diff --git a/src/main/scala/hb/dhbw/AST.scala b/src/main/scala/hb/dhbw/AST.scala
index 594a2a2..ae1e824 100644
--- a/src/main/scala/hb/dhbw/AST.scala
+++ b/src/main/scala/hb/dhbw/AST.scala
@@ -14,6 +14,7 @@ final case class FieldVar(e: Expr, f: String) extends Expr
 final case class MethodCall(e: Expr, name: String, params: List[Expr]) extends Expr
 final case class Constructor(className: String, params: List[Expr]) extends Expr
 final case class Cast(to: Type, expr: Expr) extends Expr
+final case class Lambda(p: String, expr: Expr) extends Expr
 
 object ASTBuilder {
   def fromParseTree(toAst: List[ParserClass]) = new ASTBuilderMonad().fromParseTree(toAst)
@@ -37,6 +38,7 @@ object ASTBuilder {
       case PFieldVar(e, f) => FieldVar(fromParseExpr(e, genericNames), f)
       case PCast(ntype, e) => Cast(nTypeToType(ntype, genericNames), fromParseExpr(e, genericNames))
       case PLocalVar(n) => LocalVar(n)
+      case PLambda(p, e) => Lambda(p, fromParseExpr(e, genericNames))
     }
 
     private def freshTPV() = {
diff --git a/src/main/scala/hb/dhbw/Main.scala b/src/main/scala/hb/dhbw/Main.scala
index 57fded6..9dc2327 100644
--- a/src/main/scala/hb/dhbw/Main.scala
+++ b/src/main/scala/hb/dhbw/Main.scala
@@ -53,6 +53,7 @@ object Main {
       case FieldVar(e, f) => prettyPrintExpr(e)+"."+f
       case MethodCall(e, name, params) => prettyPrintExpr(e)+"."+name+"("+params.map(prettyPrintExpr(_)).mkString(", ")+")"
       case Constructor(className, params) => "new "+className+"(" + params.map(prettyPrintExpr(_)).mkString(", ") +")"
+      case Lambda(a, expr) => "(" + a + ") -> " + prettyPrintExpr(expr)
     }
     def prettyPrintType(l: Type): String = l match {
       case RefType(name, List()) => name
diff --git a/src/main/scala/hb/dhbw/Parser.scala b/src/main/scala/hb/dhbw/Parser.scala
index d11378d..869e5fa 100644
--- a/src/main/scala/hb/dhbw/Parser.scala
+++ b/src/main/scala/hb/dhbw/Parser.scala
@@ -12,6 +12,7 @@ final case class PFieldVar(e: ParserExpr, f: String) extends ParserExpr
 final case class PMethodCall(e: ParserExpr, name: String, params: List[ParserExpr]) extends ParserExpr
 final case class PConstructor(className: String, params: List[ParserExpr]) extends ParserExpr
 final case class PCast(to: NType, expr: ParserExpr) extends ParserExpr
+final case class PLambda(param: String, expr: ParserExpr) extends ParserExpr
 
 final case class NType(name: String, params: List[NType])
 
@@ -35,7 +36,7 @@ object Parser {
     .map(ite => ite._2.map(params => params._1 :: params._2).getOrElse(List.empty))
   def variable[_: P]: P[ParserExpr] = P(ident).map(PLocalVar)
   def cast[_: P]: P[ParserExpr] = P("(" ~ typeParser ~ ")" ~ expr).map(x => PCast(x._1, x._2))
-  def expr[_: P]: P[ParserExpr] = P( (variable | constructor | cast)~ (prefixMethodCall | fieldVar).rep.map(_.toList) )
+  def expr[_: P]: P[ParserExpr] = P( (variable | lambdaExpr | constructor | cast)~ (prefixMethodCall | fieldVar).rep.map(_.toList) )
     .map(ite => ite._2.foldLeft(ite._1) { (e1 : ParserExpr, e2 : ParserExpr) =>
       e2 match{
         case PMethodCall(_, name, e3) => PMethodCall(e1, name, e3)
@@ -43,6 +44,8 @@ object Parser {
       }
     })
 
+  def lambdaExpr[_: P]: P[PLambda] = P( "(" ~ ident ~ ")" ~ "->" ~ expr).map(it => PLambda(it._1, it._2))
+
   def constructor[_: P]: P[ParserExpr] = P( kw("new") ~ methodCall).map(m => PConstructor(m.name,m.params))
 
   def classDefinition[_: P]: P[ParserClass] = P(kw("class") ~ ident ~ genericParamList.? ~ kw("extends") ~ typeParser ~ "{" ~ field.rep(0) ~ method.rep(0) ~ "}")
diff --git a/src/main/scala/hb/dhbw/TYPE.scala b/src/main/scala/hb/dhbw/TYPE.scala
index 981339e..22b2686 100644
--- a/src/main/scala/hb/dhbw/TYPE.scala
+++ b/src/main/scala/hb/dhbw/TYPE.scala
@@ -94,6 +94,14 @@ object TYPE {
         val (rty, cons) = TYPEExpr(expr, localVars, ast)
         (casttype, cons)
       }
+      case Lambda(p, expr) => {
+        val t = freshTPV()
+        val a = freshTPV()
+        val b = freshTPV()
+        val typeRet = TYPEExpr(expr, (t, p) :: localVars, ast)
+        val cons = typeRet._2 ++ List(LessDot(t, a), LessDot(typeRet._1, b))
+        (RefType("Function", List(a, b)), cons)
+      }
     }
 
     private def findMethods(m: String, numParams: Int, ast: List[Class]) =
diff --git a/src/main/scala/hb/dhbw/Unify.scala b/src/main/scala/hb/dhbw/Unify.scala
index 25a2864..4cc5d93 100644
--- a/src/main/scala/hb/dhbw/Unify.scala
+++ b/src/main/scala/hb/dhbw/Unify.scala
@@ -132,6 +132,11 @@ object Unify {
     )
   }
 
+  def eraseFRule(eq: Set[UnifyConstraint]): Set[UnifyConstraint]= eq.filter(_ match {
+    case UnifyLessDot(UnifyRefType("Function", _), UnifyRefType("Object", _)) => false
+    case _ => true
+  })
+
   def reduceRule(eq: Set[UnifyConstraint]) =  eq.flatMap(c => c match {
     case UnifyEqualsDot(UnifyRefType(an, ap), UnifyRefType(bn, bp)) => {
       if(an.equals(bn)){
@@ -318,7 +323,7 @@ object Unify {
     var eqFinish: Set[UnifyConstraint] = eq
     do{
       eqNew = doWhileSome(Unify.equalsRule,eqFinish) //We have to apply equals rule first, to get rid of circles
-      eqFinish = eraseRule(swapRule(reduceRule(matchRule(adoptRule(adaptRule(eqNew, fc), fc), fc))))
+      eqFinish = eraseRule(swapRule(reduceRule(eraseFRule(matchRule(adoptRule(adaptRule(eqNew, fc), fc), fc)))))
     }while(!eqNew.equals(eqFinish))
     eqNew
   }
diff --git a/src/test/scala/IntegrationTest.scala b/src/test/scala/IntegrationTest.scala
index b844f16..9617ef7 100644
--- a/src/test/scala/IntegrationTest.scala
+++ b/src/test/scala/IntegrationTest.scala
@@ -24,6 +24,11 @@ class IntegrationTest extends FunSuite {
     val result = FJTypeinference.typeinference("class List<A extends Object> extends Object{\n  add(a){\n  return this;\n}\n}")
     println(result.map(Main.prettyPrintAST(_)))
   }
+
+  test("lambdaIdentity"){
+    val result = FJTypeinference.typeinference("class Test extends Object{\ntest(){\nreturn (a) -> a;\n}\n}")
+    println(result.map(Main.prettyPrintAST(_)))
+  }
   /*
   test("PaperExample"){
     val result = FJTypeinference.typeinference("class List<A extends Object> extends Object{\n  add( a){\n  return this;\n}\n}\nclass Test extends Object{\nm(a){ return a.add(this);}\n}")