Twenty years of rewriting logic

Equational abstractions

The first three papers on rewriting logic were published in 1990 [4,3,2]; they were then expanded in [5,6]. Since that time, many researchers around the world have made important contributions to its foundations, tools, and applications. Since 1996, the WRLA workshop has met biennially, with the 2010 Paphos meeting being its eighth edition, and many hundreds of papers have been published on the subject (for a bibliography up to 2002 see [1]).

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This paper introduces SymPLFIED, a program-level framework that allows specification of arbitrary error detectors and the verification of their efficacy against hardware errors. SymPLFIED comprehensively enumerates all transient hardware errors in registers, memory, and computation (expressed as value errors) that potentially evade detection and cause program failure. The framework uses symbolic execution to abstract the state of erroneous values in the program and model checking to comprehensively find all errors that evade detection. We demonstrate the use of SymPLFIED on a widely deployed aircraft collision avoidance application, tcas. Our results show that the SymPLFIED framework can be used to uncover hard-to-detect corner cases caused by transient errors in programs that may not be exposed by random fault-injection based validation.

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SymPLFIED: Symbolic program-level fault injection and error detection framework

This article describes an approach to documenting control programs, whereby the control program code is annotated with logical expressions describing the set of reachable program states. This approach constitutes the application of the Floyd-Hoare paradigm to control programs. It is shown that domain knowledge gathered by control theory about control-system specifications is applicable to developing stability and performance proofs of the corresponding control programs. The analyses discussed in this article can be used in various contexts. In particular, the analyses can be used in an autocoding environment, whereby diagram-based specifications in Simulink or other languages can be turned into formally annotated target codes with extensive proofs of stability and performance. These proofs are tightly woven in the codes, which can then be verified independently by a proof checker.

From Control Systems to Control Software

This paper describes the main features of several tools concerned with the analysis of either Maude specifications, or of extensions of such specifications: the ITP, MTT, CRC, ChC, and SCC tools, and Real-Time Maude for real-time systems. These tools, together with Maude itself and its searching and model-checking capabilities, constitute Maude's formal environment.

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The maude formal tool environment

We present the Maude sufficient completeness tool, which explicitly supports sufficient completeness reasoning for partial conditional specifications having sorts and subsorts and with domains of functions defined by conditional memberships. Our tool consists of two main components: (i) a sufficient completeness analyzer that generates a set of proof obligations which if discharged, ensures sufficient completeness; and (ii) Maude’s inductive theorem prover (ITP) that is used as a backend to try to automatically discharge those proof obligations.

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A Sufficient Completeness Reasoning Tool for Partial Specifications

We present a tool for checking the sufficient completeness of left-linear, order-sorted equational specifications modulo associativity, commutativity, and identity. Our tool treats this problem as an equational tree automata decision problem using the tree automata library CETA, which we also introduce in this paper. CETA implements a semi-algorithm for checking the emptiness of a class of tree automata that are closed under Boolean operations and an equational theory containing associativity, commutativity and identity axioms. Though sufficient completeness for this class of specifications is undecidable in general, our tool is a decision procedure for subcases known to be decidable, and has specialized techniques that are effective in practice for the general case.

A sufficient completeness checker for linear order-sorted specifications modulo axioms

https://sewiki.iai.uni-bonn.de/_media/rule08/rule08-hendrix.pdf?id=rule08%3Aprogram&cache=cache

Order-sorted Equational Unification Revisited

We propose three different notions of completeness for ordersorted equational specifications supporting context-sensitive rewriting modulo axioms relative to a replacement map µ. Our three notions are: (1) a definition of µ-canonical completeness under which µ-canonical forms coincide with canonical forms; (2) a definition of semantic completeness that guarantees that the µ-operational semantics and standard initial algebra semantics are isomorphic; and (3) an appropriate definition of µ-sufficient completeness with respect to a set of constructor symbols. Based on these notions, we use equational tree automata techniques to obtain decision procedures for checking these three kinds of completeness for equational specifications satisfying appropriate requirements such as weak normalization, ground confluence and sort-decreasingness, and left-linearity. The decision procedures are implemented as an extension of the Maude sufficient completeness checker.

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Joe Hendrix

Papers

The maude formal tool environment

A Sufficient Completeness Reasoning Tool for Partial Specifications

A sufficient completeness checker for linear order-sorted specifications modulo axioms

Order-sorted Equational Unification Revisited

On the completeness of context-sensitive order-sorted specifications