Efficient Ambiguous Parsing of Mathematical Formulae

  • Claudio Sacerdoti Coen
  • Stefano Zacchiroli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3119)


Mathematical notation has the characteristic of being ambiguous: operators can be overloaded and information that can be deduced is often omitted. Mathematicians are used to this ambiguity and can easily disambiguate a formula making use of the context and of their ability to find the right interpretation.

Software applications that have to deal with formulae usually avoid these issues by fixing an unambiguous input notation. This solution is annoying for mathematicians because of the resulting tricky syntaxes and becomes a show stopper to the simultaneous adoption of tools characterized by different input languages.

In this paper we present an efficient algorithm suitable for ambiguous parsing of mathematical formulae. The only requirement of the algorithm is the existence of a “validity” predicate over abstract syntax trees of incomplete formulae with placeholders. This requirement can be easily fulfilled in the applicative area of interactive proof assistants, and in several other areas of Mathematical Knowledge Management.


Type Theory Mathematical Formula Proof Assistant Syntax Tree Abstract Data Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Claudio Sacerdoti Coen
    • 1
  • Stefano Zacchiroli
    • 1
  1. 1.Department of Computer ScienceUniversity of BolognaBolognaItaly

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