995 research outputs found
Two Decades of Maude
This paper is a tribute to JosĂ© Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
State space c-reductions for concurrent systems in rewriting logic
We present c-reductions, a state space reduction technique.
The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer
function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in
the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization
of the reduction infrastructure via Maude's meta-programming
features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools
New results on rewrite-based satisfiability procedures
Program analysis and verification require decision procedures to reason on
theories of data structures. Many problems can be reduced to the satisfiability
of sets of ground literals in theory T. If a sound and complete inference
system for first-order logic is guaranteed to terminate on T-satisfiability
problems, any theorem-proving strategy with that system and a fair search plan
is a T-satisfiability procedure. We prove termination of a rewrite-based
first-order engine on the theories of records, integer offsets, integer offsets
modulo and lists. We give a modularity theorem stating sufficient conditions
for termination on a combinations of theories, given termination on each. The
above theories, as well as others, satisfy these conditions. We introduce
several sets of benchmarks on these theories and their combinations, including
both parametric synthetic benchmarks to test scalability, and real-world
problems to test performances on huge sets of literals. We compare the
rewrite-based theorem prover E with the validity checkers CVC and CVC Lite.
Contrary to the folklore that a general-purpose prover cannot compete with
reasoners with built-in theories, the experiments are overall favorable to the
theorem prover, showing that not only the rewriting approach is elegant and
conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page
Total Haskell is Reasonable Coq
We would like to use the Coq proof assistant to mechanically verify
properties of Haskell programs. To that end, we present a tool, named
hs-to-coq, that translates total Haskell programs into Coq programs via a
shallow embedding. We apply our tool in three case studies -- a lawful Monad
instance, "Hutton's razor", and an existing data structure library -- and prove
their correctness. These examples show that this approach is viable: both that
hs-to-coq applies to existing Haskell code, and that the output it produces is
amenable to verification.Comment: 13 pages plus references. Published at CPP'18, In Proceedings of 7th
ACM SIGPLAN International Conference on Certified Programs and Proofs
(CPP'18). ACM, New York, NY, USA, 201
Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)
It has been known since the work of Duskin and Pelletier four decades ago
that KH^op, the category opposite to compact Hausdorff spaces and continuous
maps, is monadic over the category of sets. It follows that KH^op is equivalent
to a possibly infinitary variety of algebras V in the sense of Slominski and
Linton. Isbell showed in 1982 that the Lawvere-Linton algebraic theory of V can
be generated using a finite number of finitary operations, together with a
single operation of countably infinite arity. In 1983, Banaschewski and Rosicky
independently proved a conjecture of Bankston, establishing a strong negative
result on the axiomatisability of KH^op. In particular, V is not a finitary
variety--Isbell's result is best possible. The problem of axiomatising V by
equations has remained open. Using the theory of Chang's MV-algebras as a key
tool, along with Isbell's fundamental insight on the semantic nature of the
infinitary operation, we provide a finite axiomatisation of V.Comment: 26 pages. Presentation improve
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