Efficient ambiguous parsing of mathematical formulae


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First attempt: regular expressions

The Theory of Parsing, Translation, and Compiling (Volume 1): Parsing - PDF Free Download

And there are applications that require the ability to select among and manipulate very large sets of ambiguous parses. This post will introduce an experiment.


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Marpa in fact seems to have some potential for NLP. Writing an efficient ASF in not a simple matter. The naive implementation is to generate complete set of fully expanded abstract syntax trees AST's. This approach consumes resources that can become exponential in the size of the input. Translation: the naive implementation quickly becomes unuseably slow. Marpa optimizes by aggressively identifying identical subtrees of the AST's. Especially in highly ambiguous parses, many subtrees are identical, and this optimization is often a big win. It is a long sentence, possibly the longest, from her Notes -- words.

LR Parsing - LR (0) item - LR (0) Parsing table solved example -Compiler Design Lectures for Gate

A disadvantage of this example is that it is not typical of normal NLP. By modern standards it is an unusually long and complex sentence. An advantage of it, and my reason for the choice, is that it stresses the parser. The "Note A" from which this sentence is taken is one of Ada's notes on a translation of a paper on the work of her mentor and colleague, Charles Babbage. Ada's "Notes" are longer than the original paper, and far more important. In these "Notes" Ada makes the first distinction between a computer and a calculator, and between software and hardware.

In their collaboration, Babbage did all of the hardware design, and he wrote most of the actual programs in her paper. But these two revolutionary ideas, and their elaboration, are Ada's. Why would Babbage ignore obvious implications of his own invention? The answer is that, while these implications are obvious to us, they simply did not fit into the view of the world.

Computational Linguistics

In those days, algebra was leading-edge math. The ability to manipulate equations was considered an extremely advanced form of reason. For Babbage and his contemporaries, that sort of ability to reason certainly suggested the ability to distinguish between good and evil, and this in turn suggested possession of a soul.

Ada's "Notes" were written 20 years after Mary Shelly, while visiting Ada's father in Switzerland, wrote the novel Frankenstein. For Ada's contemporaries, announcing that you planned to create a machine that composed music, or did advanced mathematical reasoning, was not very different from announcing that you planned to assemble a human being in your lab.

Ada was the daughter of the poet Byron.

The problem with LaTeX

For her, pushing boundaries was a family tradition. Babbage was happy to leave these matters to Ada. As Babbage's son put it , his father. Ada's notes are worth reading, but the modern reader has to be prepared to face several layers of difficulty: They are in Victorian English. In modern English, a long complex sentence is usually considered a editing failure.

In Ada's time, following Greek and Roman examples, a periodic sentence was considered especially appropriate when making an important point.

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And good literary style and good scientific style were considered one and the same. They are mathematical, and none of math is of the kind currently studied by programmers. Ada has literally no prior literature on software to build on, and has to invent her terminology. It is almost never the modern terminology, and it can be hard to guess how it relates to modern terminology. For example, does Ada forsee objects, methods and classes?

Ada speaks of computing both symbolic results and numeric data, and attaching one to the other. She clearly understands that the symbolic results can represent operations. Ada also clearly understands that numeric data can represent not just the numbers themselves, but notes, positions in a loom, or computer operations. So we have arbitrary data, tagged with symbols that can be both names and operations.

But are these objects? Finally, she associates mathematics with philosophy. In her day, this was expected. Unfortunately, modern readers now often see that sort of discussion as irrelevant, or even as a sign of inability to come to the point.

Parsing Ada Lovelace

Ada's sentence may look like what happens when two pickups carrying out-of-date dictionaries to the landfill run into each other on the way. But there is, in fact, a good deal of structure and meaning in all those words. The theory of parsing, translation, and compiling. Volume 1: Parsing. Read more. LR Parsing: Theory and Practice. Grammars and parsing. Dependency parsing. Parsing TeX into mathematics. Inductive Dependency Parsing. Pro Perl Parsing Pro.

Pro Perl Parsing. Generalized LR Parsing.


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    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae
    Efficient ambiguous parsing of mathematical formulae Efficient ambiguous parsing of mathematical formulae

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