2017/08/24 by Sulzmann, Martin, Thiemann, Peter
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Programming Languages (cs.PL)
paper · doi:10.48550/arxiv.1708.07366
We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a reachability problem by using a canonical representation of states. The proofs-as-programs principle yields a computational interpretation of the reachability problem in terms of a coercion that transforms the parse tree for a context-free expression into a parse tree for a regular expression. It also yields a partial coercion from regular parse trees to context-free ones. The partial coercion from the trivial language of all words to a context-free expression corresponds to a predictive parser for the expression.