Allow macro definitions in settings (#493)

* Introduce MacroExpander

The job of the MacroExpander is turning a stream of possibly expandable
tokens, as obtained from the Lexer, into a stream of non-expandable tokens
(in KaTeX, even though they may well be expandable in TeX) which can be
processed by the Parser.  The challenge here is that we don't have
mode-specific lexer implementations any more, so we need to do everything on
the token level, including reassembly of sizes and colors.

* Make macros available in development server

Now one can specify macro definitions like \foo=bar as part of the query
string and use these macros in the formula being typeset.

* Add tests for macro expansions

* Handle end of input in special groups

This avoids an infinite loop if input ends prematurely.

* Simplify parseSpecialGroup

The parseSpecialGroup methos now returns a single token spanning the whole
special group, and leaves matching that string against a suitable regular
expression to whoever is calling the method.  Suggested by @cbreeden.

* Incorporate review suggestions

Add improvements suggested by Kevin Barabash during review.

* Input range sanity checks

Ensure that both tokens of a token range come from the same lexer,
and that the range has a non-negative length.

* Improved wording of two comments

src/Lexer.js

@@ -17,16 +17,50 @@ var ParseError = require("./ParseError");
 
 // The main lexer class
 function Lexer(input) {
-    this._input = input;
+    this.input = input;
+    this.pos = 0;
 }
 
-// The resulting token returned from `lex`.
+/**
-function Token(text, data, position) {
+ * The resulting token returned from `lex`.
+ *
+ * It consists of the token text plus some position information.
+ * The position information is essentially a range in an input string,
+ * but instead of referencing the bare input string, we refer to the lexer.
+ * That way it is possible to attach extra metadata to the input string,
+ * like for example a file name or similar.
+ *
+ * The position information (all three parameters) is optional,
+ * so it is OK to construct synthetic tokens if appropriate.
+ * Not providing available position information may lead to
+ * degraded error reporting, though.
+ *
+ * @param {string}  text   the text of this token
+ * @param {number=} start  the start offset, zero-based inclusive
+ * @param {number=} end    the end offset, zero-based exclusive
+ * @param {Lexer=}  lexer  the lexer which in turn holds the input string
+ */
+function Token(text, start, end, lexer) {
     this.text = text;
-    this.data = data;
+    this.start = start;
-    this.position = position;
+    this.end = end;
+    this.lexer = lexer;
 }
 
+/**
+ * Given a pair of tokens (this and endToken), compute a “Token” encompassing
+ * the whole input range enclosed by these two.
+ *
+ * @param {Token}  endToken  last token of the range, inclusive
+ * @param {string} text      the text of the newly constructed token
+ */
+Token.prototype.range = function(endToken, text) {
+    if (endToken.lexer !== this.lexer) {
+        return new Token(text); // sorry, no position information available
+    }
+    return new Token(text, this.start, endToken.end, this.lexer);
+};
+
 /* The following tokenRegex
  * - matches typical whitespace (but not NBSP etc.) using its first group
  * - matches symbol combinations which result in a single output character
@@ -52,111 +86,26 @@ var tokenRegex = new RegExp(
     ")"
 );
 
-var whitespaceRegex = /\s*/;
-
 /**
- * This function lexes a single normal token. It takes a position and
+ * This function lexes a single token.
- * whether it should completely ignore whitespace or not.
  */
-Lexer.prototype._innerLex = function(pos, ignoreWhitespace) {
+Lexer.prototype.lex = function() {
-    var input = this._input;
+    var input = this.input;
+    var pos = this.pos;
     if (pos === input.length) {
-        return new Token("EOF", null, pos);
+        return new Token("EOF", pos, pos, this);
     }
     var match = matchAt(tokenRegex, input, pos);
     if (match === null) {
         throw new ParseError(
             "Unexpected character: '" + input[pos] + "'",
-            this, pos);
+            new Token(input[pos], pos, pos + 1, this));
-    } else if (match[2]) { // matched non-whitespace
-        return new Token(match[2], null, pos + match[2].length);
-    } else if (ignoreWhitespace) {
-        return this._innerLex(pos + match[1].length, true);
-    } else { // concatenate whitespace to a single space
-        return new Token(" ", null, pos + match[1].length);
-    }
-};
-
-// A regex to match a CSS color (like #ffffff or BlueViolet)
-var cssColor = /#[a-z0-9]+|[a-z]+/i;
-
-/**
- * This function lexes a CSS color.
- */
-Lexer.prototype._innerLexColor = function(pos) {
-    var input = this._input;
-
-    // Ignore whitespace
-    var whitespace = matchAt(whitespaceRegex, input, pos)[0];
-    pos += whitespace.length;
-
-    var match;
-    if ((match = matchAt(cssColor, input, pos))) {
-        // If we look like a color, return a color
-        return new Token(match[0], null, pos + match[0].length);
-    } else {
-        throw new ParseError("Invalid color", this, pos);
-    }
-};
-
-// A regex to match a dimension. Dimensions look like
-// "1.2em" or ".4pt" or "1 ex"
-var sizeRegex = /(-?)\s*(\d+(?:\.\d*)?|\.\d+)\s*([a-z]{2})/;
-
-/**
- * This function lexes a dimension.
- */
-Lexer.prototype._innerLexSize = function(pos) {
-    var input = this._input;
-
-    // Ignore whitespace
-    var whitespace = matchAt(whitespaceRegex, input, pos)[0];
-    pos += whitespace.length;
-
-    var match;
-    if ((match = matchAt(sizeRegex, input, pos))) {
-        var unit = match[3];
-        // We only currently handle "em" and "ex" units
-        if (unit !== "em" && unit !== "ex") {
-            throw new ParseError("Invalid unit: '" + unit + "'", this, pos);
-        }
-        return new Token(match[0], {
-            number: +(match[1] + match[2]),
-            unit: unit,
-        }, pos + match[0].length);
-    }
-
-    throw new ParseError("Invalid size", this, pos);
-};
-
-/**
- * This function lexes a string of whitespace.
- */
-Lexer.prototype._innerLexWhitespace = function(pos) {
-    var input = this._input;
-
-    var whitespace = matchAt(whitespaceRegex, input, pos)[0];
-    pos += whitespace.length;
-
-    return new Token(whitespace[0], null, pos);
-};
-
-/**
- * This function lexes a single token starting at `pos` and of the given mode.
- * Based on the mode, we defer to one of the `_innerLex` functions.
- */
-Lexer.prototype.lex = function(pos, mode) {
-    if (mode === "math") {
-        return this._innerLex(pos, true);
-    } else if (mode === "text") {
-        return this._innerLex(pos, false);
-    } else if (mode === "color") {
-        return this._innerLexColor(pos);
-    } else if (mode === "size") {
-        return this._innerLexSize(pos);
-    } else if (mode === "whitespace") {
-        return this._innerLexWhitespace(pos);
     }
+    var text = match[2] || " ";
+    var start = this.pos;
+    this.pos += match[0].length;
+    var end = this.pos;
+    return new Token(text, start, end, this);
 };
 
 module.exports = Lexer;

src/MacroExpander.js

@@ -0,0 +1,70 @@
+/**
+ * This file contains the “gullet” where macros are expanded
+ * until only non-macro tokens remain.
+ */
+
+var Lexer = require("./Lexer");
+
+function MacroExpander(input, macros) {
+    this.lexer = new Lexer(input);
+    this.macros = macros;
+    this.stack = []; // contains tokens in REVERSE order
+    this.discardedWhiteSpace = [];
+}
+
+/**
+ * Recursively expand first token, then return first non-expandable token.
+ */
+MacroExpander.prototype.nextToken = function() {
+    for (;;) {
+        if (this.stack.length === 0) {
+            this.stack.push(this.lexer.lex());
+        }
+        var topToken = this.stack.pop();
+        var name = topToken.text;
+        if (!(name.charAt(0) === "\\" && this.macros.hasOwnProperty(name))) {
+            return topToken;
+        }
+        var expansion = this.macros[name];
+        if (typeof expansion === "string") {
+            var bodyLexer = new Lexer(expansion);
+            expansion = [];
+            var tok = bodyLexer.lex();
+            while (tok.text !== "EOF") {
+                expansion.push(tok);
+                tok = bodyLexer.lex();
+            }
+            expansion.reverse(); // to fit in with stack using push and pop
+            this.macros[name] = expansion;
+        }
+        this.stack = this.stack.concat(expansion);
+    }
+};
+
+MacroExpander.prototype.get = function(ignoreSpace) {
+    this.discardedWhiteSpace = [];
+    var token = this.nextToken();
+    if (ignoreSpace) {
+        while (token.text === " ") {
+            this.discardedWhiteSpace.push(token);
+            token = this.nextToken();
+        }
+    }
+    return token;
+};
+
+/**
+ * Undo the effect of the preceding call to the get method.
+ * A call to this method MUST be immediately preceded and immediately followed
+ * by a call to get.  Only used during mode switching, i.e. after one token
+ * was got in the old mode but should get got again in a new mode
+ * with possibly different whitespace handling.
+ */
+MacroExpander.prototype.unget = function(token) {
+    this.stack.push(token);
+    while (this.discardedWhiteSpace.length !== 0) {
+        this.stack.push(this.discardedWhiteSpace.pop());
+    }
+};
+
+module.exports = MacroExpander;

src/ParseError.js

@@ -2,26 +2,50 @@
  * This is the ParseError class, which is the main error thrown by KaTeX
  * functions when something has gone wrong. This is used to distinguish internal
  * errors from errors in the expression that the user provided.
+ *
+ * If possible, a caller should provide a Token or ParseNode with information
+ * about where in the source string the problem occurred.
+ *
+ * @param {string} message  The error message
+ * @param {(Token|ParseNode)=} token  An object providing position information
  */
-function ParseError(message, lexer, position) {
+function ParseError(message, token) {
     var error = "KaTeX parse error: " + message;
+    var start;
+    var end;
 
-    if (lexer !== undefined && position !== undefined) {
+    if (token && token.lexer && token.start <= token.end) {
         // If we have the input and a position, make the error a bit fancier
 
-        // Prepend some information
-        error += " at position " + position + ": ";
-
         // Get the input
-        var input = lexer._input;
+        var input = token.lexer.input;
-        // Insert a combining underscore at the correct position
+
-        input = input.slice(0, position) + "\u0332" +
+        // Prepend some information
-            input.slice(position);
+        start = token.start;
+        end = token.end;
+        if (start === input.length) {
+            error += " at end of input: ";
+        } else {
+            error += " at position " + (start + 1) + ": ";
+        }
+
+        // Underline token in question using combining underscores
+        var underlined = input.slice(start, end).replace(/[^]/g, "$&\u0332");
 
         // Extract some context from the input and add it to the error
-        var begin = Math.max(0, position - 15);
+        var left;
-        var end = position + 15;
+        if (start > 15) {
-        error += input.slice(begin, end);
+            left = "…" + input.slice(start - 15, start);
+        } else {
+            left = input.slice(0, start);
+        }
+        var right;
+        if (end + 15 < input.length) {
+            right = input.slice(end, end + 15) + "…";
+        } else {
+            right = input.slice(end);
+        }
+        error += left + underlined + right;
     }
 
     // Some hackery to make ParseError a prototype of Error
@@ -30,7 +54,7 @@ function ParseError(message, lexer, position) {
     self.name = "ParseError";
     self.__proto__ = ParseError.prototype;
 
-    self.position = position;
+    self.position = start;
     return self;
 }
 

src/Parser.js

@@ -1,7 +1,7 @@
 /* eslint no-constant-condition:0 */
 var functions = require("./functions");
 var environments = require("./environments");
-var Lexer = require("./Lexer");
+var MacroExpander = require("./MacroExpander");
 var symbols = require("./symbols");
 var utils = require("./utils");
 
@@ -46,8 +46,9 @@ var ParseError = require("./ParseError");
  * Main Parser class
  */
 function Parser(input, settings) {
-    // Make a new lexer
+    // Create a new macro expander (gullet) and (indirectly via that) also a
-    this.lexer = new Lexer(input);
+    // new lexer (mouth) for this parser (stomach, in the language of TeX)
+    this.gullet = new MacroExpander(input, settings.macros);
     // Store the settings for use in parsing
     this.settings = settings;
 }
@@ -58,10 +59,11 @@ var ParseNode = parseData.ParseNode;
  * An initial function (without its arguments), or an argument to a function.
  * The `result` argument should be a ParseNode.
  */
-function ParseFuncOrArgument(result, isFunction) {
+function ParseFuncOrArgument(result, isFunction, token) {
     this.result = result;
     // Is this a function (i.e. is it something defined in functions.js)?
     this.isFunction = isFunction;
+    this.token = token;
 }
 
 /**
@@ -75,7 +77,7 @@ Parser.prototype.expect = function(text, consume) {
     if (this.nextToken.text !== text) {
         throw new ParseError(
             "Expected '" + text + "', got '" + this.nextToken.text + "'",
-            this.lexer, this.nextToken.position
+            this.nextToken
         );
     }
     if (consume !== false) {
@@ -88,8 +90,13 @@ Parser.prototype.expect = function(text, consume) {
  * and fetches the one after that as the new look ahead.
  */
 Parser.prototype.consume = function() {
-    this.pos = this.nextToken.position;
+    this.nextToken = this.gullet.get(this.mode === "math");
-    this.nextToken = this.lexer.lex(this.pos, this.mode);
+};
+
+Parser.prototype.switchMode = function(newMode) {
+    this.gullet.unget(this.nextToken);
+    this.mode = newMode;
+    this.consume();
 };
 
 /**
@@ -100,8 +107,7 @@ Parser.prototype.consume = function() {
 Parser.prototype.parse = function() {
     // Try to parse the input
     this.mode = "math";
-    this.pos = 0;
+    this.consume();
-    this.nextToken = this.lexer.lex(this.pos, this.mode);
     var parse = this.parseInput();
     return parse;
 };
@@ -122,26 +128,29 @@ 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
+ * @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,
+ * @param {?string} breakOnTokenText  The text of the token that the expression
- *                  or `null` if something else should end the expression.
+ *                  should end with, or `null` if something else should end the
+ *                  expression.
  *
  * @return {ParseNode}
  */
-Parser.prototype.parseExpression = function(breakOnInfix, breakOnToken) {
+Parser.prototype.parseExpression = function(breakOnInfix, breakOnTokenText) {
     var body = [];
     // 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) {
         var lex = this.nextToken;
-        var pos = this.pos;
         if (endOfExpression.indexOf(lex.text) !== -1) {
             break;
         }
-        if (breakOnToken && lex.text === breakOnToken) {
+        if (breakOnTokenText && lex.text === breakOnTokenText) {
+            break;
+        }
+        if (breakOnInfix && functions[lex.text] && functions[lex.text].infix) {
             break;
         }
         var atom = this.parseAtom();
@@ -149,19 +158,11 @@ Parser.prototype.parseExpression = function(breakOnInfix, breakOnToken) {
             if (!this.settings.throwOnError && lex.text[0] === "\\") {
                 var errorNode = this.handleUnsupportedCmd();
                 body.push(errorNode);
-
-                pos = lex.position;
                 continue;
             }
 
             break;
         }
-        if (breakOnInfix && atom.type === "infix") {
-            // rewind so we can parse the infix atom again
-            this.pos = pos;
-            this.nextToken = lex;
-            break;
-        }
         body.push(atom);
     }
     return this.handleInfixNodes(body);
@@ -184,8 +185,9 @@ Parser.prototype.handleInfixNodes = function(body) {
         var node = body[i];
         if (node.type === "infix") {
             if (overIndex !== -1) {
-                throw new ParseError("only one infix operator per group",
+                throw new ParseError(
-                    this.lexer, -1);
+                    "only one infix operator per group",
+                    node.value.token);
             }
             overIndex = i;
             funcName = node.value.replaceWith;
@@ -226,8 +228,8 @@ var SUPSUB_GREEDINESS = 1;
  * Handle a subscript or superscript with nice errors.
  */
 Parser.prototype.handleSupSubscript = function(name) {
-    var symbol = this.nextToken.text;
+    var symbolToken = this.nextToken;
-    var symPos = this.pos;
+    var symbol = symbolToken.text;
     this.consume();
     var group = this.parseGroup();
 
@@ -237,8 +239,7 @@ Parser.prototype.handleSupSubscript = function(name) {
         } else {
             throw new ParseError(
                 "Expected group after '" + symbol + "'",
-                this.lexer,
+                symbolToken
-                symPos + 1
             );
         }
     } else if (group.isFunction) {
@@ -250,8 +251,7 @@ Parser.prototype.handleSupSubscript = function(name) {
         } else {
             throw new ParseError(
                 "Got function '" + group.result + "' with no arguments " +
-                    "as " + name,
+                    "as " + name, symbolToken);
-                this.lexer, symPos + 1);
         }
     } else {
         return group.result;
@@ -319,7 +319,7 @@ Parser.prototype.parseAtom = function() {
             if (!base || base.type !== "op") {
                 throw new ParseError(
                     "Limit controls must follow a math operator",
-                    this.lexer, this.pos);
+                    lex);
             } else {
                 var limits = lex.text === "\\limits";
                 base.value.limits = limits;
@@ -329,15 +329,13 @@ Parser.prototype.parseAtom = function() {
         } else if (lex.text === "^") {
             // We got a superscript start
             if (superscript) {
-                throw new ParseError(
+                throw new ParseError("Double superscript", lex);
-                    "Double superscript", this.lexer, this.pos);
             }
             superscript = this.handleSupSubscript("superscript");
         } else if (lex.text === "_") {
             // We got a subscript start
             if (subscript) {
-                throw new ParseError(
+                throw new ParseError("Double subscript", lex);
-                    "Double subscript", this.lexer, this.pos);
             }
             subscript = this.handleSupSubscript("subscript");
         } else if (lex.text === "'") {
@@ -427,8 +425,7 @@ Parser.prototype.parseImplicitGroup = function() {
         var envName = begin.value.name;
         if (!environments.hasOwnProperty(envName)) {
             throw new ParseError(
-                "No such environment: " + envName,
+                "No such environment: " + envName, begin.value.nameGroup);
-                this.lexer, begin.value.namepos);
         }
         // Build the environment object. Arguments and other information will
         // be made available to the begin and end methods using properties.
@@ -438,19 +435,17 @@ Parser.prototype.parseImplicitGroup = function() {
             mode: this.mode,
             envName: envName,
             parser: this,
-            lexer: this.lexer,
             positions: args.pop(),
         };
         var result = env.handler(context, args);
         this.expect("\\end", false);
+        var endNameToken = this.nextToken;
         var end = this.parseFunction();
         if (end.value.name !== envName) {
             throw new ParseError(
                 "Mismatch: \\begin{" + envName + "} matched " +
                 "by \\end{" + end.value.name + "}",
-                this.lexer /* , end.value.namepos */);
+                endNameToken);
-            // TODO: Add position to the above line and adjust test case,
-            // requires #385 to get merged first
         }
         result.position = end.position;
         return result;
@@ -497,11 +492,12 @@ Parser.prototype.parseFunction = function(baseGroup) {
             if (this.mode === "text" && !funcData.allowedInText) {
                 throw new ParseError(
                     "Can't use function '" + func + "' in text mode",
-                    this.lexer, baseGroup.position);
+                    baseGroup.token);
             }
 
             var args = this.parseArguments(func, funcData);
-            var result = this.callFunction(func, args, args.pop());
+            var token = baseGroup.token;
+            var result = this.callFunction(func, args, args.pop(), token);
             return new ParseNode(result.type, result, this.mode);
         } else {
             return baseGroup.result;
@@ -514,12 +510,12 @@ Parser.prototype.parseFunction = function(baseGroup) {
 /**
  * Call a function handler with a suitable context and arguments.
  */
-Parser.prototype.callFunction = function(name, args, positions) {
+Parser.prototype.callFunction = function(name, args, positions, token) {
     var context = {
         funcName: name,
         parser: this,
-        lexer: this.lexer,
         positions: positions,
+        token: token,
     };
     return functions[name].handler(context, args);
 };
@@ -542,11 +538,12 @@ Parser.prototype.parseArguments = function(func, funcData) {
     var args = [];
 
     for (var i = 0; i < totalArgs; i++) {
+        var nextToken = this.nextToken;
         var argType = funcData.argTypes && funcData.argTypes[i];
         var arg;
         if (i < funcData.numOptionalArgs) {
             if (argType) {
-                arg = this.parseSpecialGroup(argType, true);
+                arg = this.parseGroupOfType(argType, true);
             } else {
                 arg = this.parseOptionalGroup();
             }
@@ -557,7 +554,7 @@ Parser.prototype.parseArguments = function(func, funcData) {
             }
         } else {
             if (argType) {
-                arg = this.parseSpecialGroup(argType);
+                arg = this.parseGroupOfType(argType);
             } else {
                 arg = this.parseGroup();
             }
@@ -569,8 +566,7 @@ Parser.prototype.parseArguments = function(func, funcData) {
                         false);
                 } else {
                     throw new ParseError(
-                        "Expected group after '" + func + "'",
+                        "Expected group after '" + func + "'", nextToken);
-                        this.lexer, this.pos);
                 }
             }
         }
@@ -583,8 +579,7 @@ Parser.prototype.parseArguments = function(func, funcData) {
             } else {
                 throw new ParseError(
                     "Got function '" + arg.result + "' as " +
-                    "argument to '" + func + "'",
+                    "argument to '" + func + "'", nextToken);
-                    this.lexer, this.pos - 1);
             }
         } else {
             argNode = arg.result;
@@ -600,64 +595,117 @@ Parser.prototype.parseArguments = function(func, funcData) {
 
 
 /**
- * Parses a group when the mode is changing. Takes a position, a new mode, and
+ * Parses a group when the mode is changing.
- * an outer mode that is used to parse the outside.
  *
  * @return {?ParseFuncOrArgument}
  */
-Parser.prototype.parseSpecialGroup = function(innerMode, optional) {
+Parser.prototype.parseGroupOfType = function(innerMode, optional) {
     var outerMode = this.mode;
     // Handle `original` argTypes
     if (innerMode === "original") {
         innerMode = outerMode;
     }
 
-    if (innerMode === "color" || innerMode === "size") {
+    if (innerMode === "color") {
-        // color and size modes are special because they should have braces and
+        return this.parseColorGroup(optional);
-        // should only lex a single symbol inside
+    }
-        var openBrace = this.nextToken;
+    if (innerMode === "size") {
-        if (optional && openBrace.text !== "[") {
+        return this.parseSizeGroup(optional);
-            // optional arguments should return null if they don't exist
-            return null;
-        }
-        // The call to expect will lex the token after the '{' in inner mode
-        this.mode = innerMode;
-        this.expect(optional ? "[" : "{");
-        var inner = this.nextToken;
-        this.mode = outerMode;
-        var data;
-        if (innerMode === "color") {
-            data = inner.text;
-        } else {
-            data = inner.data;
-        }
-        this.consume(); // consume the token stored in inner
-        this.expect(optional ? "]" : "}");
-        return new ParseFuncOrArgument(
-            new ParseNode(innerMode, data, outerMode),
-            false);
-    } else if (innerMode === "text") {
-        // text mode is special because it should ignore the whitespace before
-        // it
-        var whitespace = this.lexer.lex(this.pos, "whitespace");
-        this.pos = whitespace.position;
     }
 
+    this.switchMode(innerMode);
+    if (innerMode === "text") {
+        // text mode is special because it should ignore the whitespace before
+        // it
+        while (this.nextToken.text === " ") {
+            this.consume();
+        }
+    }
     // By the time we get here, innerMode is one of "text" or "math".
     // We switch the mode of the parser, recurse, then restore the old mode.
-    this.mode = innerMode;
-    this.nextToken = this.lexer.lex(this.pos, innerMode);
     var res;
     if (optional) {
         res = this.parseOptionalGroup();
     } else {
         res = this.parseGroup();
     }
-    this.mode = outerMode;
+    this.switchMode(outerMode);
-    this.nextToken = this.lexer.lex(this.pos, outerMode);
     return res;
 };
 
+/**
+ * Parses a group, essentially returning the string formed by the
+ * brace-enclosed tokens plus some position information.
+ *
+ * @param {string} modeName  Used to describe the mode in error messages
+ * @param {boolean} optional  Whether the group is optional or required
+ */
+Parser.prototype.parseStringGroup = function(modeName, optional) {
+    if (optional && this.nextToken.text !== "[") {
+        return null;
+    }
+    var outerMode = this.mode;
+    this.mode = "text";
+    this.expect(optional ? "[" : "{");
+    var str = "";
+    var firstToken = this.nextToken;
+    var lastToken = firstToken;
+    while (this.nextToken.text !== (optional ? "]" : "}")) {
+        if (this.nextToken.text === "EOF") {
+            throw new ParseError(
+                "Unexpected end of input in " + modeName,
+                firstToken.range(this.nextToken, str));
+        }
+        lastToken = this.nextToken;
+        str += lastToken.text;
+        this.consume();
+    }
+    this.mode = outerMode;
+    this.expect(optional ? "]" : "}");
+    return firstToken.range(lastToken, str);
+};
+
+/**
+ * Parses a color description.
+ */
+Parser.prototype.parseColorGroup = function(optional) {
+    var res = this.parseStringGroup("color", optional);
+    if (!res) {
+        return null;
+    }
+    var match = (/^(#[a-z0-9]+|[a-z]+)$/i).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid color: '" + res.text + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", match[0], this.mode),
+        false);
+};
+
+/**
+ * Parses a size specification, consisting of magnitude and unit.
+ */
+Parser.prototype.parseSizeGroup = function(optional) {
+    var res = this.parseStringGroup("size", optional);
+    if (!res) {
+        return null;
+    }
+    var match = (/(-?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/).exec(res.text);
+    if (!match) {
+        throw new ParseError("Invalid size: '" + res.text + "'", res);
+    }
+    var data = {
+        number: +(match[1] + match[2]), // sign + magnitude, cast to number
+        unit: match[3],
+    };
+    if (data.unit !== "em" && data.unit !== "ex") {
+        throw new ParseError("Invalid unit: '" + data.unit + "'", res);
+    }
+    return new ParseFuncOrArgument(
+        new ParseNode("color", data, this.mode),
+        false);
+};
+
 /**
  * Parses a group, which is either a single nucleus (like "x") or an expression
  * in braces (like "{x+y}")
@@ -665,15 +713,18 @@ Parser.prototype.parseSpecialGroup = function(innerMode, optional) {
  * @return {?ParseFuncOrArgument}
  */
 Parser.prototype.parseGroup = function() {
+    var firstToken = this.nextToken;
     // Try to parse an open brace
     if (this.nextToken.text === "{") {
         // If we get a brace, parse an expression
         this.consume();
         var expression = this.parseExpression(false);
+        var lastToken = this.nextToken;
         // Make sure we get a close brace
         this.expect("}");
         return new ParseFuncOrArgument(
-            new ParseNode("ordgroup", expression, this.mode),
+            new ParseNode("ordgroup", expression, this.mode,
+                          firstToken, lastToken),
             false);
     } else {
         // Otherwise, just return a nucleus
@@ -687,15 +738,18 @@ Parser.prototype.parseGroup = function() {
  * @return {?ParseFuncOrArgument}
  */
 Parser.prototype.parseOptionalGroup = function() {
+    var firstToken = this.nextToken;
     // Try to parse an open bracket
     if (this.nextToken.text === "[") {
         // If we get a brace, parse an expression
         this.consume();
         var expression = this.parseExpression(false, "]");
+        var lastToken = this.nextToken;
         // Make sure we get a close bracket
         this.expect("]");
         return new ParseFuncOrArgument(
-            new ParseNode("ordgroup", expression, this.mode),
+            new ParseNode("ordgroup", expression, this.mode,
+                          firstToken, lastToken),
             false);
     } else {
         // Otherwise, return null,
@@ -718,15 +772,15 @@ Parser.prototype.parseSymbol = function() {
         // say that it is a function.
         return new ParseFuncOrArgument(
             nucleus.text,
-            true);
+            true, nucleus);
     } else if (symbols[this.mode][nucleus.text]) {
         this.consume();
         // Otherwise if this is a no-argument function, find the type it
         // corresponds to in the symbols map
         return new ParseFuncOrArgument(
             new ParseNode(symbols[this.mode][nucleus.text].group,
-                          nucleus.text, this.mode),
+                          nucleus.text, this.mode, nucleus),
-            false);
+            false, nucleus);
     } else {
         return null;
     }

src/Settings.js

@@ -23,6 +23,7 @@ function Settings(options) {
     this.displayMode = get(options.displayMode, false);
     this.throwOnError = get(options.throwOnError, true);
     this.errorColor = get(options.errorColor, "#cc0000");
+    this.macros = options.macros || {};
 }
 
 module.exports = Settings;

src/environments.js

@@ -28,10 +28,8 @@ function parseArray(parser, result) {
             row = [];
             body.push(row);
         } else {
-            // TODO: Clean up the following hack once #385 got merged
-            var pos = Math.min(parser.pos + 1, parser.lexer._input.length);
             throw new ParseError("Expected & or \\\\ or \\end",
-                                 parser.lexer, pos);
+                                 parser.nextToken);
         }
     }
     result.body = body;
@@ -106,7 +104,7 @@ defineEnvironment("array", {
         }
         throw new ParseError(
             "Unknown column alignment: " + node.value,
-            context.lexer, context.positions[1]);
+            node);
     });
     var res = {
         type: "array",

src/functions.js

@@ -55,6 +55,7 @@ var ParseError = require("./ParseError");
  *                     should parse. If the optional arguments aren't found,
  *                     `null` will be passed to the handler in their place.
  *                     (default 0)
+ *  - infix: (optional) Must be true if the function is an infix operator.
  *
  * The last argument is that implementation, the handler for the function(s).
  * It is called to handle these functions and their arguments.
@@ -91,6 +92,7 @@ function defineFunction(names, props, handler) {
         greediness: (props.greediness === undefined) ? 1 : props.greediness,
         allowedInText: !!props.allowedInText,
         numOptionalArgs: props.numOptionalArgs || 0,
+        infix: !!props.infix,
         handler: handler,
     };
     for (var i = 0; i < names.length; ++i) {
@@ -456,8 +458,7 @@ defineFunction([
     if (!utils.contains(delimiters, delim.value)) {
         throw new ParseError(
             "Invalid delimiter: '" + delim.value + "' after '" +
-                context.funcName + "'",
+            context.funcName + "'", delim);
-            context.lexer, context.positions[1]);
     }
 
     // \left and \right are caught somewhere in Parser.js, which is
@@ -536,6 +537,7 @@ defineFunction([
 // Infix generalized fractions
 defineFunction(["\\over", "\\choose"], {
     numArgs: 0,
+    infix: true,
 }, function(context) {
     var replaceWith;
     switch (context.funcName) {
@@ -551,6 +553,7 @@ defineFunction(["\\over", "\\choose"], {
     return {
         type: "infix",
         replaceWith: replaceWith,
+        token: context.token,
     };
 });
 
@@ -574,9 +577,7 @@ defineFunction(["\\begin", "\\end"], {
 }, function(context, args) {
     var nameGroup = args[0];
     if (nameGroup.type !== "ordgroup") {
-        throw new ParseError(
+        throw new ParseError("Invalid environment name", nameGroup);
-            "Invalid environment name",
-            context.lexer, context.positions[1]);
     }
     var name = "";
     for (var i = 0; i < nameGroup.value.length; ++i) {
@@ -585,6 +586,6 @@ defineFunction(["\\begin", "\\end"], {
     return {
         type: "environment",
         name: name,
-        namepos: context.positions[1],
+        nameGroup: nameGroup,
     };
 });

src/parseData.js

@@ -1,10 +1,29 @@
 /**
  * The resulting parse tree nodes of the parse tree.
+ *
+ * It is possible to provide position information, so that a ParseNode can
+ * fulfil a role similar to a Token in error reporting.
+ * For details on the corresponding properties see Token constructor.
+ * Providing such information can lead to better error reporting.
+ *
+ * @param {string}  type       type of node, like e.g. "ordgroup"
+ * @param {?object} value      type-specific representation of the node
+ * @param {string}  mode       parse mode in action for this node,
+ *                             "math" or "text"
+ * @param {Token=} firstToken  first token of the input for this node,
+ *                             will omit position information if unset
+ * @param {Token=} lastToken   last token of the input for this node,
+ *                             will default to firstToken if unset
  */
-function ParseNode(type, value, mode) {
+function ParseNode(type, value, mode, firstToken, lastToken) {
     this.type = type;
     this.value = value;
     this.mode = mode;
+    if (firstToken && (!lastToken || lastToken.lexer === firstToken.lexer)) {
+        this.lexer = firstToken.lexer;
+        this.start = firstToken.start;
+        this.end = (lastToken || firstToken).end;
+    }
 }
 
 module.exports = {

static/main.js

@@ -10,13 +10,9 @@ function init() {
     }
 
     if ("addEventListener" in permalink) {
-        permalink.addEventListener("click", function() {
+        permalink.addEventListener("click", setSearch);
-            window.location.search = "?text=" + encodeURIComponent(input.value);
-        });
     } else {
-        permalink.attachEvent("click", function() {
+        permalink.attachEvent("click", setSearch);
-            window.location.search = "?text=" + encodeURIComponent(input.value);
-        });
     }
 
     var match = (/(?:^\?|&)text=([^&]*)/).exec(window.location.search);
@@ -24,11 +20,26 @@ function init() {
         input.value = decodeURIComponent(match[1]);
     }
 
+    var macros = {};
+    var options = {};
+    var macroRegex = /(?:^\?|&)(?:\\|%5[Cc])([A-Za-z]+)=([^&]*)/g;
+    var macroString = "";
+    while ((match = macroRegex.exec(window.location.search)) !== null) {
+        options.macros = macros;
+        macros["\\" + match[1]] = decodeURIComponent(match[2]);
+        macroString += "&" + match[0].substr(1);
+    }
+
     reprocess();
 
+    function setSearch() {
+        window.location.search =
+            "?text=" + encodeURIComponent(input.value) + macroString;
+    }
+
     function reprocess() {
         try {
-            katex.render(input.value, math);
+            katex.render(input.value, math, options);
         } catch (e) {
             if (e.__proto__ == katex.ParseError.prototype) {
                 console.error(e);

test/errors-spec.js

@@ -61,16 +61,15 @@ beforeEach(function() {
 describe("Parser:", function() {
 
     describe("#handleInfixNodes", function() {
-        // TODO: The position information here is broken, should be fixed.
         it("rejects repeated infix operators", function() {
             expect("1\\over 2\\over 3").toFailWithParseError(
-                   "only one infix operator per group at position -1: " +
+                   "only one infix operator per group at position 9: " +
-                   "1\\over 2\\over ");
+                   "1\\over 2\\̲o̲v̲e̲r̲ 3");
         });
         it("rejects conflicting infix operators", function() {
             expect("1\\over 2\\choose 3").toFailWithParseError(
-                   "only one infix operator per group at position -1: " +
+                   "only one infix operator per group at position 9: " +
-                   "1\\over 2\\choos");
+                   "1\\over 2\\̲c̲h̲o̲o̲s̲e̲ 3");
         });
     });
 
@@ -91,84 +90,85 @@ describe("Parser:", function() {
     });
 
     describe("#parseAtom", function() {
-        // TODO: The positions in the following error messages appear to be
-        // off by one, i.e. they should be one character later.
         it("rejects \\limits without operator", function() {
             expect("\\alpha\\limits\\omega").toFailWithParseError(
                    "Limit controls must follow a math operator" +
-                   " at position 6: \\alpha̲\\limits\\omega");
+                   " at position 7: \\alpha\\̲l̲i̲m̲i̲t̲s̲\\omega");
         });
         it("rejects \\limits at the beginning of the input", function() {
             expect("\\limits\\omega").toFailWithParseError(
                    "Limit controls must follow a math operator" +
-                   " at position 0: ̲\\limits\\omega");
+                   " at position 1: \\̲l̲i̲m̲i̲t̲s̲\\omega");
         });
         it("rejects double superscripts", function() {
             expect("1^2^3").toFailWithParseError(
-                   "Double superscript at position 3: 1^2̲^3");
+                   "Double superscript at position 4: 1^2^̲3");
             expect("1^{2+3}_4^5").toFailWithParseError(
-                   "Double superscript at position 9: 1^{2+3}_4̲^5");
+                   "Double superscript at position 10: 1^{2+3}_4^̲5");
         });
         it("rejects double subscripts", function() {
             expect("1_2_3").toFailWithParseError(
-                   "Double subscript at position 3: 1_2̲_3");
+                   "Double subscript at position 4: 1_2_̲3");
             expect("1_{2+3}^4_5").toFailWithParseError(
-                   "Double subscript at position 9: 1_{2+3}^4̲_5");
+                   "Double subscript at position 10: 1_{2+3}^4_̲5");
         });
     });
 
     describe("#parseImplicitGroup", function() {
         it("reports unknown environments", function() {
             expect("\\begin{foo}bar\\end{foo}").toFailWithParseError(
-                   "No such environment: foo at position 11:" +
+                   "No such environment: foo at position 7:" +
-                   " \\begin{foo}̲bar\\end{foo}");
+                   " \\begin{̲f̲o̲o̲}̲bar\\end{foo}");
         });
         it("reports mismatched environments", function() {
             expect("\\begin{pmatrix}1&2\\\\3&4\\end{bmatrix}+5")
                 .toFailWithParseError(
-                   "Mismatch: \\begin{pmatrix} matched by \\end{bmatrix}");
+                   "Mismatch: \\begin{pmatrix} matched by \\end{bmatrix}" +
+                   " at position 24: …matrix}1&2\\\\3&4\\̲e̲n̲d̲{bmatrix}+5");
         });
     });
 
     describe("#parseFunction", function() {
         it("rejects math-mode functions in text mode", function() {
-            // TODO: The position info is missing here
             expect("\\text{\\sqrt2 is irrational}").toFailWithParseError(
-                   "Can't use function '\\sqrt' in text mode");
+                "Can't use function '\\sqrt' in text mode" +
+                " at position 7: \\text{\\̲s̲q̲r̲t̲2 is irrational…");
         });
     });
 
     describe("#parseArguments", function() {
         it("complains about missing argument at end of input", function() {
             expect("2\\sqrt").toFailWithParseError(
-                   "Expected group after '\\sqrt' at position 6: 2\\sqrt̲");
+                   "Expected group after '\\sqrt' at end of input: 2\\sqrt");
         });
         it("complains about missing argument at end of group", function() {
             expect("1^{2\\sqrt}").toFailWithParseError(
-                   "Expected group after '\\sqrt' at position 9: 1^{2\\sqrt̲}");
+                   "Expected group after '\\sqrt'" +
+                   " at position 10: 1^{2\\sqrt}̲");
         });
         it("complains about functions as arguments to others", function() {
             // TODO: The position looks pretty wrong here
             expect("\\sqrt\\over2").toFailWithParseError(
                    "Got function '\\over' as argument to '\\sqrt'" +
-                   " at position 9: \\sqrt\\ove̲r2");
+                   " at position 6: \\sqrt\\̲o̲v̲e̲r̲2");
         });
     });
 
     describe("#parseArguments", function() {
         it("complains about missing argument at end of input", function() {
             expect("2\\sqrt").toFailWithParseError(
-                   "Expected group after '\\sqrt' at position 6: 2\\sqrt̲");
+                   "Expected group after '\\sqrt' at end of input: 2\\sqrt");
         });
         it("complains about missing argument at end of group", function() {
             expect("1^{2\\sqrt}").toFailWithParseError(
-                   "Expected group after '\\sqrt' at position 9: 1^{2\\sqrt̲}");
+                   "Expected group after '\\sqrt'" +
+                   " at position 10: 1^{2\\sqrt}̲");
         });
         it("complains about functions as arguments to others", function() {
             // TODO: The position looks pretty wrong here
             expect("\\sqrt\\over2").toFailWithParseError(
                    "Got function '\\over' as argument to '\\sqrt'" +
-                   " at position 9: \\sqrt\\ove̲r2");
+                   " at position 6: \\sqrt\\̲o̲v̲e̲r̲2");
         });
     });
 
@@ -183,12 +183,12 @@ describe("Parser.expect calls:", function() {
         });
         it("complains about extra \\end", function() {
             expect("x\\end{matrix}").toFailWithParseError(
-                   "Expected 'EOF', got '\\end' at position 5:" +
+                   "Expected 'EOF', got '\\end' at position 2:" +
-                   " x\\end̲{matrix}");
+                   " x\\̲e̲n̲d̲{matrix}");
         });
         it("complains about top-level \\\\", function() {
             expect("1\\\\2").toFailWithParseError(
-                   "Expected 'EOF', got '\\\\' at position 3: 1\\\\̲2");
+                   "Expected 'EOF', got '\\\\' at position 2: 1\\̲\\̲2");
         });
         it("complains about top-level &", function() {
             expect("1&2").toFailWithParseError(
@@ -199,8 +199,8 @@ describe("Parser.expect calls:", function() {
     describe("#parseImplicitGroup expecting \\right", function() {
         it("rejects missing \\right", function() {
             expect("\\left(1+2)").toFailWithParseError(
-                   "Expected '\\right', got 'EOF' at position 10:" +
+                   "Expected '\\right', got 'EOF' at end of input:" +
-                   " \\left(1+2)̲");
+                   " \\left(1+2)");
         });
         it("rejects incorrectly scoped \\right", function() {
             expect("{\\left(1+2}\\right)").toFailWithParseError(
@@ -224,32 +224,42 @@ describe("Parser.expect calls:", function() {
         });
         // Can't test for the [ of an optional group since it's optional
         it("complains about missing } for color", function() {
-            expect("\\color{#ffffff {text}").toFailWithParseError(
+            expect("\\color{#ffffff{text}").toFailWithParseError(
-                   "Expected '}', got '{' at position 16:" +
+                   "Invalid color: '#ffffff{text' at position 8:" +
-                   " color{#ffffff {̲text}");
+                   " \\color{#̲f̲f̲f̲f̲f̲f̲{̲t̲e̲x̲t̲}");
         });
         it("complains about missing ] for size", function() {
             expect("\\rule[1em{2em}{3em}").toFailWithParseError(
-                   "Expected ']', got '{' at position 10:" +
+                   "Unexpected end of input in size" +
-                   " \\rule[1em{̲2em}{3em}");
+                   " at position 7: \\rule[1̲e̲m̲{̲2̲e̲m̲}̲{̲3̲e̲m̲}̲");
+        });
+        it("complains about missing ] for size at end of input", function() {
+            expect("\\rule[1em").toFailWithParseError(
+                   "Unexpected end of input in size" +
+                   " at position 7: \\rule[1̲e̲m̲");
+        });
+        it("complains about missing } for color at end of input", function() {
+            expect("\\color{#123456").toFailWithParseError(
+                   "Unexpected end of input in color" +
+                   " at position 8: \\color{#̲1̲2̲3̲4̲5̲6̲");
         });
     });
 
     describe("#parseGroup expecting }", function() {
         it("at end of file", function() {
             expect("\\sqrt{2").toFailWithParseError(
-                   "Expected '}', got 'EOF' at position 7: \\sqrt{2̲");
+                   "Expected '}', got 'EOF' at end of input: \\sqrt{2");
         });
     });
 
     describe("#parseOptionalGroup expecting ]", function() {
         it("at end of file", function() {
             expect("\\sqrt[3").toFailWithParseError(
-                   "Expected ']', got 'EOF' at position 7: \\sqrt[3̲");
+                   "Expected ']', got 'EOF' at end of input: \\sqrt[3");
         });
         it("before group", function() {
             expect("\\sqrt[3{2}").toFailWithParseError(
-                   "Expected ']', got 'EOF' at position 10: \\sqrt[3{2}̲");
+                   "Expected ']', got 'EOF' at end of input: \\sqrt[3{2}");
         });
     });
 
@@ -260,13 +270,13 @@ describe("environments.js:", function() {
     describe("parseArray", function() {
         it("rejects missing \\end", function() {
             expect("\\begin{matrix}1").toFailWithParseError(
-                   "Expected & or \\\\ or \\end at position 15:" +
+                   "Expected & or \\\\ or \\end at end of input:" +
-                   " \\begin{matrix}1̲");
+                   " \\begin{matrix}1");
         });
         it("rejects incorrectly scoped \\end", function() {
             expect("{\\begin{matrix}1}\\end{matrix}").toFailWithParseError(
                    "Expected & or \\\\\ or \\end at position 17:" +
-                   " begin{matrix}1}̲\\end{matrix}");
+                   " …\\begin{matrix}1}̲\\end{matrix}");
         });
     });
 
@@ -274,8 +284,8 @@ describe("environments.js:", function() {
         it("rejects unknown column types", function() {
             // TODO: The error position here looks strange
             expect("\\begin{array}{cba}\\end{array}").toFailWithParseError(
-                   "Unknown column alignment: b at position 18:" +
+                   "Unknown column alignment: b at position 16:" +
-                   " gin{array}{cba}̲\\end{array}");
+                   " \\begin{array}{cb̲a}\\end{array}");
         });
     });
 
@@ -298,9 +308,8 @@ describe("functions.js:", function() {
 
     describe("\\begin and \\end", function() {
         it("reject invalid environment names", function() {
-            expect("\\begin{foobar}\\end{foobar}").toFailWithParseError(
+            expect("\\begin x\\end y").toFailWithParseError(
-                   "No such environment: foobar at position 14:" +
+                   "Invalid environment name at position 8: \\begin x̲\\end y");
-                   " \\begin{foobar}̲\\end{foobar}");
         });
     });
 
@@ -311,34 +320,35 @@ describe("Lexer:", function() {
     describe("#_innerLex", function() {
         it("rejects lone surrogate char", function() {
             expect("\udcba").toFailWithParseError(
-                   "Unexpected character: '\udcba' at position 0:" +
+                   "Unexpected character: '\udcba' at position 1:" +
-                    " \u0332\udcba");
+                    " \udcba\u0332");
         });
         it("rejects lone backslash at end of input", function() {
             expect("\\").toFailWithParseError(
-                   "Unexpected character: '\\' at position 0: ̲\\");
+                   "Unexpected character: '\\' at position 1: \\̲");
         });
     });
 
     describe("#_innerLexColor", function() {
         it("reject hex notation without #", function() {
             expect("\\color{1a2b3c}{foo}").toFailWithParseError(
-                   "Invalid color at position 7: \\color{̲1a2b3c}{foo}");
+                   "Invalid color: '1a2b3c'" +
+                   " at position 8: \\color{1̲a̲2̲b̲3̲c̲}{foo}");
         });
     });
 
     describe("#_innerLexSize", function() {
         it("reject size without unit", function() {
             expect("\\rule{0}{2em}").toFailWithParseError(
-                   "Invalid size at position 6: \\rule{̲0}{2em}");
+                   "Invalid size: '0' at position 7: \\rule{0̲}{2em}");
         });
         it("reject size with bogus unit", function() {
             expect("\\rule{1au}{2em}").toFailWithParseError(
-                   "Invalid unit: 'au' at position 6: \\rule{̲1au}{2em}");
+                   "Invalid unit: 'au' at position 7: \\rule{1̲a̲u̲}{2em}");
         });
         it("reject size without number", function() {
             expect("\\rule{em}{2em}").toFailWithParseError(
-                   "Invalid size at position 6: \\rule{̲em}{2em}");
+                   "Invalid size: 'em' at position 7: \\rule{e̲m̲}{2em}");
         });
     });
 

test/katex-spec.js

@@ -57,8 +57,39 @@ var getParsed = function(expr, settings) {
     return parseTree(expr, usedSettings);
 };
 
+var stripPositions = function(expr) {
+    if (typeof expr !== "object" || expr === null) {
+        return expr;
+    }
+    if (expr.lexer && typeof expr.start === "number") {
+        delete expr.lexer;
+        delete expr.start;
+        delete expr.end;
+    }
+    Object.keys(expr).forEach(function(key) {
+        stripPositions(expr[key]);
+    });
+    return expr;
+};
+
+var parseAndSetResult = function(expr, result, settings) {
+    try {
+        return parseTree(expr, settings || defaultSettings);
+    } catch (e) {
+        result.pass = false;
+        if (e instanceof ParseError) {
+            result.message = "'" + expr + "' failed " +
+                "parsing with error: " + e.message;
+        } else {
+            result.message = "'" + expr + "' failed " +
+                "parsing with unknown error: " + e.message;
+        }
+    }
+};
+
 beforeEach(function() {
     jasmine.addMatchers({
+
         toParse: function() {
             return {
                 compare: function(actual, settings) {
@@ -68,20 +99,7 @@ beforeEach(function() {
                         pass: true,
                         message: "'" + actual + "' succeeded parsing",
                     };
-
+                    parseAndSetResult(actual, result, usedSettings);
-                    try {
-                        parseTree(actual, usedSettings);
-                    } catch (e) {
-                        result.pass = false;
-                        if (e instanceof ParseError) {
-                            result.message = "'" + actual + "' failed " +
-                                "parsing with error: " + e.message;
-                        } else {
-                            result.message = "'" + actual + "' failed " +
-                                "parsing with unknown error: " + e.message;
-                        }
-                    }
-
                     return result;
                 },
             };
@@ -145,6 +163,36 @@ beforeEach(function() {
                 },
             };
         },
+
+        toParseLike: function(util, baton) {
+            return {
+                compare: function(actual, expected) {
+                    var result = {
+                        pass: true,
+                        message: "Parse trees of '" + actual +
+                            "' and '" + expected + "' are equivalent",
+                    };
+
+                    var actualTree = parseAndSetResult(actual, result);
+                    if (!actualTree) {
+                        return result;
+                    }
+                    var expectedTree = parseAndSetResult(expected, result);
+                    if (!expectedTree) {
+                        return result;
+                    }
+                    stripPositions(actualTree);
+                    stripPositions(expectedTree);
+                    if (!util.equals(actualTree, expectedTree, baton)) {
+                        result.pass = false;
+                        result.message = "Parse trees of '" + actual +
+                            "' and '" + expected + "' are not equivalent";
+                    }
+                    return result;
+                },
+            };
+        },
+
     });
 });
 
@@ -154,8 +202,8 @@ describe("A parser", function() {
     });
 
     it("should ignore whitespace", function() {
-        var parseA = getParsed("    x    y    ");
+        var parseA = stripPositions(getParsed("    x    y    "));
-        var parseB = getParsed("xy");
+        var parseB = stripPositions(getParsed("xy"));
         expect(parseA).toEqual(parseB);
     });
 });
@@ -340,8 +388,8 @@ describe("A subscript and superscript parser", function() {
     });
 
     it("should produce the same thing regardless of order", function() {
-        var parseA = getParsed("x^2_3");
+        var parseA = stripPositions(getParsed("x^2_3"));
-        var parseB = getParsed("x_3^2");
+        var parseB = stripPositions(getParsed("x_3^2"));
 
         expect(parseA).toEqual(parseB);
     });
@@ -623,6 +671,13 @@ describe("An over parser", function() {
         expect(parse.value.denom).toBeDefined();
     });
 
+    it("should handle \\textstyle correctly", function() {
+        expect("\\textstyle 1 \\over 2")
+            .toParseLike("\\frac{\\textstyle 1}{2}");
+        expect("{\\textstyle 1} \\over 2")
+            .toParseLike("\\frac{\\textstyle 1}{2}");
+    });
+
     it("should handle nested factions", function() {
         var nestedOverExpression = "{1 \\over 2} \\over 3";
         var parse = getParsed(nestedOverExpression)[0];
@@ -1523,7 +1578,7 @@ describe("A markup generator", function() {
 
 describe("A parse tree generator", function() {
     it("generates a tree", function() {
-        var tree = katex.__parse("\\sigma^2");
+        var tree = stripPositions(katex.__parse("\\sigma^2"));
         expect(JSON.stringify(tree)).toEqual(JSON.stringify([
             {
                 "type": "supsub",
@@ -1802,3 +1857,24 @@ describe("The symbol table integraty", function() {
             .toEqual(getBuilt("\\left\\lt\\frac{1}{x}\\right\\gt"));
     });
 });
+
+describe("A macro expander", function() {
+
+    var compareParseTree = function(actual, expected, macros) {
+        var settings = new Settings({macros: macros});
+        actual = stripPositions(parseTree(actual, settings));
+        expected = stripPositions(parseTree(expected, defaultSettings));
+        expect(actual).toEqual(expected);
+    };
+
+    it("should produce individual tokens", function() {
+        compareParseTree("e^\\foo", "e^1 23", {"\\foo": "123"});
+    });
+
+    it("should allow for multiple expansion", function() {
+        compareParseTree("1\\foo2", "1aa2", {
+            "\\foo": "\\bar\\bar",
+            "\\bar": "a",
+        });
+    });
+});