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Metamath-knife - a Metamath database processing tool

A what?

Metamath is a language for expressing formal proofs in mathematics. Metamath makes few assumptions on the underlying logic and is simple enough to support a wide variety of tools. See http://us.metamath.org/#faq.

Metamath-knife can rapidly verify these proofs, providing much stronger confidence that the proof is correct. And we do mean rapid: over 28,000 proofs can be proved in less than a second.

Metamath-knife is a friendly fork of smetamath-rs (aka SMM3) by Stephan O'Rear (sorear). Here are some key differentiators:

  • It supports all Metamath proof formats. In particular, Metamath-knife adds support for all Metamath proof formats (uncompressed, compressed, package, or explicit.
  • We take extra steps to prevent errors, e.g., we have a CI pipeline (implemented using GitHub actions).
  • We remove deprecated constructs, e.g., the deprecated try!(...) has been replaced with the easier-to-read "?" construct.
  • We actively work to eliminate compiler warnings. This tends to counter errors, make the code more readable, and improve performance (e.g., by eliminating unnecessary clone() calls).

Building

Install Rust, "Rust 2021" (version 1.56.0) or later, preferably using (rustup)[https://rustup.rs], then check out this repository and run:

cargo build --release

Alternatively using cargo install:

cargo install --git https://github.com/david-a-wheeler/metamath-knife
# $HOME/.cargo/bin/metamath-knife has been installed, use it as the binary in the following instructions

Running

# The largest known Metamath database, and best test case
git clone https://github.com/metamath/set.mm

# One-shot verification using 4 threads
target/release/metamath-knife --time --jobs 4 --split --verify set.mm/set.mm

# Incremental verification
(while sleep 5; do echo; done) | target/release/metamath-knife --time --jobs 4 --split --repeat --trace-recalc --verify set.mm/set.mm
# then make small changes to the beginning, end, or middle of the DB and observe how behavior changes

Here is the command line help, which gives an idea of the options available:

A command-line tool for Metamath, including parallel and incremental verifier for Metamath databases

Usage: metamath-knife [OPTIONS] [DATABASE]

Arguments:
  [DATABASE]  Database file to load

Options:
      --text <NAME> <TEXT>        Provides raw database content on the command line
      --split                     Processes files > 1 MiB in multiple segments
      --time                      Prints milliseconds after each stage
  -v, --verify                    Checks proof validity
  -D, --discouraged <FILE>        Regenerates `discouraged` file
  -X, --axiom-use <FILE>          Generate `axiom-use` file
      --stmt-use <FILE> <LABELS>  Outputs statements directly or indirectly using the given list of statements
  -u, --verify-usage              Checks axiom usage
  -O, --outline                   Shows database outline
  -T, --dump-typesetting          Dumps typesetting information
  -t, --parse-typesetting         Parses typesetting information
  -g, --grammar                   Checks grammar
  -p, --parse-stmt                Parses all statements according to the database's grammar
      --verify-parse-stmt         Checks that printing parsed statements gives back the original formulas
  -G, --dump-grammar              Dumps the database's grammar
  -F, --dump-formula              Dumps the formulas of this database
  -S, --list-statements           List all statements of this database
      --debug                     Activates debug logs, including for the grammar building and statement parsing
      --trace-recalc              Prints segments as they are recalculated
      --free                      Explicitly deallocates working memory before exit
      --repeat                    Demonstrates incremental verifier
  -j, --jobs <JOBS>               Number of threads to use for verification
  -e, --export <LABEL>            Outputs a proof file
      --biblio <FILE>             Supplies a bibliography file for verify-markup Can be used one or two times; the second is for exthtml processing
  -m, --verify-markup             Checks comment markup and parses typesetting information
  -h, --help                      Print help
  -V, --version                   Print version

License

This is licensed under either of

The SPDX license expression for its license is "(MIT OR Apache-2.0)".

Note that this is exactly the same license as smetamath-rs (SMM3), That is intentional, because we want smetamath-rs (SMM3) to be able to re-incorporate whatever we do if they like.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.