This is my work on Golem's verifiable alethe proof production of LIA lin and nonlin Constrained Horn Clauses.
Golem is a solver for Constrained Horn Clauses (CHCs). It accepts the input in the format of (extended) SMT-LIB 2.6, as defined by CHC-COMP.
The easiest way is to download the executables from our release page. This way, all dependencies are already bundled in the executable.
Golem can be compiled on Linux and MacOS.
It uses CMake for build configuration.
Golem depends on OpenSMT for SMT solving and interpolation.
If you already have OpenSMT installed, you can pass the path using -DOPENSMT_HOME option to cmake command.
Note that Golem requires a specific version of OpenSMT, currently v2.5.2.
Otherwise, cmake will download the latest compatible version of OpenSMT and build it as a subproject.
You can view the usage in the help message after running
$ golem -h
At the moment, you should specified the SMT theory used in the CHC encoding with -l option. The supported theories are QF_LRA and QF_LIA, i.e., the linear arithmetic over reals or integers.
Golem now has limited support to automatically detect the theory from the script, so the option is no longer mandatory, but still recommended.
Golem currently supports 6 different backend algorithms for solving CHCs.
- spacer [default]
- bmc
- imc
- kind
- lawi
- tpa
- split-tpa
Spacer engine is the default one. It represents our own implementation of the algorithm from this paper. You might be familiar with the original implementation of Spacer inside Z3.
BMC engine implements the simple bounded model checking algorithm which checks for existence of increasingly longer counterexample paths in a given transition system. It uses incremental capibilities of the underlying SMT solver to speed up the process.
IMC engine implements the original McMillan's interpolation-based model-checking algorithm from this paper. Currently, it only supports transition systems.
KIND engine implements very basic k-induction algorithm from this paper. Currently, it only supports transition systems.
LAWI stands for Lazy Abstraction With Interpolants. The algorithm is described in this paper.
It is also known as Impact, which was the first tool where the algorithm was implemented.
LAWI engine supports only linear systems of Horn clauses.
TPA stands for Transition Power Abstraction. It is an algorithm we have developed recently with the goal to detect long counterexample quickly. The description of the algorithm can be found in this paper. TPA supports a subset of linear CHC systems that represent DAGs of transition systems.
split-TPA is a different instantiation of the TPA paradigm and is typically more powerful than TPA on satisfiable (safe) CHC systems.
Golem also supports multiprocessing run of the few engine simultaneously. For example, to run split-tpa, spacer and lawi in parralel golem should be called like this:
golem -l {Logic} -e split-tpa,spacer,lawi {File}Golem supports internal validation of witnesses for its answer using --validate option.
Witness for sat is a model, an interpretation of the predicates.
Witness for unsat is a proof.
This option is still experimental. For example, tpa/split-tpa does not always produce the witness yet.
To obtain the produced model or proof of unsatisfiability, use --print-witness.