Grammar

MiniLatex has a context-sensitive grammar which is be described below. The text below was written one year ago. It is incomplete, has errors, and needs to be rethought.

Terminals

  • spaces => sp* where sp is the space character.

  • ws => { sp, nl }*, where nl is the newline character

  • reservedWord => { \backslash begin, \backslash end, \backslash item \}

  • word => (Char - {sp, nl, backslash, dollarSign })+ -- Nonempty strings without whitespace characters, backslashes or dollar signs

  • specialWord => (Char - \{sp, nl, backslash, dollarSign, \& \})+

  • macroName => (Char - {sp, nl, , leftBrace, backslash})+ - reservedWord

Associated with these terminals are productions Word => word, Identifier => identifier, etc. We shall not list all of these, but rather just the terminal and a description of it.

Non-Terminals

  • Arg -- arguments for macros

  • BeginWord -- produce \begin{identifier} phrase for LaTeX environments.

  • Comment -- LaTeX comments -- % foo, bar

  • IMath -- inline mathematical text, as in $... $

  • Env-- LaTeX environments \begin{foo}.. \end{foo}

  • EnvName -- produce an environment name such as foo, or theorem.

  • Identifier -- a lowercase alphanumeric string beginning with a letter.

  • Item -- item in an enumeration or itemization environemnt

  • LatexExpression -- a custom type (algebraic data type)

  • LatexList -- a list of LatexExpressions

  • Macro -- a LaTeX macro of zero or more arguments.

  • MacroName - an identifier

  • Words - a string obtained by joining a list of Word with spaces.

Productions

The MiniLaTeX grammar is defined by its productions. This set is fairly small, just 24 if one discounts productions which could be viewed as performing lexical analysis -- the recognition of identifiers, for instance. Of the 24 productions, 11 are for general nonterminals, 7 are for environments of various kinds, and 5 are for the tabular environment. With two exceptions we present them in EBNF form. The topmost productions are for LatexList and LatexExpression

LatexList => LatexExpression+

LatexExpression => Words | Comment | IMath | DMath | Macro | Env

The productions for the first four non-terminals on the right-hand side of the above are non-recursive, straightforward, and all result in a terminal. The terminal is of the form Constructor x, where the first term is a constructor for LatexExpression and x is a string. When A is a non-terminal, A is the corresponding constructor.

Words => LXString (join Word+)

where a Word is any sequence of characters which is not a whitespace character, ∖, or \dollar, and where join is the function which joins the elements of a list of strings by single spaces to produce a string.

Comment => Comment (Char−{\n})∗
IMath => IMath Line'

where Line' is Line with no occurernce of \dollar

DMath => DMath Line′ | DMath Line′′

where Line′′ is Line with no occurrence of of a right bracket.

Macros and Environments

Let us now treat the two recursive productions. They generate LaTeX macros and environments.

Macro => Macro Macroname Arg∗

Arg => Words | IMath | Macro

Because of the use of constructions of the form

\begin{envName}
...
\end{envName}

the production of environments requires the use of a context-sensitive grammar. Here envName may take on arbitrarily many values, and, in particular, values not known at the time the parser is written. Note that the production (??) below has a nonterminal followed by a terminal on the right-hand side, while productions like Env theorem, Env whatever have nonterminal followed by a terminal on the left-hand side. The presence of a terminal on the left-hand side tells us that the grammar is context-sensitive. Parsing environments also requires potentially unbounded look-ahead, so the grammar is LL(infinity). In fact, in any real applation, it is LL(N) where N is the maximumn number of characters in a logical paragraph. The paragraph-based parsing strategy pays dividends here.

EnvName => Env identifier

Env itemize => Environment itemize Item+

Env enumerate => Environment enumerate Item+

Env tabular => Environment tabular

TableEnv passThroughIdentifier => Environment passThroughIdentifier

TextEnv genericIdentifier => Environment genericIdentifier LatexList

The set of all envNames is decomposed as follows:

specialIdentifier =>{itemize, enumerate, tabular}

passThroughIdentifier => {equation, align, eqnarray, verbatim, verse}

genericIdentifier => identifier − specialIdentifier − passThroughIdentifier

Tabular Environment

The tabular environment also requires a context-sensitive grammar.

Table =>TableHead (TableRows ncols)+

TableRows ncols => TableCells^ncols

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