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

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\section*{Background}

\noindent

Parsing is the act of transforming plain text into some

structure that can be analyzed 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 developments and novel approaches make it increasingly clear,

that this is not true anymore.

We propose to on parsers from a certification point of view. Increasingly,

parsers are part of certified compilers, like \mbox{\emph{CompCert}}, which

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

crucial 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 ad hoc 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 with the help of theorem

provers.

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 still need to be formulated in way so

that it is easy to reason about them. In our earlier work about lexing and

regular languages, we showed that this precludes well-known algorithms based

automata. However we showed also that 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 expressions. We like to extend this device to parsers and grammars.

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

whose correctness can be certified in a theorem prover.

\section*{Proposed Work}

A recent development in parsing is Parsing Expression Grammars (PEG), which

are an extension of the weel-known Context Free Grammars

(CFG)~\cite{Ford04a}. The extension introduces new regular operators, such as

negation and conjunction, on the right-hand sides of grammar rules, as well as

priority orderings. With these extensions, PEG parsing becomes much

more powerful. For example disambiguation, formerly expressed by semantic

filters, can now be expressed directly using grammar rules. 

However, there is serious disadvantage of PEG for applications: is does not

support grammrs involving left recursion~\cite{Ford02b}. Although a new PEG

parsing algorithm has been proposed that can deal with left

recursion~\cite{conf/pepm/WarthDM08}, there is no correctness proof, not even

in ``paper-and-pencil'' form. One aim of this research is to solve this sorry

state-of-affairs by either certifying this algorithm or inventing a new

one. For this we will first formalize a fixed point semantics of PEG, based on

which an efficient, certified parsing algorithm can be given given. For this

we take as starting point the paper~\cite{Ford04a}, which does not treat

left-recursion, but gives an operational semantics for PEG parsing. For the

semantics, it seems plausible that we can adapt work on Boolean

Grammars~\cite{Okhotin/04a}, which are similar to PEGs, and for which the

paper ~\cite{journals/iandc/KountouriotisNR09} gives a semantics to negation

operators, but not to Kleene's star operation.

For the parsing algorithm, we might also be able to draw inspiration from

parsers based on Cocke-Younger-Kasami (CYK)

algorithms~\cite{journals/iandc/KountouriotisNR09} and

Early~\cite{Earley70,AycHor02} parsers. The defect CYK algorithms is that the

original grammar specification needs to be transformed into a normal

form. This transformation may lead to grammar explosion and inefficient

parsing. We will investigate whether this transformation can be avoided.

Early style parsers, which have recently been certified by Ridge [???], 

need to be extended to PEG parsing in order to be helpful for us.

Finally, we want to investigate whether derivatives of regular expressions

~\cite{Brzozowski64,Almeidaetal10,OwensReppyTuron09,journals/corr/abs-1010-5023}

can be extended to parsing. Lexing based on derivatives gives rise to very

elegant regular expression matchers that can be certified in a theorem prover 

with ease.  We will study whether the idea of taking a derivative of a regular

expression can be extended to rules in grammars. The problem that needs to be

overcome again arises from possible left recursion in parsing. 

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%  \noindent {\bf Objectives:} The overall goals of the project are as follows:

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