3 March 2018
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Few computer science graduates will design and implement a general-purpose programming language during their careers. However, many graduates will design and implement—and all likely will use—special-purpose languages in their work.
These special-purpose languages are often called domain-specific languages (or DSLs). For more discussion of DSL concepts and terminology, see the accompanying notes on Domain-Specific Languages.
In this case study, we design and implement a simple internal DSL. This DSL describes simple “programs” using a set of Scala algebraic data types. We express a program as an abstract syntax tree using the DSLs data types.
The case study first builds a package of functions for creating and manipulating the abstract syntax trees. It then extends the package to translate the abstract syntax trees to a sequence of instructions for a simple “machine”.
Suppose Emerald de Gassy, the owner of the Oxford-based catering business Deli-Gate, hires us to design a domain-specific language (DSL) for describing sandwich platters. The DSL scripts will direct Deli-Gate’s robotic kitchen appliance SueChef (Sandwich and Utility Electronic Chef) to assemble platters of sandwiches.
In discussing the problem with Emerald and the Deli-Gate staff, we discover the following:
A sandwich platter consists of zero or more sandwiches. (Zero? Why not! Although a platter with no sandwiches may not be a useful, or profitable, case, there does not seem to be any harm in allowing this degenerate case. It may simplify some of the coding and representation.)
Each sandwich consists of layers of ingredients.
The categories of ingredients are breads, meats, cheeses, vegetables, and condiments.
Available breads are white, wheat, and rye.
Available meats are turkey, chicken, ham, roast beef, and tofu. (Okay, tofu is not a meat, but it is a good protein source for those who do not wish to eat meat. This is a college town after all. Oh, there is also a special meat served for football games Thanksgiving week called “bulldog”, but it is really just chicken, so we can ignore that choice for our purposes here.)
Available cheeses are American, Swiss, jack, and cheddar.
Available vegetables are tomato, lettuce, onion, and bell pepper.
Available condiments are mayo, mustard, relish, and Tabasco. (Of course, this being the South, the mayo is Blue Plate Mayonnaise and the mustard is a Creole mustard.)
Let’s define this as an internal DSL—in particular, by using a relatively deep embedding.
What is a sandwich? … Basically, it is a stack of ingredients.
Should we require the sandwich to have a bread on the bottom? … Probably. … On the top? Maybe not, to allow “open-faced” sandwiches. … What can the SueChef build? … We don’t know at this point, but let’s assume it can stack up any ingredients without restriction.
For simplicity and flexibility, let’s define a Scala data type Sandwich to model sandwiches. It wraps a possibly empty list of ingredient layers. We assume the head of the list to be the layer at the top of the sandwich.
Note: In this case study, we implement Scala algebraic data type constructors (i.e., product types) as case class or case object entities. We implement union types using a trait with subtypes for the variants.
Data type Sandwich gives the specification for a sandwich. When “executed” by the SueChef, it results in the assembly of a sandwich that satisfies the specification.
As defined, the Sandwich data type does not require there to be a bread in the stack of ingredients. However, we add function newSandwich that starts a sandwich with a bread at the bottom and a function addLayer that adds a new ingredient to the top of the sandwich. We leave the implementation of these functions as exercises.
Ingredients are in one of five categories: breads, meats, cheeses, vegetables, and condiments.
Because both the categories and the specific type of ingredient are important, we choose to represent both in the type structures and define the following types. A value of type Layer represents a single ingredient. Type Layer has five variants (subtypes) Bread, Meat, Cheese, Vegetable, and Condiment. Each of these variants itself has several variants. For example, Bread has variants (subtypes) White, Wheat, and Rye.
sealed trait Layer
sealed trait Bread extends Layer
case object White extends Bread
case object Wheat extends Bread
case object Rye extends Bread
sealed trait Meat extends Layer
case object Turkey extends Meat
case object Chicken extends Meat
case object Ham extends Meat
case object RoastBeef extends Meat
case object Tofu extends Meat
sealed trait Cheese extends Layer
case object American extends Cheese
case object Swiss extends Cheese
case object Jack extends Cheese
case object Cheddar extends Cheese
sealed trait Vegetable extends Layer
case object Tomato extends Vegetable
case object Onion extends Vegetable
case object Lettuce extends Vegetable
case object BellPepper extends Vegetable
sealed trait Condiment extends Layer
case object Mayo extends Condiment
case object Mustard extends Condiment
case object Ketchup extends Condiment
case object Relish extends Condiment
case object Tabasco extends CondimentWe need to be able to compare ingredients for equality and convert them to strings. Because the automatically generated definitions are appropriate, we do not need to do anything further.
We will need to provide an appropriate definition of equality for Sandwich because the default element-by-element equality of lists does not seem to be the appropriate equality comparison for sandwiches.
To complete the model, we define type Platter to wrap a list of sandwiches.
We also define functions newPlatter to create a new Platter and addSandwich to add a sandwich to the Platter. We leave the implementation of these functions as exercises.
Please put these functions in a Scala module SandwichDSL. You may use functions defined earlier in the exercises to implement those later in the exercises.
Define and implement the Scala functions newSandwich, addLayer, newPlatter, and addSandwich described above.
Define and implement the Scala query functions below that take an ingredient (i.e., Layer) and return true if and only if the ingredient is in the specified category.
Define and implement a Scala function noMeat that takes a sandwich and returns true if and only if the sandwich contains no meats.
According to a proposed City of Oxford ordinance, in the future it may be necessary to assemble all sandwiches in Oxford Standard Order (OSO): a slice of bread on the bottom, then zero or more meats layered above that, then zero or more cheeses, then zero or more vegetables, then zero or more condiments, and then a slice of bread on top. The top and bottom slices of bread must be of the same type.
Define and implement a Scala function inOSO that takes a sandwich and determines whether it is in OSO and another function intoOSO that takes a sandwich and a default bread and returns the sandwich with the same ingredients ordered in OSO.
Hint: Remember library functions like dropWhile.
Note: It is impossible to rearrange the layers into OSO if the sandwich does not include exactly two breads of the same type. If the sandwich does not include any breads, then the default bread type (second argument) should be specified for both. If there is at least one bread, then the bread type nearest the bottom can be chosen for both top and bottom.
Assuming that the price for a sandwich is the base price plus the sum of the prices of the individual ingredients, define and implement a Haskell function priceSandwich that takes a price list, a base price, and a sandwich and returns the price of the sandwich.
Use the following price list as a part of your testing:
Define and implement a Scala function eqSandwich that compares two sandwiches for equality.
What does equality mean for sandwiches? Although the definition of equality could differ, you can use “bag equality”. That is, two sandwiches are equal if they have the same number of layers (zero or more) of each ingredient, regardless of the order of the layers.
In this section, we look at compiling the Platter and Sandwich descriptions to issue a sequence of commands for the SueChef’s controller.
The SueChef supports the special instructions that can be issued in sequence to its controller. The algebraic data type SandwichOp below represents the instructions.
sealed trait SandwichOp
case object StartSandwich extends SandwichOp
case object FinishSandwich extends SandwichOp
case class AddBread(bread: Bread) extends SandwichOp
case class AddMeat(meat: Meat) extends SandwichOp
case class AddCheese(cheese: Cheese) extends SandwichOp
case class AddVegetable(vegetable: Vegetable) extends SandwichOp
case class AddCondiment(condiment: Condiment) extends SandwichOp
case object StartPlatter extends SandwichOp
case object MoveToPlatter extends SandwichOp
case object FinishPlatter extends SandwichOpWe also define the type Program to represent the sequence of commands resulting from compilation of a Sandwich or Platter specification.
The flow of a program is given by the following pseudocode:
StartPlatter
for each sandwich needed
StartSandwich
for each ingredient needed
Add ingredient on top
FinishSandwich
MoveToPlatter
FinishPlatterConsider a sandwich defined as follows:
The corresponding sequence of SueChef commands would be the following.
List(StartSandwich,AddBread Rye,AddMeat Ham,AddCheeseSwiss,
AddCondiment Mayo,AddBread Rye,FinishSandwich,MoveToPlatter)Define and implement a Scala function compileSandwich to convert a sandwich specification into the sequence of SueChef commands to assemble the sandwich.
Define and implement a Scala function compile to convert a platter specification into the sequence of SueChef commands to assemble the sandwiches on the platter.
The Scala source code for this case study is in file SandwichDSL_base.scala.
I devised the first version of the Sandwich DSL problem for a question on a take-exam in the Lua-based, Fall 2013 offering of CSci 658 (Software Language Engineering). I subsequently developed a full Haskell-based case study for the Fall 2014 offering of CSci 450 (Organization of Programming Languages). I then converted the case study to use Scala for the Spring 2016 offering of CSci 555 (Functional Programming).
In Spring and Fall 2017, I converted case study document from HTML to Pandoc Markdown and updated it for use in the Haskell-based, Fall 2017 offering of CSci 450. In Spring 2018, I updated the Haskell case study to be more compatible with the CSci 658 course materials.
In Spring 2018, I recreated this separate Scala-based version of the case study by combining aspects of Spring 2018 Haskell-based version with the Scala-based version from Spring 2016.
I maintain these notes as text in Pandoc’s dialect of Markdown using embedded LaTeX markup for the mathematical formulas and then translate the notes to HTML, PDF, and other forms as needed. The HTML version of this document may require use of a browser that supports the display of MathML.
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