diff --git a/zokrates_core/src/helpers/mod.rs b/zokrates_core/src/helpers/mod.rs
index b51850d2..366a2116 100644
--- a/zokrates_core/src/helpers/mod.rs
+++ b/zokrates_core/src/helpers/mod.rs
@@ -53,7 +53,7 @@ impl<T: Field> fmt::Display for DirectiveStatement<T> {
     }
 }
 
-#[derive(Clone, PartialEq, Debug, Serialize, Deserialize)]
+#[derive(Clone, PartialEq, Debug, Serialize, Deserialize, Hash, Eq)]
 pub enum Helper {
     Rust(RustHelper),
     #[cfg(feature = "wasm")]
diff --git a/zokrates_core/src/helpers/rust.rs b/zokrates_core/src/helpers/rust.rs
index b7242d17..f1bb3f4f 100644
--- a/zokrates_core/src/helpers/rust.rs
+++ b/zokrates_core/src/helpers/rust.rs
@@ -3,7 +3,7 @@ use std::fmt;
 use zokrates_embed::generate_sha256_round_witness;
 use zokrates_field::field::Field;
 
-#[derive(Clone, PartialEq, Debug, Serialize, Deserialize)]
+#[derive(Clone, PartialEq, Debug, Serialize, Deserialize, Hash, Eq)]
 pub enum RustHelper {
     Identity,
     ConditionEq,
diff --git a/zokrates_core/src/helpers/wasm.rs b/zokrates_core/src/helpers/wasm.rs
index 34d25bd8..99d51fcb 100644
--- a/zokrates_core/src/helpers/wasm.rs
+++ b/zokrates_core/src/helpers/wasm.rs
@@ -7,7 +7,7 @@ use std::rc::Rc;
 use wasmi::{ImportsBuilder, ModuleInstance, ModuleRef, NopExternals};
 use zokrates_field::field::Field;
 
-#[derive(Clone, Debug, Serialize)]
+#[derive(Clone, Debug, Serialize, PartialEq, Hash, Eq)]
 pub struct WasmHelper(
     #[serde(skip)] std::rc::Rc<ModuleRef>,
     #[serde(serialize_with = "serde_bytes::serialize")] Vec<u8>,
diff --git a/zokrates_core/src/ir/expression.rs b/zokrates_core/src/ir/expression.rs
index 35198412..db2156a8 100644
--- a/zokrates_core/src/ir/expression.rs
+++ b/zokrates_core/src/ir/expression.rs
@@ -5,7 +5,7 @@ use std::fmt;
 use std::ops::{Add, Div, Mul, Sub};
 use zokrates_field::field::Field;
 
-#[derive(Debug, Clone, Serialize, Deserialize, PartialEq)]
+#[derive(Debug, Clone, Serialize, Deserialize, PartialEq, Hash, Eq)]
 pub struct QuadComb<T: Field> {
     pub left: LinComb<T>,
     pub right: LinComb<T>,
diff --git a/zokrates_core/src/ir/mod.rs b/zokrates_core/src/ir/mod.rs
index 6d64af4e..ed78e6de 100644
--- a/zokrates_core/src/ir/mod.rs
+++ b/zokrates_core/src/ir/mod.rs
@@ -10,13 +10,13 @@ mod from_flat;
 mod interpreter;
 mod witness;
 
-use self::expression::QuadComb;
+pub use self::expression::QuadComb;
 pub use self::expression::{CanonicalLinComb, LinComb};
 
 pub use self::interpreter::{Error, ExecutionResult};
 pub use self::witness::Witness;
 
-#[derive(Debug, Serialize, Deserialize, Clone, PartialEq)]
+#[derive(Debug, Serialize, Deserialize, Clone, PartialEq, Hash, Eq)]
 pub enum Statement<T: Field> {
     Constraint(QuadComb<T>, LinComb<T>),
     Directive(Directive<T>),
@@ -32,7 +32,7 @@ impl<T: Field> Statement<T> {
     }
 }
 
-#[derive(Clone, PartialEq, Debug, Serialize, Deserialize)]
+#[derive(Clone, PartialEq, Debug, Serialize, Deserialize, Hash, Eq)]
 pub struct Directive<T: Field> {
     pub inputs: Vec<LinComb<T>>,
     pub outputs: Vec<FlatVariable>,
@@ -102,7 +102,7 @@ impl<T: Field> fmt::Display for Function<T> {
     }
 }
 
-#[derive(Serialize, Deserialize, Debug, Clone)]
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq)]
 pub struct Prog<T: Field> {
     pub main: Function<T>,
     pub private: Vec<bool>,
diff --git a/zokrates_core/src/optimizer/duplicate.rs b/zokrates_core/src/optimizer/duplicate.rs
index cfcf857d..cb3a653b 100644
--- a/zokrates_core/src/optimizer/duplicate.rs
+++ b/zokrates_core/src/optimizer/duplicate.rs
@@ -2,15 +2,142 @@
 
 use crate::ir::folder::Folder;
 use crate::ir::*;
+use std::collections::{hash_map::DefaultHasher, HashSet};
 use zokrates_field::field::Field;
 
+type Hash = u64;
+
+fn hash<T: Field>(s: &Statement<T>) -> Hash {
+    use std::hash::Hash;
+    use std::hash::Hasher;
+    let mut hasher = DefaultHasher::new();
+    s.hash(&mut hasher);
+    hasher.finish()
+}
+
 #[derive(Debug)]
-pub struct DuplicateOptimizer {}
+pub struct DuplicateOptimizer {
+    seen: HashSet<Hash>,
+}
 
 impl DuplicateOptimizer {
+    fn new() -> Self {
+        DuplicateOptimizer {
+            seen: HashSet::new(),
+        }
+    }
+
     pub fn optimize<T: Field>(p: Prog<T>) -> Prog<T> {
-        p
+        Self::new().fold_program(p)
     }
 }
 
-impl<T: Field> Folder<T> for DuplicateOptimizer {}
+impl<T: Field> Folder<T> for DuplicateOptimizer {
+    fn fold_statement(&mut self, s: Statement<T>) -> Vec<Statement<T>> {
+        let hashed = hash(&s);
+        let result = match self.seen.get(&hashed) {
+            Some(_) => vec![],
+            None => vec![s],
+        };
+
+        self.seen.insert(hashed);
+        result
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use flat_absy::FlatVariable;
+    use zokrates_field::field::FieldPrime;
+
+    #[test]
+    fn identity() {
+        use num::Zero;
+
+        let p: Prog<FieldPrime> = Prog {
+            private: vec![],
+            main: Function {
+                id: "main".to_string(),
+                statements: vec![
+                    Statement::Constraint(
+                        QuadComb::from_linear_combinations(
+                            LinComb::summand(3, FlatVariable::new(3)),
+                            LinComb::summand(3, FlatVariable::new(3)),
+                        ),
+                        LinComb::one(),
+                    ),
+                    Statement::Constraint(
+                        QuadComb::from_linear_combinations(
+                            LinComb::summand(3, FlatVariable::new(42)),
+                            LinComb::summand(3, FlatVariable::new(3)),
+                        ),
+                        LinComb::zero(),
+                    ),
+                ],
+                returns: vec![],
+                arguments: vec![],
+            },
+        };
+
+        let expected = p.clone();
+
+        assert_eq!(DuplicateOptimizer::optimize(p), expected);
+    }
+
+    #[test]
+    fn remove_duplicates() {
+        use num::Zero;
+
+        let constraint = Statement::Constraint(
+            QuadComb::from_linear_combinations(
+                LinComb::summand(3, FlatVariable::new(3)),
+                LinComb::summand(3, FlatVariable::new(3)),
+            ),
+            LinComb::one(),
+        );
+
+        let p: Prog<FieldPrime> = Prog {
+            private: vec![],
+            main: Function {
+                id: "main".to_string(),
+                statements: vec![
+                    constraint.clone(),
+                    constraint.clone(),
+                    Statement::Constraint(
+                        QuadComb::from_linear_combinations(
+                            LinComb::summand(3, FlatVariable::new(42)),
+                            LinComb::summand(3, FlatVariable::new(3)),
+                        ),
+                        LinComb::zero(),
+                    ),
+                    constraint.clone(),
+                    constraint.clone(),
+                ],
+                returns: vec![],
+                arguments: vec![],
+            },
+        };
+
+        let expected = Prog {
+            private: vec![],
+            main: Function {
+                id: "main".to_string(),
+                statements: vec![
+                    constraint.clone(),
+                    Statement::Constraint(
+                        QuadComb::from_linear_combinations(
+                            LinComb::summand(3, FlatVariable::new(42)),
+                            LinComb::summand(3, FlatVariable::new(3)),
+                        ),
+                        LinComb::zero(),
+                    ),
+                ],
+                returns: vec![],
+                arguments: vec![],
+            },
+        };
+
+        assert_eq!(DuplicateOptimizer::optimize(p), expected);
+    }
+}