The QED project aims to resolve SQL query equivalence efficiently. It has three parts:

• A SQL parser that compiles SQL queries to intermediate representations for the prover and disprover.
• A prover that validates the equivalence of queries. The prover may produce false negative results, where the queries are equivalent but the prover cannot prove it.
• A disprover that searches for database instances where the queries produce different results. The disprover may produce false positive results, where the queries are inequivalent but the disprover cannot find a database instance that distinguish the queries.

The workflow of the project starts from the parser and ends in the prover and the disprover. Currently the parser and the prover have been packaged with Nix, so they can be easily use like this:

# Please have Nix installed in your system with experimental features enabled.
# Now we enter a shell with the parser and the prover.
# Please allow the use of Cachix to accelerate your experience.
nix shell github:qed-solver/parser github:qed-solver/prover

# Assume that we have an example.sql that contains
# table schema definitions and two SQL queries.
# The parser generates example.json and example.rkt in the same directory.
# example.json is for the prover and example.rkt is for the disprover.
qed-parser example.sql

# We run the prover to verify the equivalence.
# The results are printed on stdout.
# The prover also generates example.res:
# the first line logs whether the equivalence is provable,
# the second line logs the time spent by the prover.
qed-prover example.json

Please refer to the READMEs in the repositories within this project for more details.