JavaScript Expression Notation (JSEN)

by T. Michael Keesey (keesey@gmail.com)

JSEN is a subset of JavaScript (based on the ECMA-262 5.1 standard and largely overlapping JSON) that can represent mathematical expressions, and an associated TypeScript/JavaScript library.

License

JSEN is available under the MIT license. For more details, see the LICENSE file.

Important Files

• bin/jsen.js: JSEN as a JavaScript file.
• bin/jsen.min.js: A minified version of jsen.js.
• bin/ecma262.js: ECMA-262 namespace for JSEN.
• src/jsen.ts: The TypeScript source for JSEN.
• src/jsen.d.ts: A TypeScript declaration file for JSEN.
• src/ecma262.ts: The TypeScript source for the ECMA-262 namespace.
• src/ecma262.d.ts: A TypeScript declaration for the ECMA-262 namespace.
• build.sh: UNIX shell script to build the JavaScript files from TypeScript source. Requires Java and the TypeScript compiler.

The JSEN Format

JSEN is JavaScript wherein values are interpreted as expressions.

A String is interpreted as:

• a namespace reference, if it ends with ":" (but not with "\\:");
• a qualified identifier, if it includes (but does not end with) ":"; or
• a local identifier, otherwise.

Colons (":") in strings may be escaped by a preceding backslash. Since backslashes must be escaped in JavaScript strings, this is written as two backslashes: "\\". This does not pertain to keys used as local identifiers in namespace declarations (read on).

An Array is interpreted as an application of an operation, where the first element is a string identifying the operation and the following elements (if any) are arguments. An empty array ([]) is illegal.

An Object (associative array) is interpreted either as:

• a set of declarations, where each key is a local identifier and each value is an evaluable expression, or
• a namespace, where each key is a URI and each value is a set of declarations.

All other value types (Null, Boolean, Number, Function, nested objects, etc.) are interpreted as themselves.

Examples

Constants

Here is a JSEN declaration for a namespace whose local identifiers represent approximations of numerical constants:

{
	"e": 2.718281828459045,
	"pi": 3.141592653589793
}

ECMA-262 Entities

The JSEN library optionally includes a namespace with the URI "http://ecma-international.org/ecma-262/5.1" that contains certain elements of the ECMA-262 standard. Using this, expressions like the following may be formed:

{
	"x": ["http://ecma-international.org/ecma-262/5.1:+",
			1,
			2
		],
	"y": ["http://ecma-international.org/ecma-262/5.1:Math.sin",
			["http://ecma-international.org/ecma-262/5.1:/",
				"http://ecma-international.org/ecma-262/5.1:Math.PI",
				2
			]
		],
	"z": ["http://ecma-international.org/ecma-262/5.1:Array",
			4,
			5,
			6
		]
}

When evaluated, "x" will yield 3 (JavaScript: 1 + 2), "y" will yield 1 (JavaScript: Math.sin(Math.PI / 2)), and "z" will yield [4, 5, 6] (JavaScript: Array(4, 5, 6)).

The available ECMA-262 entities are:

• Literals:

  undefined NaN Infinity

• Accessors:

  []

• Operators:

  void + - ~ ! * / % << >> >>> < > <= >= in == != === !== & ^ | && || ?:

  (Note that since colons (":") are reserved in JSEN identifiers, the ?: operator's name must be written "?\\:".)

• Top-level functions:

  isFinite isNaN Array Boolean Number

  The Array function has been modified so that a single argument yields an array with that as its single member (instead of using it to determine the length of the array).

• All constants of the Math object (Math.E, Math.LN2, etc.).

• All functions of the Math object (Math.abs, Math.acos, etc.).

Namespace References

Since repeated URIs can make expressions rather verbose, JSEN allows for arbitrary references to namespaces:

{
	"js": "http://ecma-international.org/ecma-262/5.1:",

	"x": [ "js:+", 1, 2 ],
	"y": [ "js:Math.sin", [ "js:/", "js:Math.PI", 2 ] ],
	"z": [ "js:Array", 4, 5, 6 ]
}

These references only pertain to the namespaces they were declared under, and are not externally accessible.

Notes on Identifiers

Identifiers may be declared in any order, and may refer to other identifiers. Within a namespace local names may be used.

{
	"pi": "js:Math.PI",
	"tau": [ "js:*", "pi", 2 ],

	"js": "http://ecma-international.org/ecma-262/5.1:"
}

Note that cyclical references will cause errors when evaluated. The following expression is illegal:

{
	"x": "y",
	"y": "x"
}

Non-JSON JavaScript

All of the expressions listed so far are JSON, but non-JSON JavaScript may also be used for values not possible under JSON (such as functions):

{
	"even": function( x ) { return x % 2 === 0; },
	"a":    [ "even", 2 ],
	"b":    [ "even", 3 ]
}

When evaluated, "a" will yield true and "b" will yield false.

Using JSEN

Global Functions

The simplest way to use JSEN is to use the global functions. To declare an identifier as representing the value of an expression:

jsen.decl('urn:my-namespace', 'my-id', 10); // The last argument can be any JSEN expression.

The expression may be evaluated like so:

jsen.eval('urn:my-namespace', 'my-id'); // 10

Declarations may be chained:

jsen.decl('urn:my-namespace', 'my-id', 10)
    .decl('urn:my-namespace', 'my-id-2', 20);

In addition to evaluating expresions that have been linked with an identifier through a declaration, expressions may also be evalauted on their own, without an identifier or declaration:

jsen.evalExpr('urn:my-namespace:my-id'); // 10, if the previous code has been run

EMCA-262 Entities

To use the ECMA-262 entities:

jsen.ecma262.decl();

Now you can use the entities:

jsen.decl('urn:my-namespace', 'my-array-id', ['http://ecma-international.org/ecma-262/5.1:Array', 1, 2]);
jsen.eval('urn:my-namespace', 'my-array-id'); // [1, 2]

For convenience, the ECMA-262 URI is available as a constant: jsen.ecma262.URI.

Declaring and Evaluating an Entire Namespace

Namespaces may be declared all at once. When this is done, you may use abbreviated namespace references:

jsen.decl('urn:my-namespace', {
	'js': 'http://ecma-international.org/ecma-262/5.1:',

	'my-id': 10,
	'my-array-id': ['js:Array', 1, 2]
});

You may also evaluate every identifier in a namespace at once:

jsen.eval('urn:my-namespace'); // { 'my-id': 10, 'my-array-id': [1, 2]}

Declaring and Evaluating Multiple Namespaces

A set of namespaces may be declared or evaluated all at once:

jsen.decl({

	'js': 'http://ecma-international.org/ecma-262/5.1:',

	'urn:my-namespace':
	{
		'my-id': 10,
		'my-array-id': ['js:Array', 1, 2]
	},

	'urn:my-other-namespace':
	{
		'my-id': ['js:+', 10, 10]
	}

});
jsen.eval(); // { 'urn:my-namespace': { 'my-id': 10, 'my-array-id': [1, 2]}, 'urn:my-other-namespace': { 'my-id': 20 } /* Plus all ECMA-262 entities */ }

Note that the namespace reference at the top level ('js') is available in both of the declared namespaces.

Functions As Namespaces

A function may be used as a namespace. It should expect a single argument (a local identifier). Its output need not be consistent (that is, it can be random), since JSEN stores evaluations.

jsen.decl({
	'random':    Math.random,
	'uppercase': function(localName) { return localName.toUpperCase(); }
});
jsen.eval('random', 'foo');    // A random number.
jsen.eval('random', 'foo');    // The same number.
jsen.eval('random', 'bar');    // A different random number.
jsen.eval('uppercase', 'foo'); // "FOO"

Solver Instances

Apart from the global functions, you may use a solver instance. This prevents collisions with other code using JSEN.

To create a solver instance:

var solver = jsen.solver();

Now you can use all the functions in the same manner as the global functions:

jsen.ecma262.decl(solver); // To make ECMA-262 entities available.
solver.decl({
	'urn:my-namespace': {
		'js': 'http://ecma-international.org/ecma-262/5.1:',

		'my-id': 33,
		'my-array-id': ['js:Array', 5, 6, 7]
	},
	'urn:my-other-namespace': {
		'my-id': 44
	}
});
solver.eval(); // { 'urn:my-namespace': { 'my-id': 33, 'my-array-id': [5, 6, 7]}, 'urn:my-other-namespace': { 'my-id': 44 } /* Plus all ECMA-262 entities */ }
solver.evalExpr([ 'http://ecma-international.org/ecma-262/5.1:minus', 'urn:my-namespace:my-id', 11 ]); // 22