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A recursive descent parser is built from a set of mutually-recursivefunctions, where each function directly implements one of the nonterminals of agrammar. A packrat parser uses memoization to reduce the time complexity forrecursive descent parsing from exponential to linear in the length of theinput. Recursive descent parsers are extremely simple to write, but suffer fromtwo significant problems: (i) left-recursive grammars cause the parser to getstuck in infinite recursion, and (ii) it can be difficult or impossible tooptimally recover the parse state and continue parsing after a syntax error.Both problems are solved by the pika parser, a novel reformulation of packratparsing as a dynamic programming algorithm, which requires parsing the input inreverse: bottom-up and right to left, rather than top-down and left to right.This reversed parsing order enables pika parsers to handle grammars that useeither direct or indirect left recursion to achieve left associativity,simplifying grammar writing, and also enables optimal recovery from syntaxerrors, which is a crucial property for IDEs and compilers. Pika parsingmaintains the linear-time performance characteristics of packrat parsing as afunction of input length. The pika parser was benchmarked against thewidely-used Parboiled2 and ANTLR4 parsing libraries. The pika parser performedsignificantly better than the other parsers for an expression grammar, althoughfor a complex grammar implementing the Java language specification, a largeconstant performance impact was incurred per input character. Therefore, ifperformance is important, pika parsing is best applied to simple tomoderate-sized grammars, or to very large inputs, if other parsing alternativesdo not scale linearly in the length of the input. Several new insights intoprecedence, associativity, and left recursion are presented.

Pika parsing: reformulating packrat parsing as a dynamic programming algorithm solves the left recursion and error recovery problems