Robust Verification of PEG Parser Interpreters

We formalize a chart parsing approach to PEG parsing by defining a state machine that operates on a scaffold data structure. The scaffold maintains the state matrix with entries for each pair of positions and nonterminals. Our PEG parser interpreter parses an input string relative to a given PEG grammar in Chomsky Normal Form by lazily filling the entries in the scaffold according to whether the parse succeeded, failed, or looped. We thus admit possibly left-recursive PEG grammars and add loop detection to the parser. We define invariants on this state and define a parsing step function that preserves these invariants. We define a proof-of-parse representation that can be extracted from the end state of a parse to be independently checked. We formalize and prove chart parsers for an evolving series of PEG formalizations with extensive proof reuse across these formalizations. The mix of interaction and automation in PVS proofs tend to make them reasonably robust to certain kinds of specification and design changes. We discuss other steps that can be taken to proactively build robust proofs for important classes of problems like parsing.