mut self,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            // (ResolvedValue::FieldElement(fe_1), ResolvedValue::FieldElement(fe_2)) => {
            //     Self::field_gt(fe_1, fe_2)
@ -292,9 +286,9 @@ impl<

    fn evaluate_leq_expression(
        &mut self,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            // (ResolvedValue::FieldElement(fe_1), ResolvedValue::FieldElement(fe_2)) => {
            //     Self::field_leq(fe_1, fe_2)
@ -316,9 +310,9 @@ impl<

    fn evaluate_lt_expression(
        &mut self,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match (left, right) {
            // (ResolvedValue::FieldElement(fe_1), ResolvedValue::FieldElement(fe_2)) => {
            //     Self::field_lt(fe_1, fe_2)
@ -348,7 +342,7 @@ impl<
        first: Expression<F>,
        second: Expression<F>,
        third: Expression<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let resolved_first = match self.enforce_expression(
            cs,
            file_scope.clone(),
@ -381,7 +375,7 @@ impl<
                Ok(ConstrainedValue::Integer(result))
            }
            (ConstrainedValue::Group(ge_1), ConstrainedValue::Group(ge_2)) => {
-                let result = GType::conditionally_select(cs, &resolved_first, &ge_1, &ge_2)?;
+                let result = G::conditionally_select(cs, &resolved_first, &ge_1, &ge_2)?;
                Ok(ConstrainedValue::Group(result))
            }
            (_, _) => {
@ -398,7 +392,7 @@ impl<
        function_scope: String,
        expected_types: &Vec<Type<F>>,
        array: Vec<Box<SpreadOrExpression<F>>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        // Check explicit array type dimension if given
        let mut expected_types = expected_types.clone();
        let expected_dimensions = vec![];
@ -483,7 +477,7 @@ impl<
        expected_types: &Vec<Type<F>>,
        array: Box<Expression<F>>,
        index: RangeOrExpression<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let array = match self.enforce_branch(
            cs,
            file_scope.clone(),
@ -523,7 +517,7 @@ impl<
        function_scope: String,
        identifier: Identifier<F>,
        members: Vec<CircuitFieldDefinition<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let mut program_identifier = new_scope(file_scope.clone(), identifier.to_string());

        if identifier.is_self() {
@ -598,7 +592,7 @@ impl<
        expected_types: &Vec<Type<F>>,
        circuit_identifier: Box<Expression<F>>,
        circuit_member: Identifier<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let (circuit_name, members) = match self.enforce_branch(
            cs,
            file_scope.clone(),
@ -659,7 +653,7 @@ impl<
        expected_types: &Vec<Type<F>>,
        circuit_identifier: Box<Expression<F>>,
        circuit_member: Identifier<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        // Get defined circuit
        let circuit = match self.enforce_expression(
            cs,
@ -713,7 +707,7 @@ impl<
        expected_types: &Vec<Type<F>>,
        function: Box<Expression<F>>,
        arguments: Vec<Expression<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let function_value = self.enforce_expression(
            cs,
            file_scope.clone(),
@ -751,7 +745,7 @@ impl<
    pub(crate) fn enforce_number_implicit(
        expected_types: &Vec<Type<F>>,
        value: String,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        if expected_types.len() == 1 {
            return Ok(ConstrainedValue::from_type(value, &expected_types[0])?);
        }
@ -769,7 +763,7 @@ impl<
        function_scope: String,
        expected_types: &Vec<Type<F>>,
        expression: Expression<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        let mut branch =
            self.enforce_expression(cs, file_scope, function_scope, expected_types, expression)?;

@ -787,13 +781,7 @@ impl<
        expected_types: &Vec<Type<F>>,
        left: Expression<F>,
        right: Expression<F>,
-    ) -> Result<
-        (
-            ConstrainedValue<NativeF, F, GType>,
-            ConstrainedValue<NativeF, F, GType>,
-        ),
-        ExpressionError,
-    > {
+    ) -> Result<(ConstrainedValue<F, G>, ConstrainedValue<F, G>), ExpressionError> {
        let resolved_left = self.enforce_branch(
            cs,
            file_scope.clone(),
@ -819,7 +807,7 @@ impl<
        function_scope: String,
        expected_types: &Vec<Type<F>>,
        expression: Expression<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, ExpressionError> {
+    ) -> Result<ConstrainedValue<F, G>, ExpressionError> {
        match expression {
            // Variables
            Expression::Identifier(unresolved_variable) => self.evaluate_identifier(
@ -833,7 +821,7 @@ impl<
            Expression::Integer(integer) => Ok(Self::get_integer_constant(integer)),
            Expression::FieldElement(fe) => Ok(Self::get_field_element_constant(fe)),
            Expression::Group(group_affine) => {
-                Ok(ConstrainedValue::Group(GType::constant(group_affine)?))
+                Ok(ConstrainedValue::Group(G::constant(group_affine)?))
            }
            Expression::Boolean(bool) => Ok(Self::get_boolean_constant(bool)),
            Expression::Implicit(value) => Self::enforce_number_implicit(expected_types, value),
--- a/compiler/src/constraints/field_element.rs
+++ b/compiler/src/constraints/field_element.rs
@ -13,20 +13,14 @@ use snarkos_models::{
    gadgets::r1cs::{ConstraintSystem, LinearCombination, Variable as R1CSVariable},
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn field_element_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        input_value: Option<InputValue<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        // Check that the parameter value is the correct type
        let field_option = match input_value {
            Some(input) => {
@ -58,9 +52,7 @@ impl<
        )))
    }

-    pub(crate) fn get_field_element_constant(
-        fe: FieldElement<F>,
-    ) -> ConstrainedValue<NativeF, F, GType> {
+    pub(crate) fn get_field_element_constant(fe: FieldElement<F>) -> ConstrainedValue<F, G> {
        ConstrainedValue::FieldElement(fe)
    }

@ -133,7 +125,7 @@ impl<
        cs: &mut CS,
        fe_1: FieldElement<F>,
        fe_2: FieldElement<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        Ok(match (fe_1, fe_2) {
            // if both constants, then return a constant result
            (FieldElement::Constant(fe_1_constant), FieldElement::Constant(fe_2_constant)) => {
@ -210,7 +202,7 @@ impl<
        cs: &mut CS,
        fe_1: FieldElement<F>,
        fe_2: FieldElement<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        Ok(match (fe_1, fe_2) {
            // if both constants, then return a constant result
            (FieldElement::Constant(fe_1_constant), FieldElement::Constant(fe_2_constant)) => {
@ -287,7 +279,7 @@ impl<
        cs: &mut CS,
        fe_1: FieldElement<F>,
        fe_2: FieldElement<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        Ok(match (fe_1, fe_2) {
            // if both constants, then return a constant result
            (FieldElement::Constant(fe_1_constant), FieldElement::Constant(fe_2_constant)) => {
@ -364,7 +356,7 @@ impl<
        cs: &mut CS,
        fe_1: FieldElement<F>,
        fe_2: FieldElement<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        Ok(match (fe_1, fe_2) {
            // if both constants, then return a constant result
            (FieldElement::Constant(fe_1_constant), FieldElement::Constant(fe_2_constant)) => {
@ -452,7 +444,7 @@ impl<
        cs: &mut CS,
        fe_1: FieldElement<F>,
        num: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FieldElementError> {
+    ) -> Result<ConstrainedValue<F, G>, FieldElementError> {
        Ok(match fe_1 {
            // if both constants, then return a constant result
            FieldElement::Constant(fe_1_constant) => ConstrainedValue::FieldElement(
--- a/compiler/src/constraints/function.rs
+++ b/compiler/src/constraints/function.rs
@ -14,13 +14,7 @@ use snarkos_models::{
    gadgets::r1cs::ConstraintSystem,
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    fn check_arguments_length(expected: usize, actual: usize) -> Result<(), FunctionError> {
        // Make sure we are given the correct number of arguments
        if expected != actual {
@ -38,7 +32,7 @@ impl<
        function_name: String,
        expected_types: Vec<Type<F>>,
        input: Expression<F>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FunctionError> {
+    ) -> Result<ConstrainedValue<F, G>, FunctionError> {
        // Evaluate the function input value as pass by value from the caller or
        // evaluate as an expression in the current function scope
        match input {
@ -65,7 +59,7 @@ impl<
        caller_scope: String,
        function: Function<F>,
        inputs: Vec<Expression<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FunctionError> {
+    ) -> Result<ConstrainedValue<F, G>, FunctionError> {
        let function_name = new_scope(scope.clone(), function.get_name());

        // Make sure we are given the correct number of inputs
@ -127,7 +121,7 @@ impl<
        array_type: Type<F>,
        array_dimensions: Vec<usize>,
        input_value: Option<InputValue<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FunctionError> {
+    ) -> Result<ConstrainedValue<F, G>, FunctionError> {
        let expected_length = array_dimensions[0];
        let mut array_value = vec![];

@ -180,7 +174,7 @@ impl<
        name: String,
        private: bool,
        input_value: Option<InputValue<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FunctionError> {
+    ) -> Result<ConstrainedValue<F, G>, FunctionError> {
        match _type {
            Type::IntegerType(integer_type) => {
                Ok(self.integer_from_parameter(cs, integer_type, name, private, input_value)?)
@ -203,7 +197,7 @@ impl<
        scope: String,
        function: Function<F>,
        inputs: Vec<Option<InputValue<F>>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, FunctionError> {
+    ) -> Result<ConstrainedValue<F, G>, FunctionError> {
        let function_name = new_scope(scope.clone(), function.get_name());

        // Make sure we are given the correct number of inputs
--- a/compiler/src/constraints/group.rs
+++ b/compiler/src/constraints/group.rs
@ -4,17 +4,12 @@ use snarkos_errors::gadgets::SynthesisError;
 use snarkos_models::curves::{Field, PrimeField};
 use snarkos_models::gadgets::r1cs::ConstraintSystem;

-pub(crate) fn group_from_input<
-    NativeF: Field,
-    F: Field + PrimeField,
-    GType: GroupType<NativeF, F>,
-    CS: ConstraintSystem<F>,
->(
+pub(crate) fn group_from_input<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>>(
    cs: &mut CS,
    name: String,
    private: bool,
    input_value: Option<InputValue<F>>,
-) -> Result<ConstrainedValue<NativeF, F, GType>, GroupError> {
+) -> Result<ConstrainedValue<F, G>, GroupError> {
    // Check that the parameter value is the correct type
    let group_option = match input_value {
        Some(input) => {
@ -29,11 +24,11 @@ pub(crate) fn group_from_input<

    // Check visibility of parameter
    let group_value = if private {
-        GType::alloc(cs.ns(|| name), || {
+        G::alloc(cs.ns(|| name), || {
            group_option.ok_or(SynthesisError::AssignmentMissing)
        })?
    } else {
-        GType::alloc_input(cs.ns(|| name), || {
+        G::alloc_input(cs.ns(|| name), || {
            group_option.ok_or(SynthesisError::AssignmentMissing)
        })?
    };
--- a/compiler/src/constraints/import.rs
+++ b/compiler/src/constraints/import.rs
@ -15,13 +15,7 @@ use snarkos_models::{
 use std::env::current_dir;
 use std::fs;

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub fn enforce_import(
        &mut self,
        cs: &mut CS,
--- a/compiler/src/constraints/integer/integer.rs
+++ b/compiler/src/constraints/integer/integer.rs
@ -73,21 +73,15 @@ impl<F: Field + PrimeField> CondSelectGadget<F> for Integer {
    }
 }

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
-    pub(crate) fn get_integer_constant(integer: Integer) -> ConstrainedValue<NativeF, F, GType> {
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
+    pub(crate) fn get_integer_constant(integer: Integer) -> ConstrainedValue<F, G> {
        ConstrainedValue::Integer(integer)
    }

    pub(crate) fn evaluate_integer_eq(
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Boolean(Boolean::Constant(
            match (left, right) {
                (Integer::U8(left_u8), Integer::U8(right_u8)) => left_u8.eq(&right_u8),
@ -112,7 +106,7 @@ impl<
        name: String,
        private: bool,
        integer_value: Option<InputValue<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Check that the input value is the correct type
        let integer_option = match integer_value {
            Some(input) => {
@ -168,7 +162,7 @@ impl<
        cs: &mut CS,
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Integer(match (left, right) {
            (Integer::U8(left_u8), Integer::U8(right_u8)) => {
                Integer::U8(Self::enforce_u8_add(cs, left_u8, right_u8)?)
@ -194,7 +188,7 @@ impl<
        cs: &mut CS,
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Integer(match (left, right) {
            (Integer::U8(left_u8), Integer::U8(right_u8)) => {
                Integer::U8(Self::enforce_u8_sub(cs, left_u8, right_u8)?)
@ -220,7 +214,7 @@ impl<
        cs: &mut CS,
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Integer(match (left, right) {
            (Integer::U8(left_u8), Integer::U8(right_u8)) => {
                Integer::U8(Self::enforce_u8_mul(cs, left_u8, right_u8)?)
@ -246,7 +240,7 @@ impl<
        cs: &mut CS,
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Integer(match (left, right) {
            (Integer::U8(left_u8), Integer::U8(right_u8)) => {
                Integer::U8(Self::enforce_u8_div(cs, left_u8, right_u8)?)
@ -272,7 +266,7 @@ impl<
        cs: &mut CS,
        left: Integer,
        right: Integer,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        Ok(ConstrainedValue::Integer(match (left, right) {
            (Integer::U8(left_u8), Integer::U8(right_u8)) => {
                Integer::U8(Self::enforce_u8_pow(cs, left_u8, right_u8)?)
--- a/compiler/src/constraints/integer/uint128.rs
+++ b/compiler/src/constraints/integer/uint128.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn u128_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        integer_option: Option<usize>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Type cast to u128 in rust.
        // If this fails should we return our own error?
        let u128_option = integer_option.map(|integer| integer as u128);
--- a/compiler/src/constraints/integer/uint16.rs
+++ b/compiler/src/constraints/integer/uint16.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn u16_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        integer_option: Option<usize>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Type cast to u16 in rust.
        // If this fails should we return our own error?
        let u16_option = integer_option.map(|integer| integer as u16);
--- a/compiler/src/constraints/integer/uint32.rs
+++ b/compiler/src/constraints/integer/uint32.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn u32_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        integer_option: Option<usize>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Type cast to integers.u32 in rust.
        // If this fails should we return our own error?
        let u32_option = integer_option.map(|integer| integer as u32);
--- a/compiler/src/constraints/integer/uint64.rs
+++ b/compiler/src/constraints/integer/uint64.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn u64_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        integer_option: Option<usize>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Type cast to u64 in rust.
        // If this fails should we return our own error?
        let u64_option = integer_option.map(|integer| integer as u64);
--- a/compiler/src/constraints/integer/uint8.rs
+++ b/compiler/src/constraints/integer/uint8.rs
@ -16,20 +16,14 @@ use snarkos_models::{
    },
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub(crate) fn u8_from_input(
        &mut self,
        cs: &mut CS,
        name: String,
        private: bool,
        integer_option: Option<usize>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, IntegerError> {
+    ) -> Result<ConstrainedValue<F, G>, IntegerError> {
        // Type cast to u8 in rust.
        // If this fails should we return our own error?
        let u8_option = integer_option.map(|integer| integer as u8);
--- a/compiler/src/constraints/mod.rs
+++ b/compiler/src/constraints/mod.rs
@ -41,16 +41,11 @@ use snarkos_models::{
    gadgets::r1cs::ConstraintSystem,
 };

-pub fn generate_constraints<
-    NativeF: Field,
-    F: Field + PrimeField,
-    GType: GroupType<NativeF, F>,
-    CS: ConstraintSystem<F>,
->(
+pub fn generate_constraints<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>>(
    cs: &mut CS,
    program: Program<F>,
    parameters: Vec<Option<InputValue<F>>>,
-) -> Result<ConstrainedValue<NativeF, F, GType>, CompilerError> {
+) -> Result<ConstrainedValue<F, G>, CompilerError> {
    let mut resolved_program = ConstrainedProgram::new();
    let program_name = program.get_name();
    let main_function_name = new_scope(program_name.clone(), "main".into());
--- a/compiler/src/constraints/program.rs
+++ b/compiler/src/constraints/program.rs
@ -9,13 +9,8 @@ use snarkos_models::{
 };
 use std::{collections::HashMap, marker::PhantomData};

-pub struct ConstrainedProgram<
-    NativeF: Field,
-    F: Field + PrimeField,
-    GType: GroupType<NativeF, F>,
-    CS: ConstraintSystem<F>,
-> {
-    pub identifiers: HashMap<String, ConstrainedValue<NativeF, F, GType>>,
+pub struct ConstrainedProgram<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> {
+    pub identifiers: HashMap<String, ConstrainedValue<F, G>>,
    pub _cs: PhantomData<CS>,
 }

@ -23,13 +18,7 @@ pub fn new_scope(outer: String, inner: String) -> String {
    format!("{}_{}", outer, inner)
 }

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    pub fn new() -> Self {
        Self {
            identifiers: HashMap::new(),
@ -37,18 +26,15 @@ impl<
        }
    }

-    pub(crate) fn store(&mut self, name: String, value: ConstrainedValue<NativeF, F, GType>) {
+    pub(crate) fn store(&mut self, name: String, value: ConstrainedValue<F, G>) {
        self.identifiers.insert(name, value);
    }

-    pub(crate) fn get(&self, name: &String) -> Option<&ConstrainedValue<NativeF, F, GType>> {
+    pub(crate) fn get(&self, name: &String) -> Option<&ConstrainedValue<F, G>> {
        self.identifiers.get(name)
    }

-    pub(crate) fn get_mut(
-        &mut self,
-        name: &String,
-    ) -> Option<&mut ConstrainedValue<NativeF, F, GType>> {
+    pub(crate) fn get_mut(&mut self, name: &String) -> Option<&mut ConstrainedValue<F, G>> {
        self.identifiers.get_mut(name)
    }
 }
--- a/compiler/src/constraints/statement.rs
+++ b/compiler/src/constraints/statement.rs
@ -16,13 +16,7 @@ use snarkos_models::{
    gadgets::{r1cs::ConstraintSystem, utilities::boolean::Boolean, utilities::uint32::UInt32},
 };

-impl<
-        NativeF: Field,
-        F: Field + PrimeField,
-        GType: GroupType<NativeF, F>,
-        CS: ConstraintSystem<F>,
-    > ConstrainedProgram<NativeF, F, GType, CS>
-{
+impl<F: Field + PrimeField, G: GroupType<F>, CS: ConstraintSystem<F>> ConstrainedProgram<F, G, CS> {
    fn resolve_assignee(&mut self, scope: String, assignee: Assignee<F>) -> String {
        match assignee {
            Assignee::Identifier(name) => new_scope(scope, name.to_string()),
@ -36,7 +30,7 @@ impl<
    fn get_mutable_assignee(
        &mut self,
        name: String,
-    ) -> Result<&mut ConstrainedValue<NativeF, F, GType>, StatementError> {
+    ) -> Result<&mut ConstrainedValue<F, G>, StatementError> {
        // Check that assignee exists and is mutable
        Ok(match self.get_mut(&name) {
            Some(value) => match value {
@ -54,7 +48,7 @@ impl<
        function_scope: String,
        name: String,
        range_or_expression: RangeOrExpression<F>,
-        new_value: ConstrainedValue<NativeF, F, GType>,
+        new_value: ConstrainedValue<F, G>,
    ) -> Result<(), StatementError> {
        // Resolve index so we know if we are assigning to a single value or a range of values
        match range_or_expression {
@ -98,7 +92,7 @@ impl<
        &mut self,
        circuit_name: String,
        object_name: Identifier<F>,
-        new_value: ConstrainedValue<NativeF, F, GType>,
+        new_value: ConstrainedValue<F, G>,
    ) -> Result<(), StatementError> {
        match self.get_mutable_assignee(circuit_name)? {
            ConstrainedValue::CircuitExpression(_variable, members) => {
@ -177,7 +171,7 @@ impl<
        &mut self,
        function_scope: String,
        variable: Variable<F>,
-        mut value: ConstrainedValue<NativeF, F, GType>,
+        mut value: ConstrainedValue<F, G>,
    ) -> Result<(), StatementError> {
        // Store with given mutability
        if variable.mutable {
@ -264,7 +258,7 @@ impl<
        function_scope: String,
        expressions: Vec<Expression<F>>,
        return_types: Vec<Type<F>>,
-    ) -> Result<ConstrainedValue<NativeF, F, GType>, StatementError> {
+    ) -> Result<ConstrainedValue<F, G>, StatementError> {
        // Make sure we return the correct number of values
        if return_types.len() != expressions.len() {
            return Err(StatementError::InvalidNumberOfReturns(
@ -297,7 +291,7 @@ impl<
        function_scope: String,
        statements: Vec<Statement<F>>,
        return_types: Vec<Type<F>>,
-    ) -> Result<Option<ConstrainedValue<NativeF, F, GType>>, StatementError> {
+    ) -> Result<Option<ConstrainedValue<F, G>>, StatementError> {
        let mut res = None;
        // Evaluate statements and possibly return early
        for statement in statements.iter() {
@ -323,7 +317,7 @@ impl<
        function_scope: String,
        statement: ConditionalStatement<F>,
        return_types: Vec<Type<F>>,
-    ) -> Result<Option<ConstrainedValue<NativeF, F, GType>>, StatementError> {
+    ) -> Result<Option<ConstrainedValue<F, G>>, StatementError> {
        let expected_types = vec![Type::Boolean];
        let condition = match self.enforce_expression(
            cs,
@ -378,7 +372,7 @@ impl<
        stop: Integer,
        statements: Vec<Statement<F>>,
        return_types: Vec<Type<F>>,
-    ) -> Result<Option<ConstrainedValue<NativeF, F, GType>>, StatementError> {
+    ) -> Result<Option<ConstrainedValue<F, G>>, StatementError> {
        let mut res = None;

        for i in start.to_usize()..stop.to_usize() {
@ -409,8 +403,8 @@ impl<
    fn enforce_assert_eq_statement(
        &mut self,
        cs: &mut CS,
-        left: ConstrainedValue<NativeF, F, GType>,
-        right: ConstrainedValue<NativeF, F, GType>,
+        left: ConstrainedValue<F, G>,
+        right: ConstrainedValue<F, G>,
    ) -> Result<(), StatementError> {
        Ok(match (left, right) {
            (ConstrainedValue::Boolean(bool_1), ConstrainedValue::Boolean(bool_2)) => {
@ -451,7 +445,7 @@ impl<
        function_scope: String,
        statement: Statement<F>,
        return_types: Vec<Type<F>>,
-    ) -> Result<Option<ConstrainedValue<NativeF, F, GType>>, StatementError> {
+    ) -> Result<Option<ConstrainedValue<F, G>>, StatementError> {
        let mut res = None;
        match statement {
            Statement::Return(expressions) => {
--- a/compiler/src/constraints/value.rs
+++ b/compiler/src/constraints/value.rs
@ -14,45 +14,37 @@ use snarkos_models::{
    },
 };
 use std::fmt;
-use std::marker::PhantomData;

 #[derive(Clone, PartialEq, Eq)]
-pub struct ConstrainedCircuitMember<
-    NativeF: Field,
-    F: Field + PrimeField,
-    GType: GroupType<NativeF, F>,
->(pub Identifier<F>, pub ConstrainedValue<NativeF, F, GType>);
+pub struct ConstrainedCircuitMember<F: Field + PrimeField, G: GroupType<F>>(
+    pub Identifier<F>,
+    pub ConstrainedValue<F, G>,
+);

 #[derive(Clone, PartialEq, Eq)]
-pub enum ConstrainedValue<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> {
+pub enum ConstrainedValue<F: Field + PrimeField, G: GroupType<F>> {
    Integer(Integer),
    FieldElement(FieldElement<F>),
-    Group(GType),
+    Group(G),
    Boolean(Boolean),

-    Array(Vec<ConstrainedValue<NativeF, F, GType>>),
+    Array(Vec<ConstrainedValue<F, G>>),

    CircuitDefinition(Circuit<F>),
-    CircuitExpression(
-        Identifier<F>,
-        Vec<ConstrainedCircuitMember<NativeF, F, GType>>,
-    ),
+    CircuitExpression(Identifier<F>, Vec<ConstrainedCircuitMember<F, G>>),

    Function(Option<Identifier<F>>, Function<F>), // (optional circuit identifier, function definition)
-    Return(Vec<ConstrainedValue<NativeF, F, GType>>),
+    Return(Vec<ConstrainedValue<F, G>>),

-    Mutable(Box<ConstrainedValue<NativeF, F, GType>>),
-    Static(Box<ConstrainedValue<NativeF, F, GType>>),
+    Mutable(Box<ConstrainedValue<F, G>>),
+    Static(Box<ConstrainedValue<F, G>>),
    Unresolved(String),
-    Void(PhantomData<NativeF>),
 }

-impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
-    ConstrainedValue<NativeF, F, GType>
-{
+impl<F: Field + PrimeField, G: GroupType<F>> ConstrainedValue<F, G> {
    pub(crate) fn from_other(
        value: String,
-        other: &ConstrainedValue<NativeF, F, GType>,
+        other: &ConstrainedValue<F, G>,
    ) -> Result<Self, ValueError> {
        let other_type = other.to_type();

@ -71,7 +63,7 @@ impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
            Type::FieldElement => Ok(ConstrainedValue::FieldElement(FieldElement::Constant(
                F::from_str(&value).unwrap_or_default(),
            ))),
-            Type::Group => Ok(ConstrainedValue::Group(GType::constant(value)?)),
+            Type::Group => Ok(ConstrainedValue::Group(G::constant(value)?)),
            Type::Boolean => Ok(ConstrainedValue::Boolean(Boolean::Constant(
                value.parse::<bool>()?,
            ))),
@ -107,9 +99,7 @@ impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>>
    }
 }

-impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> fmt::Display
-    for ConstrainedValue<NativeF, F, GType>
-{
+impl<F: Field + PrimeField, G: GroupType<F>> fmt::Display for ConstrainedValue<F, G> {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        match *self {
            ConstrainedValue::Integer(ref value) => write!(f, "{}", value),
@ -155,14 +145,11 @@ impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> fmt::D
            ConstrainedValue::Mutable(ref value) => write!(f, "mut {}", value),
            ConstrainedValue::Static(ref value) => write!(f, "static {}", value),
            ConstrainedValue::Unresolved(ref value) => write!(f, "unresolved {}", value),
-            ConstrainedValue::Void(_) => unreachable!(),
        }
    }
 }

-impl<NativeF: Field, F: Field + PrimeField, GType: GroupType<NativeF, F>> fmt::Debug
-    for ConstrainedValue<NativeF, F, GType>
-{
+impl<F: Field + PrimeField, G: GroupType<F>> fmt::Debug for ConstrainedValue<F, G> {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "{}", self)
    }
--- a/compiler/src/group/edwards_bls12.rs
+++ b/compiler/src/group/edwards_bls12.rs
@ -5,7 +5,7 @@ use snarkos_curves::edwards_bls12::{EdwardsAffine, EdwardsParameters, Fq};
 use snarkos_curves::templates::twisted_edwards_extended::GroupAffine;
 use snarkos_errors::gadgets::SynthesisError;
 use snarkos_gadgets::curves::edwards_bls12::EdwardsBlsGadget;
-use snarkos_models::curves::{AffineCurve, ModelParameters};
+use snarkos_models::curves::AffineCurve;
 use snarkos_models::gadgets::curves::{FpGadget, GroupGadget};
 use snarkos_models::gadgets::r1cs::ConstraintSystem;
 use snarkos_models::gadgets::utilities::alloc::AllocGadget;
@ -22,7 +22,7 @@ pub enum EdwardsGroupType {
    Allocated(EdwardsBlsGadget),
 }

-impl GroupType<<EdwardsParameters as ModelParameters>::BaseField, Fq> for EdwardsGroupType {
+impl GroupType<Fq> for EdwardsGroupType {
    fn constant(string: String) -> Result<Self, GroupError> {
        let value = Self::edwards_affine_from_str(string)?;

--- a/compiler/src/group/mod.rs
+++ b/compiler/src/group/mod.rs
@ -5,11 +5,10 @@ use snarkos_models::gadgets::utilities::alloc::AllocGadget;
 use snarkos_models::gadgets::utilities::eq::{ConditionalEqGadget, EqGadget};
 use snarkos_models::gadgets::utilities::select::CondSelectGadget;
 use std::fmt::Debug;
-// use snarkos_models::gadgets::utilities::select::CondSelectGadget;

 pub mod edwards_bls12;

-pub trait GroupType<NativeF: Field, F: Field>:
+pub trait GroupType<F: Field>:
    Sized
    + Clone
    + Debug
--- a/compiler/tests/mod.rs
+++ b/compiler/tests/mod.rs
@ -12,15 +12,12 @@ pub mod statement;
 use leo_compiler::{compiler::Compiler, errors::CompilerError, ConstrainedValue};

 use leo_compiler::group::edwards_bls12::EdwardsGroupType;
-use snarkos_curves::edwards_bls12::{EdwardsParameters, Fq};
-use snarkos_models::curves::ModelParameters;
+use snarkos_curves::edwards_bls12::Fq;
 use snarkos_models::gadgets::r1cs::TestConstraintSystem;
 use std::env::current_dir;

-pub type EdwardsTestCompiler =
-    Compiler<<EdwardsParameters as ModelParameters>::BaseField, Fq, EdwardsGroupType>;
-pub type EdwardsConstrainedValue =
-    ConstrainedValue<<EdwardsParameters as ModelParameters>::BaseField, Fq, EdwardsGroupType>;
+pub type EdwardsTestCompiler = Compiler<Fq, EdwardsGroupType>;
+pub type EdwardsConstrainedValue = ConstrainedValue<Fq, EdwardsGroupType>;

 pub(crate) fn get_output(program: EdwardsTestCompiler) -> EdwardsConstrainedValue {
    let mut cs = TestConstraintSystem::<Fq>::new();
--- a/leo/commands/build.rs
+++ b/leo/commands/build.rs
@ -9,8 +9,7 @@ use snarkos_curves::bls12_377::Bls12_377;

 use clap::ArgMatches;
 use leo_compiler::group::edwards_bls12::EdwardsGroupType;
-use snarkos_curves::edwards_bls12::{EdwardsParameters, Fq};
-use snarkos_models::curves::ModelParameters;
+use snarkos_curves::edwards_bls12::Fq;
 use std::convert::TryFrom;
 use std::env::current_dir;

@ -19,10 +18,7 @@ pub struct BuildCommand;

 impl CLI for BuildCommand {
    type Options = ();
-    type Output = (
-        Compiler<<EdwardsParameters as ModelParameters>::BaseField, Fq, EdwardsGroupType>,
-        bool,
-    );
+    type Output = (Compiler<Fq, EdwardsGroupType>, bool);

    const NAME: NameType = "build";
    const ABOUT: AboutType = "Compile the current package as a program";
@ -66,11 +62,8 @@ impl CLI for BuildCommand {
        main_file_path.push(MAIN_FILE_NAME);

        // Compute the current program checksum
-        let program = Compiler::<
-            <EdwardsParameters as ModelParameters>::BaseField,
-            Fq,
-            EdwardsGroupType,
-        >::init(package_name.clone(), main_file_path.clone())?;
+        let program =
+            Compiler::<Fq, EdwardsGroupType>::init(package_name.clone(), main_file_path.clone())?;
        let program_checksum = program.checksum()?;

        // Generate the program on the constraint system and verify correctness
--- a/leo/commands/setup.rs
+++ b/leo/commands/setup.rs
@ -13,8 +13,7 @@ use snarkos_utilities::bytes::ToBytes;
 use clap::ArgMatches;
 use leo_compiler::group::edwards_bls12::EdwardsGroupType;
 use rand::thread_rng;
-use snarkos_curves::edwards_bls12::{EdwardsParameters, Fq};
-use snarkos_models::curves::ModelParameters;
+use snarkos_curves::edwards_bls12::Fq;
 use std::convert::TryFrom;
 use std::env::current_dir;
 use std::time::Instant;
@ -25,7 +24,7 @@ pub struct SetupCommand;
 impl CLI for SetupCommand {
    type Options = ();
    type Output = (
-        Compiler<<EdwardsParameters as ModelParameters>::BaseField, Fq, EdwardsGroupType>,
+        Compiler<Fq, EdwardsGroupType>,
        Parameters<Bls12_377>,
        PreparedVerifyingKey<Bls12_377>,
    );