CUDD [git mirror], BuDDy [SourceForge], and JDD are general-purpose BDD libraries. In Rust, the crate cudd-sys provides bindings for CUDD and the crate cudd builds a higher-level API upon that.
In “Using Datalog with Binary Decision Diagrams for Program Analysis” (John Whaley, Dzintars Avots, Michael Carbin, and Monica S. Lam, 2005), the authors use BDDs to power a Datalog engine, bddbddb. They show that program analyses implemented with it are faster than hand-tuned implementations and use dramatically fewer lines of code, and they use it to solve previously unsolved problems like context-sensitive pointer analysis for large programs.
I might implement this myself and use it for analyses in my compiler.
The source for bddbddb [git] is available, as well as for its dependencies JavaBDD [git] and joeq [git].
Similarly to bddbddb, hsdatalog is a compiler in Haskell from Datalog to relational algebra and an interpreter for relational algebra using BDDs.