Generalized Rewrite Theories

Abstract

Since its introduction, more than a decade ago, rewriting logic has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. In particular, the Maude system now supports subsorting and conditions in the equational logic for data, and also frozen arguments to block undesired nested rewritings; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories

Domain science and engineering from computer science to the sciences of informatics. Part I: Engineering

“…Then, by now "classical", formal specification languages Alloy [16], CafeOBJ [9], CSP [13], Event B [1], ASM [23], CASL [7], DC [27], Maude [6,20,5], MSCs [15], RSL [10], TLA+ [17], Z [26], Petri Nets [24], Statecharts [11], VDM [8], etc. need be further explored, formal interfaces of satisfaction established, and new, formal, or at least mathematical specification languages be developed.…”

Semantics and pragmatics of Real-Time Maude

“…In the general version of rewrite theories over MEL theories defined in [7], a rewrite theory is a tuple R = (Σ , E , ϕ, R) consisting of: (i) a MEL theory (Σ , E ); (ii) a function ϕ: Σ → P f (N) assigning to each function symbol f :…”

“…A key goal of this work is to document the tool's theoretical foundations, based on a simplified semantics of real-time rewrite theories [23,28] made possible by some recent developments in the foundations of rewriting logic [7]; these simplified theoretical foundations are explained in Section 3. We also give a precise description of the semantics of Real-Time Maude specifications and of its symbolic execution and formal analysis commands.…”

Theoroidal Maps as Algebraic Simulations

“…Indeed, there are several rewriting logic language implementations, including CafeOBJ [11], ELAN [3], and Maude [7,8]. Rewriting logic then has inference rules to infer all the possible concurrent computations in a system [16,4], in the sense that, given two states…”

“…The definition is exactly the same except for item (4), where the implication must actually be an equivalence.…”