A Linear First-Order Functional Intermediate Language for Verified Compilers

We present the linear first-order intermediate language IL for verified compilers. IL is a functional language with calls to a nondeterministic environment. We give IL terms a second, imperative semantic interpretation and obtain a register transfer language. For the imperative interpretation we establish a notion of live variables. Based on live variables, we formulate a decidable property called coherence ensuring that the functional and the imperative interpretation of a term coincide. We formulate a register assignment algorithm for IL and prove its correctness. The algorithm translates a functional IL program into an equivalent imperative IL program. Correctness follows from the fact that the algorithm reaches a coherent program after consistently renaming local variables. We prove that the maximal number of live variables in the initial program bounds the number of different variables in the final coherent program. The entire development is formalized in Coq.Comment: Addressed comments from reviewers (ITP 2015): (1) Added discussion of a paper in related work (2) Added definition of renamed-apart in appendix (3) Formulation changes in a coupe of place

Program development using abstract interpretation (and the ciao system preprocessor)

The technique of Abstract Interpretation has allowed the development of very sophisticated global program analyses which are at the same time provably correct and practical. We present in a tutorial fashion a novel program development framework which uses abstract interpretation as a fundamental tool. The framework uses modular, incremental abstract interpretation to obtain information about the program. This information is used to validate programs, to detect bugs with respect to partial specifications written using assertions (in the program itself and/or in system librarles), to genérate and simplify run-time tests, and to perform high-level program transformations such as múltiple abstract specialization, parallelization, and resource usage control, all in a provably correct way. In the case of validation and debugging, the assertions can refer to a variety of program points such as procedure entry, procedure exit, points within procedures, or global computations. The system can reason with much richer information than, for example, traditional types. This includes data structure shape (including pointer sharing), bounds on data structure sizes, and other operational variable instantiation properties, as well as procedure-level properties such as determinacy, termination, non-failure, and bounds on resource consumption (time or space cost). CiaoPP, the preprocessor of the Ciao multi-paradigm programming system, which implements the described functionality, will be used to illustrate the fundamental ideas

Symmetry as Bias: Rediscovering Special Relativity

This paper describes a rational reconstruction of Einstein's discovery of special relativity, validated through an implementation: the Erlanger program. Einstein's discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases, defined through different postulated symmetries of the universe, and a hypothesis space for physical theories. The invariance principle mutually constrains these two spaces. The invariance principle enables detecting when an evolving physical theory becomes inconsistent with its bias, and also when the biases for theories describing different phenomena are inconsistent. Structural properties of the invariance principle facilitate generating a new bias when an inconsistency is detected. After a new bias is generated. this principle facilitates reformulating the old, inconsistent theory by treating the latter as a limiting approximation. The structural properties of the invariance principle can be suitably generalized to other types of biases to enable primal-dual learning

Computable de Finetti measures

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable.Comment: 32 pages. Final journal version; expanded somewhat, with minor corrections. To appear in Annals of Pure and Applied Logic. Extended abstract appeared in Proceedings of CiE '09, LNCS 5635, pp. 218-23

Symmetry-Preserving Program Representations for Learning Code Semantics

Large Language Models (LLMs) have shown promise in automated program reasoning, a crucial aspect of many security tasks. However, existing LLM architectures for code are often borrowed from other domains like natural language processing, raising concerns about their generalization and robustness to unseen code. A key generalization challenge is to incorporate the knowledge of code semantics, including control and data flow, into the LLM architectures. Drawing inspiration from examples of convolution layers exploiting translation symmetry, we explore how code symmetries can enhance LLM architectures for program analysis and modeling. We present a rigorous group-theoretic framework that formally defines code symmetries as semantics-preserving transformations and provides techniques for precisely reasoning about symmetry preservation within LLM architectures. Using this framework, we introduce a novel variant of self-attention that preserves program symmetries, demonstrating its effectiveness in generalization and robustness through detailed experimental evaluations across different binary and source code analysis tasks. Overall, our code symmetry framework offers rigorous and powerful reasoning techniques that can guide the future development of specialized LLMs for code and advance LLM-guided program reasoning tasks

Holography in a background-independent effective theory

We discuss the meaning of the strong equivalence principle when applied to a quantum field theory. We show that, because of unitary inequivalence of accelerated frames, the only way for the equivalence principle to apply exactly is to add a boundary term representing the decoherence of degrees of freedom leaving the observable region of the bulk. We formulate the constraints necessary for the equivalence principle to hold at the level of the partition function and argue that, when the non-unitary part is expressed as a functional integral over the horizon, holography arises naturally as a consequence of the equivalence principle.Comment: Matches published versio

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200