This repository holds the source code of a dependently-typed parser written in Coq, which proves its own correctness by parsing parse trees.

• To build the library: Coq 8.4
• To step through the examples: GNU Emacs 23.4.1, Proof General 4.3

• To build the library: make

All file names are relative to src/Parsers/

• BooleanRecognizer.v - parser returning bools, written before the dependently typed one (section 1.2, section 7.1)
• ContextFreeGrammar.v - definition of a context free grammar (section 2.1), and of parse trees (section 2.2)
• Grammars/ABStar.v - definition of the grammar for the regular expression (ab)* (section 2.1.1)
• BooleanRecognizer.v - soundness and completeness of parser returning bools (section 2.3)
• MinimalParse.v - definition of "minimal" parse trees (section 4)
• DependentlyTyped.v - declaration of the interface and implementation of the parser (section 5, figures 1 and 2)
• DependentlyTypedMinimalOfParseFactored.v - instantiation of the parser that parses parse trees and returns minimal parse trees (section 5; the deloop of the 5.1 is deloop_once in this file
• DependentlyTypedMinimal.v - instantiation of parser returning MinParseTreeOf nt s + (MinParseTreeOf nt s -> False); a slightly different factoring of the components from what appears in section 5.4
• MinimalParseOfParse.v - construction of ParseTreeOf from MinParseTreeOf (not needed in paper due to slightly different factoring from what appears in 5.4), also a direct construction of MinParseOf from ParseTreeOf, superseded by the construction of DependentlyTypedMinimalOfParseFactored.v and the paper
• DependentlyTypedMinimalOfParseFactoredFull.v - single definition to construct MinParseTreeOf from ParseTreeOf: minimal_parse_nonterminal__of__parse corresponds to min_parse of section 5.4
• DependentlyTypedSum.v - helper for DependentlyTypedMinimalOfParseFactored.v; the extra 300 lines of code mentioned in 7.2