Chapter 11
Project: A Programming Language

The evaluator, which determines the meaning of expressions in a programming language, is just another program.

Hal Abelson and Gerald Sussman, Structure and Interpretation of Computer Programs

When a student asked the master about the nature of the cycle of Data and Control, Yuan-Ma replied ‘Think of a compiler, compiling itself.’

Master Yuan-Ma, The Book of Programming

Building your own programming language is surprisingly easy (as long as you do not aim too high) and very enlightening.

The main thing I want to show in this chapter is that there is no magic involved in building your own language. I’ve often felt that some human inventions were so immensely clever and complicated that I’d never be able to understand them. But with a little reading and tinkering, such things often turn out to be quite mundane.

We will build a programming language called Egg. It will be a tiny, simple language, but one that is powerful enough to express any computation you can think of. It will also allow simple abstraction based on functions.

Parsing

The most immediately visible part of a programming language is its syntax, or notation. A parser is a program that reads a piece of text and produces a data structure that reflects the structure of the program contained in that text. If the text does not form a valid program, the parser should complain and point out the error.

Our language will have a very simple and uniform syntax. Everything in Egg is an expression. An expression can be a variable, a number, a string, or an application. Applications are used for function calls, but also for constructs like if or while.

To keep the parser simple, strings in Egg do not support anything like backslash escapes. A string is simply a sequence of characters that are not double quotes, wrapped in double quotes. A number is a sequence of digits. Variable names can consist of any character that is not whitespace and does not have a special meaning in the syntax.

Applications are written the way they are in JavaScript, by putting parentheses after an expression, and having any number of arguments separated by commas between those parentheses.

do(define(x, 10),
   if(>(x, 5)),
      print("large"),
      print("small"))

The uniformity of the Egg language means that things which are operators in JavaScript (such as >) are normal variables in this language, applied just like other functions. And since the syntax has no concept of a block, we need a do construct (like above) to represent doing multiple things in sequence.

The data structure the parser will use to describe a program will consist of expression objects, each of which has a type property indicating the kind of expression it is and other properties to describe its content.

Expresions of type "value" represent literal strings or numbers. Their value property contains the string or number value that they represent. Expressions of type "word" are used for identifiers (names). Such objects have a name property that holds the identifier’s name, as a string. Finally, "apply" expressions represent applications. They have an operator property that refers to the expression that is being applied, and an args property that refers to an array of argument expressions.

The >(x, 5) part of the program above would be represented like this:

{
  type: "apply",
  operator: {type: "word", name: ">"},
  args: [
    {type: "word", name: "x"},
    {type: "value", value: 5}
  ]
}

Such a data structure is called a syntax tree. If you imagine the objects as dots, and the links between them as lines between those dots, it has a tree-like shape. The fact that expressions contain other expressions, which in turn might contain more expression, is similar to the way branches split and split again.

The structure of a syntax tree

Contrast this to the parser we wrote for the configuration file format in Chapter 9, which had a very simple structure: it split the input into lines, and handled those lines one at a time. There were only a few simple forms that a line was allowed to have.

Here we must find a different approach. Expressions are not separated into lines, and they have a recursive structure. Application expressions contain other expressions.

Fortunately, this problem can be solved elegantly by writing a parser function that is recursive in a way that reflects the recursive nature of the language.

We define a function parseExpression, which takes a string as input, and returns an object containing the data structure for the expression at the start of the string, along with the part of the string left after parsing this expression. When parsing sub-expressions (the argument to an application, for example), this function can be called again, yielding the argument expression as well as the text that remains. This text may in turn contain more arguments, or may be the closing parenthesis that ends the list of arguments.

This is the first part of the parser:

function parseExpression(program) {
  program = skipSpace(program);
  var match, expr;
  if (match = /^"([^"]*)"/.exec(program))
    expr = {type: "value", value: match[1]};
  else if (match = /^\d+\b/.exec(program))
    expr = {type: "value", value: Number(match[0])};
  else if (match = /^[^\s(),"]+/.exec(program))
    expr = {type: "word", name: match[0]};
  else
    throw new SyntaxError("Unexpected syntax: " + program);

  return parseApply(expr, program.slice(match[0].length));
}

function skipSpace(string) {
  var first = string.search(/\S/);
  if (first == -1) return "";
  return string.slice(first);
}

Because Egg allows any amount of whitespace between its elements, we have to repeatedly cut the whitespace off the start of the program string. This is what the skipSpace function helps with.

After skipping any leading space, parseExpression uses three regular expressions to spot the three simple (atomic) elements that Egg supports: strings, numbers, and words. The parser constructs a different kind of data structure depending on which one matches. If none match, the input is not a valid expression, and it throws an error. SyntaxError is a standard error object type, which is raised when an attempt is made to run an invalid JavaScript program.

We can then cut off the part that we matched from the program string and pass that, along with the object for the expression, to parseApply, which checks whether the expression is an application. If so, it parses a parenthesized list of arguments.

function parseApply(expr, program) {
  program = skipSpace(program);
  if (program[0] != "(")
    return {expr: expr, rest: program};

  program = skipSpace(program.slice(1));
  expr = {type: "apply", operator: expr, args: []};
  while (program[0] != ")") {
    var arg = parseExpression(program);
    expr.args.push(arg.expr);
    program = skipSpace(arg.rest);
    if (program[0] == ",")
      program = skipSpace(program.slice(1));
    else if (program[0] != ")")
      throw new SyntaxError("Expected ',' or ')'");
  }
  return parseApply(expr, program.slice(1));
}

If the next character in the program is not an opening parenthesis, this is not an application, and parseApply simply returns the expression it was given.

Otherwise, it skips the opening parenthesis, and creates the syntax tree object for this application expression. It then recusively calls parseExpression to parse each argument until a closing parenthesis is found. The recursion is indirect, through parseApply and parseExpression calling each other.

Because an application expression can itself be applied (such as in multiplier(2)(1)), parseApply must, after it has parsed an application, call itself again to check whether another pair of parentheses follow.

This is all we need to parse Egg. We wrap it in a convenient parse function which verifies that it has reached the end of the input string after parsing the program, and which gives us the program’s data structure.

function parse(program) {
  var result = parseExpression(program);
  if (skipSpace(result.rest).length > 0)
    throw new SyntaxError("Unexpected text after program");
  return result.expr;
}

console.log(parse("+(a, 10)"));
// → {type: "apply",
//    operator: {type: "word", name: "+"},
//    args: [{type: "word", name: "a"},
//           {type: "value", value: 10}]}

It works! It doesn’t give us very helpful information when it fails, and doesn’t store the line and column on which each expression starts, which might be helpful when reporting errors later on, but it’s good enough for our purposes.

The evaluator

What can we do with the syntax tree for a program? Run it, of course! And that is what the evaluator does. You give it a syntax tree and an environment object that associates names with values, and it will evaluate the expression that the tree represents and return the value that this produces.

function evaluate(expr, env) {
  switch(expr.type) {
    case "value":
      return expr.value;

    case "word":
      if (expr.name in env)
        return env[expr.name];
      else
        throw new ReferenceError("Undefined variable: " +
                                 expr.name);
    case "apply":
      if (expr.operator.type == "word" &&
          expr.operator.name in specialForms)
        return specialForms[expr.operator.name](expr.args,
                                                env);
      var op = evaluate(expr.operator, env);
      if (typeof op != "function")
        throw new TypeError("Applying a non-function.");
      return op.apply(null, expr.args.map(function(arg) {
        return evaluate(arg, env);
      }));
  }
}

var specialForms = Object.create(null);

The evaluator has code for each of the expression types. A literal value expression simply produces its value. (For example, the expression 100 just evaluates to the number 100.) For a variable, we must check whether it is actually defined in the environment, and if it is, fetch the variable’s value.

Applications are more involved. If they are a special form, like if, we do not evaluate anything, and simply pass the argument expressions, along with the environment, to the function that handles this form. If it is a normal call, we evaluate the operator, verify that it is a function, and call it with the result of evaluating the arguments.

We will use plain JavaScript function values to represent Egg’s function values. We will come back to this later, when the special form called fun is defined.

The recursive structure of evaluate resembles the similar structure of the parser. Both mirror the structure of the language itself. It would also be possible integrate the parser with the evaluator, and evaluate during parsing, but splitting them up this way makes the program more readable.

This is really all that is needed to interpret Egg. It is that simple. But without defining a few special forms and adding some useful values to the environment, you can’t do anything with this language yet.

Special forms

The specialForms object is used to define special syntax in Egg. It associates words with functions that evaluate such special forms. It is currently empty. Let’s add some forms.

specialForms["if"] = function(args, env) {
  if (args.length != 3)
    throw new SyntaxError("Bad number of args to if");

  if (evaluate(args[0], env) !== false)
    return evaluate(args[1], env);
  else
    return evaluate(args[2], env);
};

Egg’s if construct expects exactly three arguments. It will evaluate the first, and if the result isn’t the value false, it will evaluate the second. Otherwise, the third gets evaluated. Because this if form is an expression, not a statement as it is in JavaScript, it has a value—namely, the result of the second or third argument.

Egg differs from JavaScript in how it handles the condition value to if. It will not treat things like zero or the empty string as false, but only the precise value false.

The reason we need to represent if as a special form, rather than a regular function, is that all arguments to functional are evaluated before the function is called, whereas if should only evaluate either its second or its third argument, depending on the value of the first.

The while form is similar:

specialForms["while"] = function(args, env) {
  if (args.length != 2)
    throw new SyntaxError("Bad number of args to while");

  while (evaluate(args[0], env) !== false)
    evaluate(args[1], env);

  // Since undefined does not exist in Egg, we return false,
  // for lack of a meaningful result.
  return false;
};

Another basic building block is do, which executes all its arguments from top to bottom. Its value is the value produced by the last argument.

specialForms["do"] = function(args, env) {
  var value = false;
  args.forEach(function(arg) {
    value = evaluate(arg, env);
  });
  return value;
};

To be able to create variables and give them new values, we also create a form called define. It expects a word as its first argument, and an expression producing the value to assign to that word as its second argument. Since define, like everything, is an expression, it must return a value. We’ll make it return the value that was assigned (just like JavaScript’s “=” operator).

specialForms["define"] = function(args, env) {
  if (args.length != 2 || args[0].type != "word")
    throw new SyntaxError("Bad use of define");
  var value = evaluate(args[1], env);
  env[args[0].name] = value;
  return value;
};

The environment

The environment accepted by evaluate is an object with properties whose names correspond to variable names, and whose values correspond to the values those variables are bound to. Let’s define an environment object to represent the global scope.

To be able to use the if construct we just defined, let’s add support for Boolean values in this global scope. Since there are only two boolean values, we do not need special syntax for them. We simply bind two variables to the values true and false, and use those.

var topEnv = Object.create(null);

topEnv["true"] = true;
topEnv["false"] = false;

We can now evaluate a simple expression that inverts a Boolean value.

var prog = parse("if(true, false, true)");
console.log(evaluate(prog, topEnv));
// → false

To supply basic arithmetic and comparison operators, we will also add some functions to the environment. In the interest of keeping the code short, we’ll use new Function to synthesize a bunch of operator functions in a loop, rather than defining them all individually.

["+", "-", "*", "/", "==", "<", ">"].forEach(function(op) {
  topEnv[op] =
    new Function("a, b", "return a " + op + " b;");
});

A way to output values is also very useful, so we’ll wrap console.log in a function and call it print.

topEnv["print"] = function(value) {
  console.log(value);
  return value;
};

That gives us enough elementary tools to write simple programs. The following run function provides a convenient way to write and run them. It creates a fresh environment, and parses and evaluates the strings we give it as a single program.

function run() {
  var env = Object.create(topEnv);
  var program = Array.prototype.slice
    .call(arguments, 0).join("\n");
  return evaluate(parse(program), env);
}

The use of Array.prototype.slice.call above is a trick to turn an array-like object, such as arguments, into a real array, so that we can call join on it. It takes all the arguments given to run and treats them as the lines of a program.

run("do(define(total, 0),",
    "   define(count, 1),",
    "   while(<(count, 11),",
    "         do(define(total, +(total, count)),",
    "            define(count, +(count, 1)))),",
    "   print(total))");
// → 55

This is the program we’ve seen several times before, which computes the sum of the numbers 1 to 10, expressed in Egg. It is clearly uglier than the equivalent JavaScript program, but not bad for a language implemented in less than 150 lines of code.

Functions

A programming language without functions is a poor programming language indeed.

Fortunately, it is not hard to add a fun construct, which treats its last argument as the function’s body, and all arguments before that as the names of the function’s arguments.

specialForms["fun"] = function(args, env) {
  if (!args.length)
    throw new SyntaxError("Functions need a body");
  function name(expr) {
    if (expr.type != "word")
      throw new SyntaxError("Arg names must be words");
    return expr.name;
  }
  var argNames = args.slice(0, args.length - 1).map(name);
  var body = args[args.length - 1];

  return function() {
    if (arguments.length != argNames.length)
      throw new TypeError("Wrong number of arguments");
    var localEnv = Object.create(env);
    for (var i = 0; i < arguments.length; i++)
      localEnv[argNames[i]] = arguments[i];
    return evaluate(body, localEnv);
  };
};

Functions in Egg have their own local environment, just like in JavaScript. We use Object.create to make a new object that has access to the variables in the outer environment (its prototype), but can also contain new variables without modifying that outer scope.

The function created by the fun form creates this local environment, and adds the argument variables to it. It then evaluates the function body in this environment, and returns the result.

run("do(define(plusOne, fun(a, +(a, 1))),",
    "   print(plusOne(10)))");
// → 11

run("do(define(pow, fun(base, exp,",
    "     if(==(exp, 0),",
    "        1,",
    "        *(base, pow(base, -(exp, 1)))))),",
    "   print(pow(2, 10)))");
// → 1024

Compilation

What we have built is an interpreter. During evaluation, it acts directly on the representation of the program produced by the parser.

Compilation is the process of adding another step between the parsing and the running of a program, which transforms the program into something that can be evaluated more efficiently by doing as much work as possible in advance. For example, in well-designed languages it is obvious, for each use of a variable, which variable is being referred to, without actually running the program. This can be used to avoid looking up the variable by name every time it is accessed, and directly fetch it from some predetermined memory location.

Traditionally, compilation involves converting the program to machine code, the raw format that a computer’s processor can execute. But any process that converts a program to a different representation can be thought of as compilation.

It would be possible to write an alternative evaluation strategy for Egg, one that first converts the program to a JavaScript program, uses new Function to invoke the JavaScript compiler on it, and then runs the result. When done right, this would make Egg run very fast, while still being quite simple to implement.

If you are interested in this topic and willing to spend some time on it, I encourage you to try to implement such a compiler as an exercise.

Cheating

When we defined if and while, you probably noticed that they were more or less trivial wrappers around JavaScript’s own if and while. Similarly, the values in Egg are just regular old JavaScript values.

If you compare the implementation of Egg, built on top of JavaScript, with the amount of work and complexity required to build a programming language directly on the raw functionality provided by a machine, the difference is huge. Regardless, this example hopefully gave you an impression of the way programming languages work.

And when it comes to getting something done, cheating is more effective than doing everything yourself. Though the toy language in this chapter doesn’t do anything that couldn’t be done better in JavaScript, there are situations where writing small languages helps get real work done.

Such a language does not have to resemble a typical programming language. If JavaScript didn’t come equipped with regular expressions, you could write your own parser and evaluator for such a sublanguage.

Or imagine you are building a giant robotic dinosaur, and need to program its behavior. JavaScript might not be the most effective way to do this. You might instead opt for a language that looks like this:

behavior walk
  perform when
    destination ahead
  actions
    move left-foot
    move right-foot

behavior attack
  perform when
    Godzilla in-view
  actions
    fire laser-eyes
    launch arm-rockets

This is what is usually called a domain-specific language, a language tailored to express a narrow domain of knowledge. Such a language can be more expressive than a general-purpose language because it is designed to express exactly the things that need expressing in its domain, and nothing else.

Exercises

Arrays

Add support for arrays to Egg by adding the following three functions to the top scope: array(...) which constructs an array containing the argument values, length(array) to get an array’s length, and element(array, n) to fetch the nth element from an array.

// Modify these definitions...

topEnv["array"] = "...";

topEnv["length"] = "...";

topEnv["element"] = "...";

run("do(define(sum, fun(array,",
    "     do(define(i, 0),",
    "        define(sum, 0),",
    "        while(<(i, length(array)),",
    "          do(define(sum, +(sum, element(array, i))),",
    "             define(i, +(i, 1)))),",
    "        sum))),",
    "   print(sum(array(1, 2, 3))))");
// → 6

The easiest way to do this is to represent Egg arrays with JavaScript arrays.

The values added to the top environment must be functions. Array.prototype.slice can be used to convert an arguments array-like object into a regular array.

Closure

The way we have defined fun allows functions in Egg to “close over” the surrounding environment, allowing the function’s body to use local values that were visible at the time the function was defined, just like JavaScript functions do.

The program below illustrates this: function f returns a function that adds its argument to f's argument, meaning that it needs access to the local scope inside f to be able to use variable a.

run("do(define(f, fun(a, fun(b, +(a, b)))),",
    "   print(f(4)(5)))");
// → 9

Go back to the definition of the fun form and explain which mechanism causes this to work.

Again, we are riding along on a JavaScript mechanism to get the equivalent feature in Egg. Special forms are passed the local environment in which they are evaluated, so that they can evaluate their sub-forms in that environment. The function returned by fun closes over the env argument given to its enclosing function, and uses that to create the function’s local environment when it is called.

This means that the prototype of the local environment will be the environment in which the function was created, which makes it possible to access variables in that environment from the function. This is all there is to implementing closure (though to compile it in a way that is actually efficient, you’d need to do some more work).

Comments

It would be nice if we could write comments in Egg. For example, whenever we find a hash sign (“#”), we could treat the rest of the line as a comment and ignore it, similar to “//” in JavaScript.

We do not have to make any big changes to the parser to support this. We can simply change skipSpace to skip comments as if they are whitespace, so that all the points where skipSpace is called will now also skip comments. Make this change.

// This is the old skipSpace. Modify it...
function skipSpace(string) {
  var first = string.search(/\S/);
  if (first == -1) return "";
  return string.slice(first);
}

console.log(parse("# hello\nx"));
// → {type: "word", name: "x"}

console.log(parse("a # one\n   # two\n()"));
// → {type: "apply",
//    operator: {type: "word", name: "x"},
//    args: []}

Make sure your solution handles multiple comments in a row, with potentially whitespace between or after them.

A regular expression is probably the easiest way to solve this. Write something that matches “whitespace or a comment, zero or more times”. Use the exec or match method, and look at the length of the first element in the returned array (the whole match) to find out how many characters to slice off.

Fixing scope

Currently, the only way to assign a variable a value is define. This construct acts both as a way to define new variables and to give existing ones a new value.

This ambiguity causes a problem. When you try to give a non-local variable a new value, you will end up defining a local one with the same name instead. (Some languages work like this by design, but I’ve always found it a silly way to handle scope.)

Add a special form set, similar to define, which gives a variable a new value, updating the variable in an outer scope if it doesn’t already exist in the inner scope. If the variable is not defined at all, throw a ReferenceError.

The technique of representing scopes as simple objects, which has made things very convenient so far, will get in your way a little at this point. You might want to use the Object.getPrototypeOf function, which returns the prototype of an object. Also remember that scopes do not derive from Object.prototype, so if you want to call hasOwnProperty on them, you have to use this clumsy expression:

Object.prototype.hasOwnProperty.call(scope, name);

This fetches the hasOwnProperty method from the Object prototype, and then calls it on a scope object.

specialForms["set"] = function(args, env) {
  // Your code here.
};

run("do(define(x, 4),",
    "   define(setx, fun(val, set(x, val))),",
    "   setx(50),",
    "   print(x))");
// → 50
run("set(quux, true)");
// → Some kind of ReferenceError

You will have to loop through one scope at a time, using Object.getPrototypeOf to go the next outer scope. For each scope, use hasOwnProperty to find out if the variable, indicated by the name property of the first argument to set, exists in that scope. If it does, set it to the result of evaluating the second argument to set, and return that value.

If the outermost scope is reached (Object.getPrototypeOf returns null) and we haven’t found the variable yet, it doesn’t exist, and an error should be thrown.