ReLoC

This is the Coq development of ReLoC. It consists of the formalization of all the logical rules, tactics, and examples. Please take a look at the most recent paper which contains a more in-depth description of ReLoC.

Usage guide

See the small ReLoC docs/guide.md and the Iris ProofGuide.md.

Building

This project has been tested with Coq 8.12.0.

OPAM

Make sure that you have Iris OPAM repository enabled:

opam repo add iris-dev https://gitlab.mpi-sws.org/iris/opam.git

Then install the ReLoC development as usual:

opam install .

Manually

Install the development versions of Iris, std++, and a coq86-devel branch of Autosubst.

Run make and make install.

Examples

We have formalized a variety of different examples in ReLoC. Hopefully they can illustrate the usage of the logic.

• lib
  • Y.v - symbolic execution rules and refinements for different fixed point combinators
  • lock.v - symbolic execution rules for a simple spin lock
  • counter.v - symbolic execution rules and refinements for two different counters
  • list.v - rules for the recursive type of lists
  • polyeq.v - polymoprhic equality predicate
• examples
  • bit.v - "representation independence example" for a simple bit interface
  • or.v - expressing non-determinism with concurrency
  • symbol.v and namegen.v - generative ADTs for symbol and name generation
  • stack/refinement.v - Treiber stack refines sequential stack
  • cell.v - higher-order cell objects
  • ticket_lock.v - ticket lock refines spin lock
  • various.v - lots of examples with higher-order functions with local state, in the style of "The effects of higher-order state and control on local relational reasoning" paper
  • coinflip.v and lateearlychoice.v - examples with prophecy variable
• experimental more "experimental" stuff
  • helping/helping_stack.v - linearizability of stack with helping, see this technical appendix for a detailed description
  • hocap/ - hocap style specifications for a concurrent counter and a refinement proof for a ticket lock
  • cka.v - some axioms from the CKA equational theory

Differences with the old version

This version (ReLoC v2) is build directly on top of heap_lang of Iris, instead of having an ad-hoc object language. It should be easy to port the existing programs to heap_lang. The main differences is the absence of Pack and Fold constructors (the existential types are given transparently, and for recursive types you only need an unfolding function rec_unfold, see e.g. examples/stack/CG_stack.v).

On the level of logic, the main proposition is now of the form

REL e1 << e2 @ E : A

We found it beneficial to get rid of the typing environments Γ and Δ, because usually we want to reason about closed programs at the top level anyway. The type A is now not a syntactic construction, but a relation A : lrel Σ in logic over the type of values. The syntax for the REL proposition was also adjusted to match the syntax of WP more closely.

The old logical judgment {Δ;Γ;E} ⊧ e1 ≤log≤ e2 : τ is redefined on top of the REL proposition. See the files typing/interp.v and typing/soundness.v.

For more information see the guide.