diff --git a/schala-lang/src/typechecking.rs b/schala-lang/src/typechecking.rs
index ec2f459..0fdfc48 100644
--- a/schala-lang/src/typechecking.rs
+++ b/schala-lang/src/typechecking.rs
@@ -117,6 +117,29 @@ impl PolyType {
 #[derive(Debug, PartialEq, Clone)]
 struct Substitution(HashMap<Rc<String>, MonoType>);
 
+impl Substitution {
+  fn new() -> Substitution {
+    Substitution(HashMap::new())
+  }
+
+  fn bind_variable(name: &Rc<String>, var: &MonoType) -> Substitution {
+    Substitution(hashmap! {
+      name.clone() => var.clone()
+    })
+  }
+
+  fn merge(self, other: Substitution) -> Substitution {
+    let mut map = HashMap::new();
+    for (name, ty) in self.0.into_iter() {
+      map.insert(name, ty);
+    }
+    for (name, ty) in other.0.into_iter() {
+      map.insert(name, ty);
+    }
+    Substitution(map)
+  }
+}
+
 
 #[derive(Debug)]
 struct TypeEnvironment {
@@ -267,6 +290,21 @@ impl Infer {
   fn infer_block(&mut self, block: &Vec<parsing::Statement>) -> Result<MonoType, InferError> {
     Ok(MonoType::Const(TypeConst::Unit))
   }
+
+  fn unify(&mut self, a: MonoType, b: MonoType) -> Result<Substitution, InferError> {
+    use self::InferError::*; use self::MonoType::*;
+    Ok(match (a, b) {
+      (Const(ref a), Const(ref b)) if a == b => Substitution::new(),
+      (Var(ref name), ref var) => Substitution::bind_variable(name, var),
+      (ref var, Var(ref name)) => Substitution::bind_variable(name, var),
+      (Function(box a1, box b1), Function(box a2, box b2)) => {
+        let s1 = self.unify(a1, a2)?;
+        let s2 = self.unify(b1.apply_substitution(&s1), b2.apply_substitution(&s1))?;
+        s1.merge(s2)
+      },
+      (a, b) => return Err(CannotUnify(a, b))
+    })
+  }
 }