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The goal of this project is to generate a number of approaches (in multiple languages) that address the Expression Problem.

As coined by Philip Wadler [1], the Expression Problem is a new name for an old problem. The goal is to define a datatype by cases, where one can add new cases to the datatype and new functions over the datatype, without recompiling existing code, and while retaining static type safety.

There are various "solutions" to the Expression Problem. Each solution varies in the amount of code a user must write to implement them, and the language features they require.

In this project, we explore a number of such solutions. Our concern is not with the individual solutions to the Expression Problem (of which there are many), but rather the engineering of these. We provide an alternative, namely, to regenerate all code after modifying the domain.

Let's start with a language for a simple form of arithmetic expressions. We first model the domain using Scala in BaseDomain:

trait BaseDomain {
  abstract class TypeRep { 
    def name: String = getClass.getName
  type BaseTypeRep <: TypeRep
  val baseTypeRep:BaseTypeRep  

  object base {
    val inner:String = "inner"
    val left:String  = "left"
    val right:String = "right"
    val that:String  = "that"

  abstract class Element
  case class Attribute(name:String, tpe:TypeRep) extends Element
  abstract class Operation(val name:String, val returnType:Option[TypeRep], val parameters:Seq[(String, TypeRep)] = Seq.empty) extends Element

  abstract class Atomic(val name: String, val attributes: Seq[Attribute])
  abstract class Unary(override val name:String) extends Atomic(name, Seq(Attribute(base.inner, baseTypeRep)))
  abstract class Binary(override val name:String) extends Atomic(name, Seq(Attribute(base.left, baseTypeRep), Attribute(base.right, baseTypeRep)))

  class ProducerOperation(override val name:String, override val parameters:Seq[(String, TypeRep)]) extends Operation(name,Some(baseTypeRep),parameters)
  class BinaryMethod(override val name:String, override val returnType:Option[TypeRep]) extends Operation(name, returnType, Seq((base.that, baseTypeRep)))

  class AtomicInst(val e:Atomic, val i:Option[Any]) 
  class UnaryInst(override val e:Atomic, val inner:AtomicInst) extends AtomicInst(e, None)
  class BinaryInst(override val e:Atomic, val left:AtomicInst, val right:AtomicInst) extends AtomicInst(e, None)

trait ModelDomain extends BaseDomain {
  case class Model(name:String,          
    types:Seq[Atomic], ops:Seq[Operation],
    last:Model = emptyModel()) {
        ...    // implementation omitted

For more details on ModelDomain check out this Scala file. Once these concepts are identified, the designer chooses a programming language and implements a desired solution.

Application Domain

The desired application domain (in this case mathematical expressions) extends these traits to provide a specific domain within which to work. The entire evolution history is modeled, from an initial state M0 through successive evolutions. The following MathDomain describes the common domain used in the literature when describing the Expression Problem.

trait MathDomain extends BaseDomain with ModelDomain {  
  case object Exp extends TypeRep {
    override def name:String = "Exp"
  type BaseTypeRep = Exp.type
  val baseTypeRep:BaseTypeRep = Exp
object MathDomain extends MathDomain

trait Evolution {                                
  val domain: ModelDomain
  def getModel: domain.Model

trait M0 extends Evolution {                      
  val domain:MathDomain
  import domain._
  val litValue:String = "value"

  case object Double extends TypeRep
  case object Lit extends Atomic("Lit", Seq(Attribute(litValue, Double)))
  case object Add extends Binary("Add")

  case object Eval extends Operation("eval", Some(Double)) 
  class LitInst(d:Double) extends AtomicInst(Lit, Some(d))
  val m0 = Model("m0", Seq(Lit, Add), Seq(Eval))
  override def getModel = m0

trait M1 extends Evolution { self: M0 =>         
  val domain:MathDomain
  case object Sub extends Binary("Sub")
  val m1 = Model("m1", Seq(Sub), Seq.empty, last=m0)  
  override def getModel = m1

trait M2 extends Evolution { self: M0 with M1 =>  
  val domain:MathDomain
  import domain._
  case object String extends TypeRep
  case object PrettyP extends Operation("print",Some(String)) 
  val m2 = Model("m2", Seq.empty, Seq(PrettyP), last=m1)
  override def getModel = m2

trait M3 extends Evolution { self: M0 with M1 with M2 =>
  val domain:MathDomain

  case object Mult extends domain.Binary("Mult")
  case object Neg extends domain.Unary("Neg")
  case object Divd extends domain.Binary("Divd")

  val m3 = domain.Model("m3", Seq(Neg, Mult, Divd), Seq.empty, last = m2)
  override def getModel = m3

trait M4 extends Evolution {
  self: M0 with M1 with M2 with M3 =>
  val domain:MathDomain

  case object Simplify extends domain.ProducerOperation("simplify")
  case class List(generic:domain.TypeRep) extends domain.TypeRep
  case object Collect extends domain.Operation("collect", Some(List(Double)))

  val m4 = domain.Model("m4",Seq.empty, Seq(Simplify, Collect), last = m3)
  override def getModel = m4

In this application domain, an initial model (M0) is extended four times, adding new data types and operations. We have encoded a number of approaches to the Expression Problem that generates solutions in Java. To request the code generation, the following are the completed implementations

OO Solution

A straight object-oriented approach requires operations to be added to each data type class. As new subtypes are created, each can be placed in its own class and there is no trouble with existing code; however, defining new operations means that all existing subtypes need to have new methods added to their class. As such, this is not a solution to the EP problem:

git clone localhost:9000/oo/m4/m4.git

Retrieve ZIP file with generated source files

Visitor Solution

The Visitor Design Pattern is not an acceptable solution to the Expression Problem because defining new data variants (i.e., Neg which negates an expression) requires modifications to all existing Visitor classes. However, using our approach, we can simply resynthesize all classes with every change to the Application Domain.

git clone localhost:9000/scalaVisitor/m4/m4.git

Retrieve ZIP file with generated source files

Covariant Java Solution

The Modularity 2016 paper The Expression Problem, Trivially! by Yanling Wang and Bruno C. d. S. Oliveira [2] describes an approach using covariant type refinement of return types and fields. Unlike existing solutions in Java-like languages, this solution does not use any kind of generics.

git clone localhost:9000/trivially/m4/m4.git

Retrieve ZIP file with generated source files

Interpreter Design Pattern

The TCS 2003 paper Solving Expression problem using Interpreter Pattern by Bruce Kim [3] describes an approach to solving the EP problem using the Interpreter Design Pattern.

git clone localhost:9000/interpreter/m4/m4.git

Retrieve ZIP file with generated source files

Object Algebras

The ECOOP 2012 paper Extensibility for the Masses by Bruno C. d. S. Oliveira & William R. Cook [4] describes an approach to solving the EP problem using Object Algebras.

git clone localhost:9000/algebra/m4/m4.git

Retrieve ZIP file with generated source files

C++ Solution

C++ solutions exist as well. In a blog Expression Problem and its solutions Eli Bendersky outlines an approach for using the visitor design pattern as implemented in C++.

git clone localhost:9000/cpp/m3/m3.git

This solution only generates for the first three evolutions. It compiles as follows:

g++ *.cpp -Icpputest/include -Lcpputest/cpputest_build/lib -lCppUTest -lCppUTestExt

The CPPUnit test project contains the necessary includes and libraries to cleanly compile this code and confirm all test cases.

Retrieve ZIP file with generated source files


  1. Wadler, Philip, Email to to Java Genericity Mailing List
  2. Wang, Yanling and Bruno C. d. S. Oliveira, The Expression Problem, Trivially!, MODULARITY 2016, pp. 37-41.
  3. Kim, Bruce, Some Challenging Typing Issues in Object-Oriented Languages: Extended Abstract, TCS 82(8) 2003.
  4. d. S. Oliveira, Bruno C. and William R. Cook Extensibility for the Masses, ECOOP 2012


Synthesize a number of approaches (in multiple languages) that address the Expression Problem






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