Racemic 4-(4-tert-butyl­phen­yl)-2,6-dimethyl­cyclo­hex-3-enecarboxylic acid

The chirality of the title compound, C19H26O2, is solely generated by the presence of the double bond in the cyclo­hexene ring. This compound was synthesized to study the inter­action of the two enanti­omers in the solid state. The resultant racemate is made up of carboxylic acid RS dimers. Inter­molecular O—H⋯O hydrogen bonds produce centrosymmetric R 2 2(8) rings which dimerize the two chiral enanti­omers through their carboxyl groups

Completeness for a First-order Abstract Separation Logic

Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which completeness is not possible. An important element in concrete SL is the points-to predicate which denotes a singleton heap. SL with the points-to predicate has been shown to be non-recursively enumerable. In this paper, we develop a first-order SL, called FOASL, with an abstracted version of the points-to predicate. We prove that FOASL is sound and complete with respect to an abstract semantics, of which the standard SL semantics is an instance. We also show that some reasoning principles involving the points-to predicate can be approximated as FOASL theories, thus allowing our logic to be used for reasoning about concrete program verification problems. We give some example theories that are sound with respect to different variants of separation logics from the literature, including those that are incompatible with Reynolds's semantics. In the experiment we demonstrate our FOASL based theorem prover which is able to handle a large fragment of separation logic with heap semantics as well as non-standard semantics.Comment: This is an extended version of the APLAS 2016 paper with the same titl

Coeffects: Unified static analysis of context-dependence

Monadic effect systems provide a unified way of tracking effects of computations, but there is no unified mechanism for tracking how computations rely on the environment in which they are executed. This is becoming an important problem for modern software – we need to track where distributed computations run, which resources a program uses and how they use other capabilities of the environment. We consider three examples of context-dependence analysis: liveness analysis, tracking the use of implicit parameters (similar to tracking of resource usage in distributed computation), and calculating caching requirements for dataflow programs. Informed by these cases, we present a unified calculus for tracking context dependence in functional languages together with a categorical semantics based on indexed comonads. We believe that indexed comonads are the right foundation for constructing context-aware languages and type systems and that following an approach akin to monads can lead to a widespread use of the concept

The Problem of Excess Reserves, Then and Now

Recent research has pointed out the importance of the inequational exchange law (P*Q);(R*S) ≤ (P;R)*(Q;S) for concurrent processes. In particular, it has been shown that this law is equivalent to validity of the concurrency rule for Hoare triples. Unfortunately, the law does not hold in the relationally based setting of algebraic separation logic. However, we show that under mild conditions the reverse inequation (P;R)*(Q;S) ≤ (P*Q);(R*S) still holds there. Separating conjunction * in that calculus can be interpreted as true concurrency on disjointly accessed resources. From the reverse exchange law we derive slightly restricted but still reasonably useful variants of the concurrency rule. Moreover, using a corresponding definition of locality, we obtain also a variant of the frame rule. By this, the relational setting can also be applied for modular and concurrency reasoning. Finally, we present several variations of the approach to further interpret the results

Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.Comment: Accepted at ICTAC 201

Towards Scientific Incident Response

A scientific incident analysis is one with a methodical, justifiable approach to the human decision-making process. Incident analysis is a good target for additional rigor because it is the most human-intensive part of incident response. Our goal is to provide the tools necessary for specifying precisely the reasoning process in incident analysis. Such tools are lacking, and are a necessary (though not sufficient) component of a more scientific analysis process. To reach this goal, we adapt tools from program verification that can capture and test abductive reasoning. As Charles Peirce coined the term in 1900, “Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea.” We reference canonical examples as paradigms of decision-making during analysis. With these examples in mind, we design a logic capable of expressing decision-making during incident analysis. The result is that we can express, in machine-readable and precise language, the abductive hypotheses than an analyst makes, and the results of evaluating them. This result is beneficial because it opens up the opportunity of genuinely comparing analyst processes without revealing sensitive system details, as well as opening an opportunity towards improved decision-support via limited automation

Local reasoning about the presence of bugs: Incorrectness Separation Logic

There has been a large body of work on local reasoning for proving the absence of bugs, but none for proving their presence. We present a new formal framework for local reasoning about the presence of bugs, building on two complementary foundations: 1) separation logic and 2) incorrectness logic. We explore the theory of this new incorrectness separation logic (ISL), and use it to derive a begin-anywhere, intra-procedural symbolic execution analysis that has no false positives by construction. In so doing, we take a step towards transferring modular, scalable techniques from the world of program verification to bug catching

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

A Higher-Order Logic for Concurrent Termination-Preserving Refinement

Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared memory primitives. However, existing logics for proving concurrent refinement either neglect properties such as termination, or only handle first-order state. In this paper, we address these limitations by extending Iris, a recent higher-order concurrent separation logic, with support for reasoning about termination-preserving refinements. To demonstrate the power of these extensions, we prove the correctness of an efficient implementation of a higher-order, session-typed language. To our knowledge, this is the first program logic capable of giving a compiler correctness proof for such a language. The soundness of our extensions and our compiler correctness proof have been mechanized in Coq