Minimal Parsing Language (MPL)

This is minimal parser combinator of Minimal Parsing Language (MPL) like Top-Down Parsing Language (TDPL). It creates a abstract syntax tree (AST) for each input.

Getting Started

1. implement Variable
2. insert each rule into HashMap
3. minimal_parse()

• Optional
  • implement Input
    • supports [T] and str by default
  • implement Position
    • supports u*, i*, and f* by default
  • implement Span
    • supports StartAndLenSpan by default
  • implement Terminal
    • supports SliceTerminal, StrTerminal, and U8SliceTerminal by default
  • implement Output
    • supports () by default
  • implement Rules
    • supports HashMap by default
  • implement Parse
    • supports [T], str, and [u8] by default

Example

use crate::ParenthesesVariable::*;
use mpl::parse::Parse;
use mpl::rules::{RightRule, RightRuleKind::*};
use mpl::span::StartAndLenSpan;
use mpl::symbols::{StrTerminal::*, Variable};
use mpl::trees::AST;
use std::collections::HashMap;

#[derive(Clone, Debug, Hash, Eq, PartialEq)]
enum ParenthesesVariable {
    Open,
    Parentheses,
    Close,
}

impl Variable for ParenthesesVariable {}

/// ```
/// Open = '(' Parentheses / ()
/// Parentheses = Open Close / f
/// Close = ")" Open / f
/// ```
fn main() {
    let mut rules = HashMap::new();

    rules.insert(
        Open,
        RightRule::from_right_rule_kind((T(Char('(')), V(Parentheses)), Empty),
    );
    rules.insert(
        Parentheses,
        RightRule::from_right_rule_kind((V(Open), V(Close)), Failure),
    );
    rules.insert(
        Close,
        RightRule::from_right_rule_kind((T(Str(")")), V(Open)), Failure),
    );

    let input = "(()(()))";

    // all of the span
    let all_of_the_span = StartAndLenSpan::<u32, u16>::from_start_len(0, input.len() as u16);

    let result: Result<
        AST<ParenthesesVariable, StartAndLenSpan<u32, u16>, ()>,
        AST<ParenthesesVariable, StartAndLenSpan<u32, u16>, ()>,
    > = input.minimal_parse(&rules, &Open, &all_of_the_span);

    if let Ok(ast) = result {
        println!("{}", ast);
    }
}

Test Examples

• Number
• Parentheses
• Wav Riff

Parsers written with MPL

• WAV AST : RIFF waveform Audio Format

MPL

Definition of MPL grammar

A MPL grammar G is a tuple G = (V, Σ, R, S) in which:

• V is a finite set of variables.
• Σ is a finite set of original terminal symbols.
• T is an union of Σ or M (Σ ∪ M) (M (= {(), f}) is a finite set of metasymbols).
• R is a finite set of rules of the form
  • A = B C / D
    A in V (A ∈ V),
    B, C, D in E (E = T ∪ V) (T ∩ V = ∅) (B, C, D ∈ E).
    For any variable A there is exactly one rule with A to the left of =.
• S in V (S ∈ V) is the start variable.

Empty

() is a metasymbol that always succeeds without consuming input.

Empty = () () / ()

Failure

f is a metasymbol that always fails without consuming input.

Failure = f f / f

Extended MPL

Since one of the goals of MPL is to create an AST, it also supports two features in terms of ease of use and speed.

Any

? is a metasymbol representing any single input like wildcard character. This succeeds if there is any input left, and fails if there is no input left.

Any = ? () / f

To extend the difinition of MPL grammar, let ? ∈ M.

All

* is a metasymbol representing All remaining input like wildcard character. This will succeed even if the remaining inputs are zero.

All = * () / f

Same as All = ? All / ().

To extend the difinition of MPL grammar, let * ∈ M.

Difference between TDPL and MPL

The biggest difference between the two grammars is the rule form. There are two rule forms in TDPL.

A..BC/D, A,B,C,D in V.
A..a, a in ∑ ∪ {ε, f}, f is a metasymbol not in ∑ and ε is the null string.

MPL, on the other hand, has one rule form.

TODO

• Visualize AST
• Add RowColSpan
• Create parser from MPLG file.
• Error Handling
• Packrat Parsing
• Left Recursion

Practice

Sequence

A <- e1 e2

A = e1 e2 / f

Choice

A <- e1 / e2

A = e1 () / e2

Zero or more

A <- e*

A = e A / ()

Not predicate

A <- !e .

A = B ? / f
B = e * / ()

References

• Alexander Birman. The TMG Recognition Schema. PhD thesis, Princeton University, February 1970
• Alfred V. Aho and Jeffrey D. Ullman. The Theory of Parsing, Translation and Compiling - Vol. I: Parsing. Prentice Hall, Englewood Cliffs, N.J., 1972.
• Bryan Ford. 2002. Packrat parsing: a practical linear-time algorithm with backtracking. Ph.D. Dissertation. Massachusetts Institute of Technology.
• Bryan Ford. 2004. Parsing expression grammars: a recognition-based syntactic foundation. In Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages. 111–122.
• Hutchison, Luke AD. "Pika parsing: reformulating packrat parsing as a dynamic programming algorithm solves the left recursion and error recovery problems." arXiv preprint arXiv:2005.06444 (2020).