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.
Below is a sketch of the Abstractions.
case class DataType(name: String)
case class DataTypeCase(name: String, attributes: Seq[Attribute]) {
def isRecursive(): Boolean
def isNonRecursive(): Boolean = !isRecursive
}
object DataTypeCase {
def atomic(name: String): DataTypeCase = DataTypeCase(name, Seq.empty)
def unary(name: String): DataTypeCase = DataTypeCase(name, Seq(Attribute.inner))
def binary(name: String): DataTypeCase = DataTypeCase(name, Seq(Attribute.left, Attribute.right))
}
object Attribute {
def inner():Attribute = Attribute("inner", TypeRep.DataType(domain.baseDataType))
def left():Attribute = Attribute("left", TypeRep.DataType(domain.baseDataType))
def right():Attribute = Attribute("right", TypeRep.DataType(domain.baseDataType))
}
trait Tag { }
case class Operation(name: String,
returnType: TypeRep = TypeRep.Unit,
parameters: Seq[Parameter] = Seq.empty, tags:Seq[Tag] = Seq.empty) {
def isBinary(): Boolean
def isProducer(): Boolean
}
object Operation {
val asTree: Operation = Operation("astree", TypeRep.Tree)
}
case class Parameter(name: String, tpe: TypeRep)
object Parameter {
def that:Parameter = Parameter("that", TypeRep.DataType(domain.baseDataType))
}
trait TypeRep {
type HostType
def isModelBase(model:GenericModel):Boolean = this == TypeRep.DataType(model.baseDataType)
}
object TypeRep {
type OfHostType[T] = TypeRep { type HostType = T }
case object Unit extends TypeRep
case object String extends TypeRep
case object Int extends TypeRep
case object Double extends TypeRep
case object Boolean extends TypeRep
case object Tree extends TypeRep
case object Sequence[T] extends TypeRep
case object Array[T] extends TypeRep
case object Arrow[A,B] extends TypeRep
case class DataType(tpe:DataType) extends TypeRep
}
Each evolution stage is modeled with a GenericModel, which captures the newly defined data types and operations together with the former model(s) that it extends.
Below is a sketch of the GenericModel.
class GenericModel(val name:String,
val typeCases:Seq[DataTypeCase],
val ops:Seq[Operation],
val former:Seq[GenericModel],
val baseDataType: DataType,
val optimizations: Set[(DataTypeCase,Operation)] = Set.empty) {
def isDomainBase:Boolean
def isBottom:Boolean
def toSeq: Seq[GenericModel]
def inChronologicalOrder: Seq[GenericModel]
override def equals(that: Any): Boolean
def before(other: GenericModel): Boolean
def beforeorEqual(other: GenericModel): Boolean
def earlier(other: GenericModel): GenericModel
def later(other: GenericModel): GenericModel
def notComparableTo(other:GenericModel): Boolean
def hasBinaryMethod: Boolean
def hasProducerOperation: Boolean
def operationsPresentEarlier(): Set[Operation]
def operationsPresentEarlier(tpeCase: DataTypeCase) : Set[Operation]
def flatten: Model
def linearize: Model
def findTypeCase(tpe:DataTypeCase): Option[GenericModel]
def findOperation(op:Operation): Option[GenericModel]
def supports(tpe:DataTypeCase): Boolean
def supports(op:Operation): Boolean
def pastDataTypes: Seq[DataTypeCase]
def pastOperations: Seq[Operation]
def isEmpty: Boolean
def lastModelWithOperation: Seq[GenericModel]
def lastModelWithDataTypes: Seq[GenericModel]
def base: GenericModel
def evolve(name:String, types: Seq[DataTypeCase], ops: Seq[Operation], optimizations:Set[(DataTypeCase,Operation)] = Set.empty): GenericModel
def extend(str:String, past:Seq[GenericModel]) : GenericModel
def merge(name:String, typeCases:Seq[DataTypeCase], ops:Seq[Operation], others:Seq[GenericModel]) : GenericModel
def optimize(new_opts: Set[(DataTypeCase,Operation)]) : GenericModel
def haveImplementation(potentialRequest:PotentialRequest): Set[GenericModel]
}
sealed class Model (
name:String,
typeCases:Seq[DataTypeCase],
ops:Seq[Operation],
bdt: DataType,
optimizations: Set[(DataTypeCase,Operation)],
val last:Option[Model] = None) extends GenericModel (name, typeCases, ops, last.toSeq, bdt, optimizations) {
}
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. Below is a sketch of the M0 and M1 evolutions:
trait Evolution {
def getModel: GenericModel
}
object MathDomain extends Evolution {
def getModel:GenericModel = baseModel
def baseModel:GenericModel = GenericModel.base("MathDomain", "Exp")
def tests: Seq[TestCase] = Seq.empty
}
object M0 extends Evolution {
override implicit def getModel:GenericModel = MathDomain.baseModel.evolve("m0", Seq(Lit, Add), Seq(Eval))
lazy val litValue = Attribute ("value", TypeRep.Double)
lazy val Lit = DataTypeCase("Lit", Seq(litValue))
lazy val Add = DataTypeCase.binary("Add")(MathDomain.getModel)
lazy val Eval = Operation("eval", TypeRep.Double)
}
object M1 extends Evolution {
override implicit def getModel:GenericModel = M0.getModel.evolve("m1", Seq(Sub), Seq.empty)
lazy val Sub:DataTypeCase = DataTypeCase.binary("Sub")(MathDomain.getModel)
}
In this application domain, an initial model (M0) is extended (with M1), adding new data types and operations. Full Details on the many evolution stages are found in the domain subproject.
Once you have downloaded the code from GitHub, use the following statement
from within the $HOME directory.
sbt "language-java/runMain org.combinators.ep.language.java.GenerateAllJ"
This will initiate the generation of Java code for all approaches for the following system:
To generate Scala code for the above system, use the command:
sbt "language-newScala/runMain org.combinators.ep.language.scala.codegen.GenerateAllJ"
The generation time will vary, based upon your computer, but it should take about 45 minutes to generate all solutions, in Java, for the EP approaches that are implemented in EPCoGen.
The resulting files can be found in $HOME/target/ep-java-j directory.
Follow instructions in README.md on how to compile the code, execute test cases, and generate statistics for the different EP solutions.
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:
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.
The Interpreter approach appears promising in that each evolution stage contains its
own classes. m0 defines classes for the Lit and Add data type cases, and the Eval operation
causes methods to be defined in each class with the necessary logic. Subsequent stages which extend
operations containing the logic must also create their own Lit and Add data type classes.
Following the Interpreter design pattern creates a code structure where each stage is
placed in its own package, together with an Exp class that represents a data type for that
stage. Each data type case is defined in its own class, like m0.Add or m1.Sub.
However, Interpreter requires the duplicateion of non-trivial logic in subsequent stages for every Producer Operation that exists, so it cannot be a valid solution to the Expression Problem.
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.
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.
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.
The ECOOP 2021 paper Covariant Conversions (CoCo): A Design Pattern for Type-Safe Modular Software Evolution in Object-Oriented Systems by Jan Bessai, George Heineman, and Boris Duedder [5] describes an approach to solving the EP problem using Covariant Conversions.
There are a collection of additional Extension Graphs developed to experiment with different arrangements of evolutions. To generate Java Generated code, execute the following:
sbt "language-java/runMain org.combinators.ep.language.java.GenerateAllD1D2"
and the files will appear in target/ep-java-d1d2
For Scala generated code, execute the following:
sbt "language-newScala/runMain org.combinators.ep.language.scala.codegen.GenerateAllD1D2"
and the files will appear in target/ep-scala-d1d2
Below are a number of systems, and replace the GenerateXXX with the values below to generate
all approaches for these systems.
Follow instructions in README.md on how to compile the code, execute test cases, and generate statistics for the different EP solutions.
GenerateAllD1D2- a merge including a producer method, followed by an evolution that added a new operation.
GenerateAllMain- a comprehensive network, with multiple variations that explore situations with optimized implementations. The next two systems are also part of this family and are created using this same initial execution.
- A merge based off of another merge.
- Overriding implementations (like a hotpatch fix).
GenerateAllMerging- A merge of three branches.
GenerateAllExtended- Explores adding operations and data types after a merge.
EPCoGen is compiled with Scala version 2.12.17.
All examples validated on Linux and Windows, using sbt 1.7.2 , Scala version 2.12.17 and Java 11 (OpenJDK).
Java code is generated using JavaParser version 3.19.0.
All JUnit tests are compiled using JUnit 4.12 and Java compiler is directed to compile only assuming Java 1.8 compatibility.
The images above were generated using GraphViz online based on output generated by our GraphViz code.
All generated Scala code is compiled using Scala version 3.3.3 and version 3.2.19 of the Scalactic testing framework
Python scripts require Python 3. Only the scipy package needs to be installed.
- Wadler, Philip, Email to the Java Genericity Mailing List
- Wang, Yanling and C. d. S. Oliveira, Bruno, The Expression Problem, Trivially!, MODULARITY 2016, pp. 37-41.
- Kim, Bruce, Some Challenging Typing Issues in Object-Oriented Languages: Extended Abstract, TCS 82(8) 2003.
- d. S. Oliveira, Bruno C. and William R. Cook Extensibility for the Masses, ECOOP 2012
- Bessai, Jan and Heineman, George and Düdder, Boris, Covariant Conversions (CoCo): A Design Pattern for Type-Safe Modular Software Evolution in Object-Oriented Systems, ECOOP 2021.
