The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the subgraph, but are not part of it.
We introduce the patch graph rewriting framework, a visual graph rewriting language with precise formal semantics. The language has rich expressive power in two ways. Firstly, rules can flexibly constrain the permitted shapes of patches touching matching subgraphs. Secondly, rules can freely transform patches. While the framework is designed to be easy to understand, it subsumes many approaches to graph rewriting.
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function symbols is the same for all term rewriting rules of the system, local ones, where a single renaming for every rule is used, and a combination, where one symbol set is renamed globally while the other set is renamed locally. Preservation of semantic properties like convertibility and termination is analysed for the different isomorphism notions. The notions of…
A Coinductive Framework for Infinitary Rewriting and Equational Reasoning (Extended Version)
我们提出了一个共归纳的框架，定义无穷类似物的方程推理和重写统一的方式。我们定义关系=^infty，无限等式推理的概念，和->^infty，无限重写的标准概念如下：=^infty：= nu R。（<-_root + ->_root + lift（R））^* ->^infty：= mu R. nu S（->_root + lift（R））^* ; lift（S）其中lift（R）：= {（f（s_1，.，s_n），f（t_1，.，t_n））|s_1 R t_1，.，s_n R t_n } + id，其中mu是最小不动点算子，nu是最大不动点算子.该设置捕获任意序数长度的重写序列，但它既不需要序数也不需要度量收敛。这使得该框架特别适合于定理证明器中的形式化。
The Kappa biochemistry and the MØD organic chemistry frameworks are amongst the most intensely developed applications of rewriting-based methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute a number of original developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochas…
The purposes of this note are the following two; we first generalize Okada-Takeuti's well quasi ordinal diagram theory, utilizing the recent result of Dershowitz-Tzameret's version of tree embedding theorem with gap conditions. Second, we discuss possible use of such strong ordinal notation systems for the purpose of a typical traditional termination proof method for term rewriting systems, especially for second-order (pattern-matching-based) rewriting systems including a rewrite-theoretic version of Buchholz's hydra game.
A version of the situation calculus in which situations are represented as first-order terms is presented. Fluents can be computed from the term structure, and actions on the situations correspond to rewrite rules on the terms. Actions that only depend on or influence a subset of the fluents can be described as rewrite rules that operate on subterms of the terms in some cases. If actions are bidirectional then efficient completion methods can be used to solve planning problems. This representation for situations and actions is most similar to the fluent calculus of Thielscher \cite{Thielscher9…
In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit trail system for individual graphs and graph hierarchies. This provides us with a compact way to maintain the history of updates of an object, including its multiple versions. The main application of the designed framework is an audit trail of updates to knowledge represented by hierarchies of graphs. Therefore, we introduce the notion of rule hierarchy that…
In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than beta-eta-equivalence, like those induced by parametricity and dinaturality. We show that the Yoneda type isomorphisms yield a rewriting over types, that we call Yoneda reduction, which can be used to eliminate quantifiers from a polymorphic type, replacing them with a combination of monomorphic type constructors. We establish some sufficient conditions under w…
Runtime verification (RV) consists in dynamically verifying that the event traces generated by single runs of a system under scrutiny (SUS) are compliant with the formal specification of its expected properties. RML (Runtime Monitoring Language) is a simple but expressive Domain Specific Language for RV; its semantics is based on a trace calculus formalized by a deterministic rewriting system which drives the implementation of the interpreter of the monitors generated by the RML compiler from the specifications. While determinism of the trace calculus ensures better performances of the generat…
