KaTeX/src/Parser.js

var functions = require("./functions");
var environments = require("./environments");
var Lexer = require("./Lexer");
var symbols = require("./symbols");
var utils = require("./utils");

var parseData = require("./parseData");
var ParseError = require("./ParseError");

/**
 * This file contains the parser used to parse out a TeX expression from the
 * input. Since TeX isn't context-free, standard parsers don't work particularly
 * well.
 *
 * The strategy of this parser is as such:
 *
 * The main functions (the `.parse...` ones) take a position in the current
 * parse string to parse tokens from. The lexer (found in Lexer.js, stored at
 * this.lexer) also supports pulling out tokens at arbitrary places. When
 * individual tokens are needed at a position, the lexer is called to pull out a
 * token, which is then used.
 *
 * The main functions also take a mode that the parser is currently in
 * (currently "math" or "text"), which denotes whether the current environment
 * is a math-y one or a text-y one (e.g. inside \text). Currently, this serves
 * to limit the functions which can be used in text mode.
 *
 * The main functions then return an object which contains the useful data that
 * was parsed at its given point, and a new position at the end of the parsed
 * data. The main functions can call each other and continue the parsing by
 * using the returned position as a new starting point.
 *
 * There are also extra `.handle...` functions, which pull out some reused
 * functionality into self-contained functions.
 *
 * The earlier functions return `ParseResult`s, which contain a ParseNode and a
 * new position.
 *
 * The later functions (which are called deeper in the parse) sometimes return
 * ParseFuncOrArgument, which contain a ParseResult as well as some data about
 * whether the parsed object is a function which is missing some arguments, or a
 * standalone object which can be used as an argument to another function.
 */

/**
 * Main Parser class
 */
function Parser(input, settings) {
    // Make a new lexer
    this.lexer = new Lexer(input);
    // Store the settings for use in parsing
    this.settings = settings;
}

var ParseNode = parseData.ParseNode;
var ParseResult = parseData.ParseResult;

/**
 * An initial function (without its arguments), or an argument to a function.
 * The `result` argument should be a ParseResult.
 */
function ParseFuncOrArgument(result, isFunction) {
    this.result = result;
    // Is this a function (i.e. is it something defined in functions.js)?
    this.isFunction = isFunction;
}

/**
 * Checks a result to make sure it has the right type, and throws an
 * appropriate error otherwise.
 */
Parser.prototype.expect = function(result, text) {
    if (result.text !== text) {
        throw new ParseError(
            "Expected '" + text + "', got '" + result.text + "'",
            this.lexer, result.position
        );
    }
};

/**
 * Main parsing function, which parses an entire input.
 *
 * @return {?Array.<ParseNode>}
 */
Parser.prototype.parse = function(input) {
    // Try to parse the input
    var parse = this.parseInput(0, "math");
    return parse.result;
};

/**
 * Parses an entire input tree.
 */
Parser.prototype.parseInput = function(pos, mode) {
    // Parse an expression
    var expression = this.parseExpression(pos, mode, false);
    // If we succeeded, make sure there's an EOF at the end
    this.expect(expression.peek, "EOF");
    return expression;
};

var endOfExpression = ["}", "\\end", "\\right", "&", "\\\\", "\\cr"];

/**
 * Parses an "expression", which is a list of atoms.
 *
 * @param {boolean} breakOnInfix Should the parsing stop when we hit infix
 *                  nodes? This happens when functions have higher precendence
 *                  than infix nodes in implicit parses.
 *
 * @param {?string} breakOnToken The token that the expression should end with,
 *                  or `null` if something else should end the expression.
 *
 * @return {ParseResult}
 */
Parser.prototype.parseExpression = function(pos, mode, breakOnInfix, breakOnToken) {
    var body = [];
    var lex = null;
    // Keep adding atoms to the body until we can't parse any more atoms (either
    // we reached the end, a }, or a \right)
    while (true) {
        lex = this.lexer.lex(pos, mode);
        if (endOfExpression.indexOf(lex.text) !== -1) {
            break;
        }
        if (breakOnToken && lex.text === breakOnToken) {
            break;
        }
        var atom = this.parseAtom(pos, mode);
        if (!atom) {
            break;
        }
        if (breakOnInfix && atom.result.type === "infix") {
            break;
        }
        body.push(atom.result);
        pos = atom.position;
    }
    var res = new ParseResult(this.handleInfixNodes(body, mode), pos);
    res.peek = lex;
    return res;
};

/**
 * Rewrites infix operators such as \over with corresponding commands such
 * as \frac.
 *
 * There can only be one infix operator per group.  If there's more than one
 * then the expression is ambiguous.  This can be resolved by adding {}.
 *
 * @returns {Array}
 */
Parser.prototype.handleInfixNodes = function (body, mode) {
    var overIndex = -1;
    var func;
    var funcName;

    for (var i = 0; i < body.length; i++) {
        var node = body[i];
        if (node.type === "infix") {
            if (overIndex !== -1) {
                throw new ParseError("only one infix operator per group",
                    this.lexer, -1);
            }
            overIndex = i;
            funcName = node.value.replaceWith;
            func = functions.funcs[funcName];
        }
    }

    if (overIndex !== -1) {
        var numerNode, denomNode;

        var numerBody = body.slice(0, overIndex);
        var denomBody = body.slice(overIndex + 1);

        if (numerBody.length === 1 && numerBody[0].type === "ordgroup") {
            numerNode = numerBody[0];
        } else {
            numerNode = new ParseNode("ordgroup", numerBody, mode);
        }

        if (denomBody.length === 1 && denomBody[0].type === "ordgroup") {
            denomNode = denomBody[0];
        } else {
            denomNode = new ParseNode("ordgroup", denomBody, mode);
        }

        var value = func.handler(funcName, numerNode, denomNode);
        return [new ParseNode(value.type, value, mode)];
    } else {
        return body;
    }
};

// The greediness of a superscript or subscript
var SUPSUB_GREEDINESS = 1;

/**
 * Handle a subscript or superscript with nice errors.
 */
Parser.prototype.handleSupSubscript = function(pos, mode, symbol, name) {
    var group = this.parseGroup(pos, mode);

    if (!group) {
        throw new ParseError(
            "Expected group after '" + symbol + "'", this.lexer, pos);
    } else if (group.isFunction) {
        // ^ and _ have a greediness, so handle interactions with functions'
        // greediness
        var funcGreediness = functions.funcs[group.result.result].greediness;
        if (funcGreediness > SUPSUB_GREEDINESS) {
            return this.parseFunction(pos, mode);
        } else {
            throw new ParseError(
                "Got function '" + group.result.result + "' with no arguments " +
                    "as " + name,
                this.lexer, pos);
        }
    } else {
        return group.result;
    }
};

/**
 * Parses a group with optional super/subscripts.
 *
 * @return {?ParseResult}
 */
Parser.prototype.parseAtom = function(pos, mode) {
    // The body of an atom is an implicit group, so that things like
    // \left(x\right)^2 work correctly.
    var base = this.parseImplicitGroup(pos, mode);

    // In text mode, we don't have superscripts or subscripts
    if (mode === "text") {
        return base;
    }

    // Handle an empty base
    var currPos;
    if (!base) {
        currPos = pos;
        base = undefined;
    } else {
        currPos = base.position;
    }

    var superscript;
    var subscript;
    var result;
    while (true) {
        // Lex the first token
        var lex = this.lexer.lex(currPos, mode);

        if (lex.text === "^") {
            // We got a superscript start
            if (superscript) {
                throw new ParseError(
                    "Double superscript", this.lexer, currPos);
            }
            result = this.handleSupSubscript(
                lex.position, mode, lex.text, "superscript");
            currPos = result.position;
            superscript = result.result;
        } else if (lex.text === "_") {
            // We got a subscript start
            if (subscript) {
                throw new ParseError(
                    "Double subscript", this.lexer, currPos);
            }
            result = this.handleSupSubscript(
                lex.position, mode, lex.text, "subscript");
            currPos = result.position;
            subscript = result.result;
        } else if (lex.text === "'") {
            // We got a prime
            var prime = new ParseNode("textord", "\\prime", mode);

            // Many primes can be grouped together, so we handle this here
            var primes = [prime];
            currPos = lex.position;
            // Keep lexing tokens until we get something that's not a prime
            while ((lex = this.lexer.lex(currPos, mode)).text === "'") {
                // For each one, add another prime to the list
                primes.push(prime);
                currPos = lex.position;
            }
            // Put them into an ordgroup as the superscript
            superscript = new ParseNode("ordgroup", primes, mode);
        } else {
            // If it wasn't ^, _, or ', stop parsing super/subscripts
            break;
        }
    }

    if (superscript || subscript) {
        // If we got either a superscript or subscript, create a supsub
        return new ParseResult(
            new ParseNode("supsub", {
                base: base && base.result,
                sup: superscript,
                sub: subscript
            }, mode),
            currPos);
    } else {
        // Otherwise return the original body
        return base;
    }
};

// A list of the size-changing functions, for use in parseImplicitGroup
var sizeFuncs = [
    "\\tiny", "\\scriptsize", "\\footnotesize", "\\small", "\\normalsize",
    "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"
];

// A list of the style-changing functions, for use in parseImplicitGroup
var styleFuncs = [
    "\\displaystyle", "\\textstyle", "\\scriptstyle", "\\scriptscriptstyle"
];

/**
 * Parses an implicit group, which is a group that starts at the end of a
 * specified, and ends right before a higher explicit group ends, or at EOL. It
 * is used for functions that appear to affect the current style, like \Large or
 * \textrm, where instead of keeping a style we just pretend that there is an
 * implicit grouping after it until the end of the group. E.g.
 *   small text {\Large large text} small text again
 * It is also used for \left and \right to get the correct grouping.
 *
 * @return {?ParseResult}
 */
Parser.prototype.parseImplicitGroup = function(pos, mode) {
    var start = this.parseSymbol(pos, mode);

    if (!start || !start.result) {
        // If we didn't get anything we handle, fall back to parseFunction
        return this.parseFunction(pos, mode);
    }

    var func = start.result.result;
    var body;

    if (func === "\\left") {
        // If we see a left:
        // Parse the entire left function (including the delimiter)
        var left = this.parseFunction(pos, mode);
        // Parse out the implicit body
        body = this.parseExpression(left.position, mode, false);
        // Check the next token
        this.expect(body.peek, "\\right");
        var right = this.parseFunction(body.position, mode);
        return new ParseResult(
            new ParseNode("leftright", {
                body: body.result,
                left: left.result.value.value,
                right: right.result.value.value
            }, mode),
            right.position);
    } else if (func === "\\begin") {
        // begin...end is similar to left...right
        var begin = this.parseFunction(pos, mode);
        var envName = begin.result.value.name;
        if (!environments.hasOwnProperty(envName)) {
            throw new ParseError(
                "No such environment: " + envName,
                this.lexer, begin.result.value.namepos);
        }
        // Build the environment object. Arguments and other information will
        // be made available to the begin and end methods using properties.
        var env = environments[envName];
        var args = [null, mode, envName];
        var newPos = this.parseArguments(
            begin.position, mode, "\\begin{" + envName + "}", env, args);
        args[0] = newPos;
        var result = env.handler.apply(this, args);
        var endLex = this.lexer.lex(result.position, mode);
        this.expect(endLex, "\\end");
        var end = this.parseFunction(result.position, mode);
        if (end.result.value.name !== envName) {
            throw new ParseError(
                "Mismatch: \\begin{" + envName + "} matched " +
                "by \\end{" + end.result.value.name + "}",
                this.lexer, end.namepos);
        }
        result.position = end.position;
        return result;
    } else if (utils.contains(sizeFuncs, func)) {
        // If we see a sizing function, parse out the implict body
        body = this.parseExpression(start.result.position, mode, false);
        return new ParseResult(
            new ParseNode("sizing", {
                // Figure out what size to use based on the list of functions above
                size: "size" + (utils.indexOf(sizeFuncs, func) + 1),
                value: body.result
            }, mode),
            body.position);
    } else if (utils.contains(styleFuncs, func)) {
        // If we see a styling function, parse out the implict body
        body = this.parseExpression(start.result.position, mode, true);
        return new ParseResult(
            new ParseNode("styling", {
                // Figure out what style to use by pulling out the style from
                // the function name
                style: func.slice(1, func.length - 5),
                value: body.result
            }, mode),
            body.position);
    } else {
        // Defer to parseFunction if it's not a function we handle
        return this.parseFunction(pos, mode);
    }
};

/**
 * Parses an entire function, including its base and all of its arguments
 *
 * @return {?ParseResult}
 */
Parser.prototype.parseFunction = function(pos, mode) {
    var baseGroup = this.parseGroup(pos, mode);

    if (baseGroup) {
        if (baseGroup.isFunction) {
            var func = baseGroup.result.result;
            var funcData = functions.funcs[func];
            if (mode === "text" && !funcData.allowedInText) {
                throw new ParseError(
                    "Can't use function '" + func + "' in text mode",
                    this.lexer, baseGroup.position);
            }

            var args = [func];
            var newPos = this.parseArguments(
                baseGroup.result.position, mode, func, funcData, args);
            var result = functions.funcs[func].handler.apply(this, args);
            return new ParseResult(
                new ParseNode(result.type, result, mode),
                newPos);
        } else {
            return baseGroup.result;
        }
    } else {
        return null;
    }
};


/**
 * Parses the arguments of a function or environment
 *
 * @param {string} func  "\name" or "\begin{name}"
 * @param {{numArgs:number,numOptionalArgs:number|undefined}} funcData
 * @param {Array} args  list of arguments to which new ones will be pushed
 * @return the position after all arguments have been parsed
 */
Parser.prototype.parseArguments = function(pos, mode, func, funcData, args) {
    var totalArgs = funcData.numArgs + funcData.numOptionalArgs;
    if (totalArgs === 0) {
        return pos;
    }

    var newPos = pos;
    var baseGreediness = funcData.greediness;
    var positions = [newPos];

    for (var i = 0; i < totalArgs; i++) {
        var argType = funcData.argTypes && funcData.argTypes[i];
        var arg;
        if (i < funcData.numOptionalArgs) {
            if (argType) {
                arg = this.parseSpecialGroup(newPos, argType, mode, true);
            } else {
                arg = this.parseOptionalGroup(newPos, mode);
            }
            if (!arg) {
                args.push(null);
                positions.push(newPos);
                continue;
            }
        } else {
            if (argType) {
                arg = this.parseSpecialGroup(newPos, argType, mode);
            } else {
                arg = this.parseGroup(newPos, mode);
            }
            if (!arg) {
                throw new ParseError(
                    "Expected group after '" + func + "'",
                    this.lexer, newPos);
            }
        }
        var argNode;
        if (arg.isFunction) {
            var argGreediness =
                functions.funcs[arg.result.result].greediness;
            if (argGreediness > baseGreediness) {
                argNode = this.parseFunction(newPos, mode);
            } else {
                throw new ParseError(
                    "Got function '" + arg.result.result + "' as " +
                    "argument to '" + func + "'",
                    this.lexer, arg.result.position - 1);
            }
        } else {
            argNode = arg.result;
        }
        args.push(argNode.result);
        positions.push(argNode.position);
        newPos = argNode.position;
    }

    args.push(positions);

    return newPos;
};


/**
 * Parses a group when the mode is changing. Takes a position, a new mode, and
 * an outer mode that is used to parse the outside.
 *
 * @return {?ParseFuncOrArgument}
 */
Parser.prototype.parseSpecialGroup = function(pos, mode, outerMode, optional) {
    // Handle `original` argTypes
    if (mode === "original") {
        mode = outerMode;
    }

    if (mode === "color" || mode === "size") {
        // color and size modes are special because they should have braces and
        // should only lex a single symbol inside
        var openBrace = this.lexer.lex(pos, outerMode);
        if (optional && openBrace.text !== "[") {
            // optional arguments should return null if they don't exist
            return null;
        }
        this.expect(openBrace, optional ? "[" : "{");
        var inner = this.lexer.lex(openBrace.position, mode);
        var data;
        if (mode === "color") {
            data = inner.text;
        } else {
            data = inner.data;
        }
        var closeBrace = this.lexer.lex(inner.position, outerMode);
        this.expect(closeBrace, optional ? "]" : "}");
        return new ParseFuncOrArgument(
            new ParseResult(
                new ParseNode(mode, data, outerMode),
                closeBrace.position),
            false);
    } else if (mode === "text") {
        // text mode is special because it should ignore the whitespace before
        // it
        var whitespace = this.lexer.lex(pos, "whitespace");
        pos = whitespace.position;
    }

    if (optional) {
        return this.parseOptionalGroup(pos, mode);
    } else {
        return this.parseGroup(pos, mode);
    }
};

/**
 * Parses a group, which is either a single nucleus (like "x") or an expression
 * in braces (like "{x+y}")
 *
 * @return {?ParseFuncOrArgument}
 */
Parser.prototype.parseGroup = function(pos, mode) {
    var start = this.lexer.lex(pos, mode);
    // Try to parse an open brace
    if (start.text === "{") {
        // If we get a brace, parse an expression
        var expression = this.parseExpression(start.position, mode, false);
        // Make sure we get a close brace
        var closeBrace = this.lexer.lex(expression.position, mode);
        this.expect(closeBrace, "}");
        return new ParseFuncOrArgument(
            new ParseResult(
                new ParseNode("ordgroup", expression.result, mode),
                closeBrace.position),
            false);
    } else {
        // Otherwise, just return a nucleus
        return this.parseSymbol(pos, mode);
    }
};

/**
 * Parses a group, which is an expression in brackets (like "[x+y]")
 *
 * @return {?ParseFuncOrArgument}
 */
Parser.prototype.parseOptionalGroup = function(pos, mode) {
    var start = this.lexer.lex(pos, mode);
    // Try to parse an open bracket
    if (start.text === "[") {
        // If we get a brace, parse an expression
        var expression = this.parseExpression(start.position, mode, false, "]");
        // Make sure we get a close bracket
        var closeBracket = this.lexer.lex(expression.position, mode);
        this.expect(closeBracket, "]");
        return new ParseFuncOrArgument(
            new ParseResult(
                new ParseNode("ordgroup", expression.result, mode),
                closeBracket.position),
            false);
    } else {
        // Otherwise, return null,
        return null;
    }
};

/**
 * Parse a single symbol out of the string. Here, we handle both the functions
 * we have defined, as well as the single character symbols
 *
 * @return {?ParseFuncOrArgument}
 */
Parser.prototype.parseSymbol = function(pos, mode) {
    var nucleus = this.lexer.lex(pos, mode);

    if (functions.funcs[nucleus.text]) {
        // If there exists a function with this name, we return the function and
        // say that it is a function.
        return new ParseFuncOrArgument(
            new ParseResult(nucleus.text, nucleus.position),
            true);
    } else if (symbols[mode][nucleus.text]) {
        // Otherwise if this is a no-argument function, find the type it
        // corresponds to in the symbols map
        return new ParseFuncOrArgument(
            new ParseResult(
                new ParseNode(symbols[mode][nucleus.text].group,
                              nucleus.text, mode),
                nucleus.position),
            false);
    } else {
        return null;
    }
};

Parser.prototype.ParseNode = ParseNode;

module.exports = Parser;