This paper introduces reFL ect , a functional programming language with reflection features intended for applications in hardware design and verification. The reFL ect language is strongly typed and similar to ML, but has quotation and antiquotation constructs. These may be used to construct and decompose expressions in the reFL ect language itself. The paper motivates and presents the syntax and type system of this language, which brings together a new combination of pattern-matching and reflection features targeted specifically at our application domain. It also gives an operational semantics based on a new use of contexts as expression constructors, and it presents a scheme for compiling reFL ect programs into the λ-calculus using the same context mechanism.

Abstract. Given a theory T and two formulas A and B jointly unsatisfiable in T , a theory interpolant of A and B is a formula I such that (i) its non-theory symbols are shared by A and B, (ii) it is entailed by A in T , and (iii) it is unsatisfiable with B in T . Theory interpolants are used in model checking to accelerate the computation of reachability relations. We present a novel method for computing ground interpolants for ground formulas in the theory of equality. Our algorithm computes interpolants from colored congruence graphs representing derivations in the theory of equality. These graphs can be produced by conventional congruence closure algorithms in a straightforward manner. By working with graphs, rather than at the level of individual proof steps, we are able to derive interpolants that are pleasingly simple (conjunctions of Horn clauses) and smaller than those generated by other tools.

We propose a new format for writing proofs, which we call structured calculational proof. The format is similar to the calculational style of proof already familiar to many computer scientists, but extends it by allowing large proofs to be hierarchically decomposed into smaller ones. In fact, structured calculational proof can be seen as an alternative presentation of natural deduction. Natural deduction is a well established style of reasoning which uses hierarchical decomposition to great effect, but which is traditionally expressed in a notation that is inconvenient for writing calculational proofs.The hierarchical nature of structured calculational proofs can be used for proof browsing. We comment on how browsing can increase the value of a proof, and discuss the possibilities offered by electronic publishing for the presentation and dissemination of papers containing browsable proofs.

Abstract. We give a fresh theoretical foundation for designing comprehensive SMT solvers, generalizing in a practically motivated direction. We define parametric theories that most appropriately express the "logic" of common data types. Our main result is a combination theorem for decision procedures for disjoint theories of this kind. Virtually all of the deeply nested data structures (lists of arrays of sets of . . . ) that arise in verification work are covered.

Today's microelectronics industry is increasingly confronted with the challenge of developing and validating software that closely interacts with hardware. These interactions make it difficult to design and validate the hardware and software separately; instead, a verifiable co-design is required that takes them into account. This paper demonstrates a new approach to co-validation of hardware/software interfaces by formal, symbolic co-execution of an executable hardware model combined with the software that interacts with it. We illustrate and evaluate our technique on three realistic benchmarks in which software I/O is subject to hardware-specific protocol rules: a real-time clock, a temperature sensor on an I 2 C bus, and an Ethernet MAC. We provide experimental results that show our approach is both feasible as a bug-finding technique and scales to handle a significant degree of concurrency in the combined hardware/software model.