Monadic parser in JavaScript

May 13, 2009 by asmyczek

After exploring Haskell for some time, I find myself often adopting functional concepts in my daily work. The exposure to functional programming has even affected the set of tools and frameworks I use. For example, having to parse a custom data format I first tend to search for a Parsec clone implemented in the currently used language. This time it was for JavaScript, but a quick Google search did not reveal any relevant projects. Therefore following is the initial attempt to a probably first general purpose parser library for JavaScript, ‘p4js’.

‘p4js’ is a monadic parser library that provides the basic monadic operators return and bind, but this is maybe a topic for another blog post. Let’s start with a quick introduction (for non Parsec users).

A parser in p4js is an object that provides the basic combinators (parsing functions). The function $P() creates a parser object that can be executed on an input using the parse(input) function. The most basic combinator is $P().item(). It reads one char from the input and pushes it to the result array, for example $P().item().parse(‘abc’) will return the array ['a']. If you expect to read a number char, use $P().digit(). This combinator will read the char only if it is a number, otherwise it will throw a parser exception.

Every combinator returns the parser object itself. This enables the chaining of combinators to build more complex parsers. For example the parser

var p = $P().item().item().item();

will return the array ['a', 'b', 'c'] for p.parse(‘abs’).
To combine the results of multiple combinators into one value, chain those between the do_() and reduce() actions, for example:

var p = $P().do_().item().item().item().reduce(
    function(result_array) { return result_array.join(''); }
);

p.parse(‘abc’); will return ['abc'].The function passed to reduce() is called only with the results of the combinators executed between do_() and reduce(). The result of this function is pushed as one value to the result array. In the parser chain, every do_() action requires a matching reduce(), or one of its customization element(), join() etc.

It gets more exciting with the combinators many() and choice(). many(p) or many1(p) applies parser p on the input as many times as possible. For example $P().many($P().digit()).parse(’123abc’) will return ['1', '2', '3']. Combining this with a reduce function that converts the result into an integer, we get a parser for natural numbers:

var p = $P().do_().many1($P().digit()).reduce(
    function(r) { return parseInt(r.join('')); }
);

This parser can be quite useful already, so we can register it with the default library calling p.register(‘nat’) and use it from now on as $P().nat().

choice(p1, p2, …) tries to apply parsers pn in the argument order and returns the first successful parsed value or throws an exception if non of the parsers succeeded. The following example uses choice() to parse a number with optional decimal points:

var p = $P().do_().nat().choice(
    $P().symbol(".").nat().reduce(
        function(r) { while(r[2] > 1.0) r[2] /= 10; return r[0] + r[2]; }),
    $P().element(0)).register('num');

First we use nat() to read the integer part of the number. Than we try to read a ‘.’ followed by an nat() for the decimal part. In case this succeeds we compute the decimal number and return the result. Otherwise we use $P().element(0) to return the first element of the first nat() call, the integer part.

The full floating number parser I will leave as an exercise for the reader.

The current library provides only a dozen combinators, but it is enough to have quite some fun already. Following are few examples:

  • a CSV parser,
  • a small calculator and
  • the tiny math processor that uses the parser not only to parse the input into expression tree, but also to perform expression evaluation and function derivation on the tree, and to draw function graphs (on browsers that support the canvas tag).

For more details see the source code and additional examples on GitHub.

Categories: JavaScript
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