package lambdapi

Lambdapi, a proof assistant based on the λΠ-calculus modulo rewriting

>>>>> User Manual <<<<<

Issues can be reported on the issue tracker.

Questions can be asked on the forum.

User interfaces

• Emacs

• VSCode

Libraries

Lambdapi libraries can be found on the Opam repository of Lambdapi libraries.

Examples

• tutorial (learn Lambdapi in 15 minutes)

• some logic definitions

• inductive-recursive type definition

• inductive-inductive type definition

• library on natural numbers, integers and polymorphic lists

Some users

• Melanie Taprogge: extension of the LEO-III automated theorem prover for higher-order logic producing Lambdapi proofs [github] [MSc thesis]

• Alessio Coltellacci and Stephan Merz: extension of the Alethe proof verifier Carcara for SMT solvers producing Lambdapi proofs [github] [SMT'24]

• Alessio Coltellacci and Stephan Merz: encoding of TLA+ set theory in Lambdapi [ABZ'23]

• Jean-Paul Bodeveix and Anne Grieu: certification of Event-B proofs generated by Rodin in Lambdapi

• Frédéric Blanqui: translation of HOL-Light proofs to Coq [github] [LPAR'24]

• Nicolas Margulies: a formalization of cubical type theory in Lambdapi [github]

• Thomas Traversié: implementation of set theory with pointed graphs [LFMTP'22]

• Luc Chabassier: formalization of some category theory [github] and of extensional type theory [github]

• Quentin Garchery: certification of Why3 proof task transformations in Lambdapi [PhD thesis]

• Gabriel Hondet: translation of PVS statements to Lambdapi [github] [PhD thesis]

Operating systems

Lambdapi requires a Unix-like system. It might be possible to make it work on Windows too with Cygwin or "bash on Windows".

Installation via Opam

opam install lambdapi

gives you the command lambdapi.

The Emacs extension is available on MELPA.

The VSCode extension is available on the Marketplace.

To browse the source code documentation, you can do:

opam install odig
odig doc lambdapi

To install Lambdapi libraries, see the opam-lambdapi-repository.

Remark: To install Opam, see here.

To make sure that programs installed via opam are in your path, you should have in your .bashrc (or any other shell initial file) the following line that can be automatically added when you do opam init:

test -r ~/.opam/opam-init/init.sh && . ~/.opam/opam-init/init.sh > /dev/null 2> /dev/null || true

To update your path, you can also do:

eval `opam env`

Compilation from the sources

You can get the sources using git as follows:

git clone https://github.com/Deducteam/lambdapi.git

Dependencies are described in lambdapi.opam. The command why3 config detect must be run for Why3 to know the available provers for the why3 tactic.

Using Opam, a suitable OCaml environment can be setup as follows:

cd lambdapi
opam install .
why3 config detect

To compile Lambdapi, just run the command make in the source directory. This produces the _build/install/default/bin/lambdapi binary. Use the --help option for more information. Other make targets are:

make                        # Build lambdapi
make doc                    # Build the user documentation (avalaible on readthedocs)
make bnf                    # Build the BNF grammar
make odoc                   # Build the developer documentation
make install                # Install lambdapi
make install_emacs_mode     # Install emacs mode
make install_vim_mode       # Install vim mode

You can run lambdapi without installing it with dune exec -- lambdapi.

For running tests, one also needs alcotest and alt-ergo.

For building the source code documentation, one needs odoc. The starting file of the source code html documentation is _build/default/_doc/_html/lambdapi/index.html.

For building the User Manual, see doc/README.md.

The following commands can be used to clean up the repository:

make clean     # Removes files generated by OCaml.
make distclean # Same as clean, but also removes library checking files.
make fullclean # Same as distclean, but also removes downloaded libraries.