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\LARGE\bf Certified Parsing\\[-10mm]

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\section*{Background}

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\noindent

Parsing is the act of transforming plain text into some

structure that can be analysed by computers for further processing. 

One might think that parsing has been studied to death and after

\emph{yacc} and \emph{lex} no new results can be obtained in this area. 

However recent results and novel approaches make it increasingly clear,

that this is not true anymore.

We propose to approach the subject of parsing from a certification point 

of view. Parsers are increasingly part of certified compilers, like CompCert, 

which are guaranteed to be correct and bug-free. Such certified compilers are 

important in areas where software just cannot fail. However, so far the

parsers of these compilers have been left out of the certification.

This is because parsing algorithms are often adhoc and their semantics

is not clearly specified. Unfortunately, this means parsers can harbour 

errors that potentially invalidate the whole certification and correctness 

of the compiler. In this project, we like to change that.

Only in the last few years, theorem provers have become good enough

for establishing the correctness of some standard lexing and

parsing algorithms. For this, the algorithms need to be formulated

in way so that it is easy to reason about them. In earlier work

about lexing and regular languages, the authors showed that this 

precludes algorithms working over graphs. However regular

languages can be formulated and reasoned about entirely in terms 

regular expressions, which can be easily represented in theorem

provers. This work uses the device of derivatives of regular 

languages. We like to extend this work to parsers and grammars.

The aim is to come up with elegant and useful parsing algorithms

whose correctness and absence of bugs can be certified in a theorem 

prover. 

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