TRX: A Formally Verified Parser Interpreter

Abstract

Abstract. Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq, capable of producing formally correct parsers. We are using parsing expression grammars (PEGs), a formalism essentially representing recursive descent parsing, which we consider an attractive alternative to context-free grammars (CFGs). From this formalization we can extract a parser for an arbitrary PEG grammar with the warranty of total correctness, i.e., the resulting parser is terminating and correct with respect to its grammar and the semantics of PEGs; both properties formally proven in Coq.

A verified packrat parser interpreter for parsing expression grammars

“…Our focus is on constructive definitions that yield easy implementations. The notions of structural well-formedness and pattern well-formedness are, along with the use of abstract proof-of-parse trees, the major differences with respect to the verified PEG parser TRX [15].…”

“…In contrast with prior work [11,15], we choose not to define parsing as a relationship between an expression, a string and a result, but as a step of a parsing function that corresponds to the actual computation and that verifies a certain number of properties. To do so, we choose to define an output type that represents a computational path, that we call an abstract syntax tree as a parse tree that represent the full trace of the parse covering both successful and failed branches.…”

“…This representation of the computational path as an explicit proof of correctness (soundness and completeness) for our reference parser, makes it easier to observe and explain both success and failure. Unlike the TRX verified PEG parser [15], we choose to use this structure and to avoid defining parsing through rules. We believe that this approach is richer, as it provides explicit information on the computational path, and as it is easy to show that the rules of parsing are verified at each node of an Ast tree.…”

“…Usually, as we mentioned and as in [11] and [15], the parsing is defined as a relationship between the inputs and the outputs that verifies a certain number of derivation rules corresponding to all the parsing cases. Lemmas that link the properties of the grammar to the parsing relationship 8 8 Those lemmas are the following : (1) If the parsing fails, the grammar is of type P ⊥ (2) If the parsing succeed without consuming any input, the grammar is of type P 0 (3) If the parsing succeed consuming at least one token, the grammar is of type P >0 .…”

“…Bernardy and Jansson [3] have formalized Valiant's algorithm for parsing context-free languages in Agda [4]. Koprowski and Binsztok [15] present a Coq verification of a parser interpreter called TRX for PEGs. The CakeML compiler which has been verified using HOL4 employs a similar verified PEG parser interpreter [16].…”