Data Definitions in the ACL2 Sedan

We present a data definition framework that enables the convenient specification of data types in ACL2s, the ACL2 Sedan. Our primary motivation for developing the data definition framework was pedagogical. We were teaching undergraduate students how to reason about programs using ACL2s and wanted to provide them with an effective method for defining, testing, and reasoning about data types in the context of an untyped theorem prover. Our framework is now routinely used not only for pedagogical purposes, but also by advanced users. Our framework concisely supports common data definition patterns, e.g. list types, map types, and record types. It also provides support for polymorphic functions. A distinguishing feature of our approach is that we maintain both a predicative and an enumerative characterization of data definitions. In this paper we present our data definition framework via a sequence of examples. We give a complete characterization in terms of tau rules of the inclusion/exclusion relations a data definition induces, under suitable restrictions. The data definition framework is a key component of counterexample generation support in ACL2s, but can be independently used in ACL2, and is available as a community book.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Enhancements to ACL2 in Versions 6.2, 6.3, and 6.4

We report on improvements to ACL2 made since the 2013 ACL2 Workshop.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Extending ACL2 with SMT Solvers

We present our extension of ACL2 with Satisfiability Modulo Theories (SMT) solvers using ACL2's trusted clause processor mechanism. We are particularly interested in the verification of physical systems including Analog and Mixed-Signal (AMS) designs. ACL2 offers strong induction abilities for reasoning about sequences and SMT complements deduction methods like ACL2 with fast nonlinear arithmetic solving procedures. While SAT solvers have been integrated into ACL2 in previous work, SMT methods raise new issues because of their support for a broader range of domains including real numbers and uninterpreted functions. This paper presents Smtlink, our clause processor for integrating SMT solvers into ACL2. We describe key design and implementation issues and describe our experience with its use.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

Stateman: Using Metafunctions to Manage Large Terms Representing Machine States

When ACL2 is used to model the operational semantics of computing machines, machine states are typically represented by terms recording the contents of the state components. When models are realistic and are stepped through thousands of machine cycles, these terms can grow quite large and the cost of simplifying them on each step grows. In this paper we describe an ACL2 book that uses HIDE and metafunctions to facilitate the management of large terms representing such states. Because the metafunctions for each state component updater are solely responsible for creating state expressions (i.e., "writing") and the metafunctions for each state component accessor are solely responsible for extracting values (i.e., "reading") from such state expressions, they can maintain their own normal form, use HIDE to prevent other parts of ACL2 from inspecting them, and use honsing to uniquely represent state expressions. The last feature makes it possible to memoize the metafunctions, which can improve proof performance in some machine models. This paper describes a general-purpose ACL2 book modeling a byte-addressed memory supporting "mixed" reads and writes. By "mixed" we mean that reads need not correspond (in address or number of bytes) with writes. Verified metafunctions simplify such "read-over-write" expressions while hiding the potentially large state expression. A key utility is a function that determines an upper bound on the value of a symbolic arithmetic expression, which plays a role in resolving writes to addresses given by symbolic expressions. We also report on a preliminary experiment with the book, which involves the production of states containing several million function calls.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

ACL2(ml):machine-learning for ACL2

ACL2(ml) is an extension for the Emacs interface of ACL2. This tool uses machine-learning to help the ACL2 user during the proof-development. Namely, ACL2(ml) gives hints to the user in the form of families of similar theorems, and generates auxiliary lemmas automatically. In this paper, we present the two most recent extensions for ACL2(ml). First, ACL2(ml) can suggest now families of similar function definitions, in addition to the families of similar theorems. Second, the lemma generation tool implemented in ACL2(ml) has been improved with a method to generate preconditions using the guard mechanism of ACL2. The user of ACL2(ml) can also invoke directly the latter extension to obtain preconditions for his own conjectures.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Integrating multiple sources to answer questions in Algebraic Topology

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and deduction. The architecture allows the system not only to interface several systems, but also to make them cooperate in shared calculations.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Verified AIG Algorithms in ACL2

And-Inverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, these tricky algorithms are implemented with optimized C or C++ routines with no guarantee of correctness. Meanwhile, many interactive theorem provers can now employ SAT or SMT solvers to automatically solve finite goals, but no theorem prover makes use of these advanced, AIG-based approaches. We have developed two ways to represent AIGs within the ACL2 theorem prover. One representation, Hons-AIGs, is especially convenient to use and reason about. The other, Aignet, is the opposite; it is styled after modern AIG packages and allows for efficient algorithms. We have implemented functions for converting between these representations, random vector simulation, conversion to CNF, etc., and developed reasoning strategies for verifying these algorithms. Aside from these contributions towards verifying AIG algorithms, this work has an immediate, practical benefit for ACL2 users who are using GL to bit-blast finite ACL2 theorems: they can now optionally trust an off-the-shelf SAT solver to carry out the proof, instead of using the built-in BDD package. Looking to the future, it is a first step toward implementing verified AIG simplification algorithms that might further improve GL performance.Comment: In Proceedings ACL2 2013, arXiv:1304.712

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it