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The PML₂ programming language and proof assistant

The PML₂ language provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in terms of classical logic), it supports general recursion and a very general form of (implicit, non-coercive) subtyping. In the system, equational properties of programs are expressed using two new type formers, and they are proved by constructing terminating programs. Although proofs rely heavily on equational reasoning, equalities are exclusively managed by the type-checker. This means that the user only has to choose which equality to use, and not where to use it, as is usually done in mathematical proofs. In the system, writing proofs mostly amounts to applying lemmas (possibly recursive function calls), and to perform case analyses (pattern matchings).

Related documents and prototypes:

Dependencies and compilation

PML₂ requiere a Unix-like system. It should work well on Linux as well as on MacOS. It might also be possible to make it work on Windows with Cygwyn or with "bash on Windows").

List of dependencies:

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

opam switch 4.05.0
eval `opam config env`
opam install ocamlfind ocamlbuild
opam install bindlib.5.0.1 earley.2.0.0

To compile PML₂, just run the command make in the source directory. This produces the main.native binary, which can be run on files with the .pml extension (use ./main.native --help for more informations).

make install   # optionally install the program.
make doc       # optionally produce the ocamldoc documentation

Organization of the repository

This folder contains files related to the PML2 project.

The source files can be found in the following folders:

  • util contains a set of libraries not directly related to PML2,
  • parser contains a low level AST of the language and the parser,
  • kernel contains the core of PML2 (type checking, equivalence, AST...),
  • pml2 contains the main program.

Other directories:

  • editors contains PML2 modes for editors (vim and emacs only),
  • lib contains the PML2 standard library (very small),
  • test contains most of our examples of PML2 programs,

The directories tmp and attic are not relevant as the contain files used for debugging the newest features including termination checking and old code that we want to keep somewhere.

Where to start in the code

My advice to start looking at the code would be to take a look at the three different abstract syntax representations.

  • The main abstract syntax is implemented as a GADT in kernel/,
  • The abstract syntax after parsing can be found in parser/, together with the first level of type checking (sorting),
  • The graph representation of terms for the decision of equivalence can be found in ast/

The implementation of type checking can be found in kernel/, and the function for comparing expressions (including the unification functions) are in kernel/