Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms

We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to generate verified code automatically. Meta-F* is implemented as an F* effect, which, given the powerful effect system of F*, heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F* type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F* provides substantial gains in proof development, efficiency, and robustness.Comment: Full version of ESOP'19 pape

Decision Procedure for Entailment of Symbolic Heaps with Arrays

This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays in the succedent are not existentially bound. This condition is independent of the condition proposed by the CADE-2017 paper by Brotherston et al, namely, one of them does not imply the other. For improving efficiency of the decision procedure, some techniques are also presented. The main idea of the decision procedure is a novel translation of an entailment of symbolic heaps into a formula in Presburger arithmetic, and to combine it with an external SMT solver. This paper also gives experimental results by an implementation, which shows that the decision procedure works efficiently enough to use

SteelCore: An extensible concurrent separation logic for effectful dependently typed programs

Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and program logics, extending the reasoning principles that apply within the host effectful type theory itself. Concretely, our main contribution is a semantics for concurrent separation logic (CSL) within the F* proof assistant in a manner that enables dependently typed, effectful F* programs to make use of concurrency and to be specified and verified using a full-featured, extensible CSL. In contrast to prior approaches, we directly derive the partial-correctness Hoare rules for CSL from the denotation of computations in the effectful semantics of non-deterministically interleaved atomic actions. Demonstrating the flexibility of our semantics, we build generic, verified libraries that support various concurrency constructs, ranging from dynamically allocated, storable spin locks, to protocol-indexed channels. We conclude that our effectful semantics provides a simple yet expressive basis on which to layer domain-specific languages and logics for verified, concurrent programming.Fil: Swamy, Nikhil. Microsoft Research; Estados UnidosFil: Rastogi, Aseem. Microsoft Research; IndiaFil: Fromherz, Aymeric. University of Carnegie Mellon; Estados UnidosFil: Merigoux, Denis. Institut National de Recherche en Informatique et en Automatique; FranciaFil: Ahman, Danel. University of Ljubljana; EsloveniaFil: Martínez, Guido. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentin

Embedded Finite Models beyond Restricted Quantifier Collapse

We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as interpreted vocabulary over an infinite domain: denoted in the past as embedded finite model theory. We extend the analysis of "collapse results": the ability to eliminate first-order quantifiers over the infinite domain in favor of quantification over the finite structure. We investigate several weakenings of collapse, one allowing higher-order quantification over the finite structure, another allowing expansion of the theory. We also provide results comparing collapse for unary signatures with general signatures, and new analyses of collapse for natural decidable theories

Compiling higher-order specifications to SMT solvers : how to deal with rejection constructively

Modern verification tools frequently rely on compiling high-level specifications to SMT queries. However, the high-level specification language is usually more expressive than the available solvers and therefore some syntactically valid specifications must be rejected by the tool. In such cases, the challenge is to provide a comprehensible error message to the user that relates the original syntactic form of the specification to the semantic reason it has been rejected. In this paper we demonstrate how this analysis may be performed by combining a standard unification-based type-checker with type classes and automatic generalisation. Concretely, type-checking is used as a constructive procedure for under-approximating whether a given specification lies in the subset of problems supported by the solver. Any resulting proof of rejection can be transformed into a detailed explanation to the user. The approach is compositional and does not require the user to add extra typing annotations to their program. We subsequently describe how the type system may be leveraged to provide a sound and complete compilation procedure from suitably typed expressions to SMT queries, which we have verified in Agda