Chapter 11Project: A Programming Language
The evaluator, which determines the meaning of expressions in a programming language, is just another program.
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.’
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 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 such as 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 between those parentheses, separated by commas.
do(define(x, 10), if(>(x, 5), print("large"), print("small")))
The uniformity of the Egg language means that
things that 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 to represent doing multiple things in sequence.
The data structure that 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.
Expressions 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 they have an args
property that
refers to an array of argument expressions.
The >(x, 5)
part of the previous program 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 treelike shape. The fact that expressions contain other expressions, which in turn might contain more expressions, is similar to the way branches split and split again.
Contrast this to the parser we wrote for the configuration file format in Chapter 9, which had a 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 subexpressions (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 the input does not match
one of these three forms, it is
not a valid expression, and the parser 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 recursively 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 follows.
This is all we
need to parse Egg. We wrap it in a convenient parse
function that
verifies that it has reached the end of the input string after parsing
the expression (an Egg program is a single expression), and that
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, 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 to
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. This if
form is more similar to JavaScript’s ternary ?:
operator than to JavaScript’s if
. It is an expression, not a statement,
and it produces 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 functions are evaluated before the function is called, whereas
if
should evaluate only either its second or its third argument,
depending on the value of the first.
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, we must
have access to Boolean values. 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 negates 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
function values 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
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 treats all the 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 that 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 to 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(...)
to
construct 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
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 following program 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 subforms 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 like 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: "a"}, // 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 as
a way both to define new variables and to give existing ones a new value.
This ambiguity causes a problem. When you try to give a nonlocal 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
(which is
another standard error type).
The technique of representing scopes as simple objects,
which has made things 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 whether 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 then 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.