We describe a family of decision procedures that extend the decision procedure for quantifier-free constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term algebra homomorphisms) mapping algebraic data type values into values in other decidable theories (e.g. sets, multisets, lists, integers, booleans). Each instance of our decision procedure family is sound; we identify a widely applicable many-to-one condition on abstraction functions that implies the completeness. Complete instances of our decision procedure include the following correctness statements: 1) a functional data structure implementation satisfies a recursively specified invariant, 2) such data structure conforms to a contract given in terms of sets, multisets, lists, sizes, or heights, 3) a transformation of a formula (or lambda term) abstract syntax tree changes the set of free variables in the specified way.

The actor programming model offers a promising model for developing reliable parallel and distributed code. Actors provide flexibility and scalability: local execution may be interleaved, and distributed nodes may operate asynchronously. The resulting nondeterminism is captured by nondeterministic processing of messages. To automate testing, researchers have developed several tools tailored to specific actor systems. As actor languages and libraries continue to evolve, such tools have to be reimplemented. Because many actor systems are compiled to Java bytecode, we have developed Basset, a general framework for testing actor systems compiled to Java bytecode. We illustrate Basset by instantiating it for the Scala programming language and for the ActorFoundry library for Java. Our implementation builds on Java PathFinder, a widely used model checker for Java. Experiments show that Basset can effectively explore executions of actor programs; e.g., it discovered a previously unknown bug in a Scala application.