Context-free grammars with graph control

Context-free grammars with graph control provide a general framework for the various types of context-free grammars with regulated rewriting. The vertices or edges of the directed graph are labeled with the productions of the grammar. The only strings in the language generated by the grammar are those whose derivations correspond to labeled paths in the graph. Inclusion relations among the various classes of context-free grammars with regulated rewriting such as programmed grammars (without failure fields), matrix grammars, periodically time-variant grammars, state grammars, and grammars with regular control are easily obtained and the graph provides insight into the nature of the restriction. Adding negative context to context-free grammars with graph control, we obtain a class of grammars equivalent to the context-free programmed grammars

Towards language-to-language transformation

This paper proposes a simplicity-oriented approach and framework for language-to-language transformation of, in particular, graphical languages. Key to simplicity is the decomposition of the transformation specification into sub-rule systems that separately specify purpose-specific aspects. We illustrate this approach by employing a variation of Plotkin’s Structural Operational Semantics (SOS) for pattern-based transformations of typed graphs in order to address the aspect ‘computation’ in a graph rewriting fashion. Key to our approach are two generalizations of Plotkin’s structural rules: the use of graph patterns as the matching concept in the rules, and the introduction of node and edge types. Types do not only allow one to easily distinguish between different kinds of dependencies, like control, data, and priority, but may also be used to define a hierarchical layering structure. The resulting Type-based Structural Operational Semantics (TSOS) supports a well-structured and intuitive specification and realization of semantically involved language-to-language transformations adequate for the generation of purpose-specific views or input formats for certain tools, like, e.g., model checkers. A comparison with the general-purpose transformation frameworks ATL and Groove, illustrates along the educational setting of our graphical WebStory language that TSOS provides quite a flexible format for the definition of a family of purpose-specific transformation languages that are easy to use and come with clear guarantees

Cyclic Datatypes modulo Bisimulation based on Second-Order Algebraic Theories

Cyclic data structures, such as cyclic lists, in functional programming are tricky to handle because of their cyclicity. This paper presents an investigation of categorical, algebraic, and computational foundations of cyclic datatypes. Our framework of cyclic datatypes is based on second-order algebraic theories of Fiore et al., which give a uniform setting for syntax, types, and computation rules for describing and reasoning about cyclic datatypes. We extract the "fold" computation rules from the categorical semantics based on iteration categories of Bloom and Esik. Thereby, the rules are correct by construction. We prove strong normalisation using the General Schema criterion for second-order computation rules. Rather than the fixed point law, we particularly choose Bekic law for computation, which is a key to obtaining strong normalisation. We also prove the property of "Church-Rosser modulo bisimulation" for the computation rules. Combining these results, we have a remarkable decidability result of the equational theory of cyclic data and fold.Comment: 38 page

Graphical Reasoning in Compact Closed Categories for Quantum Computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.Comment: 21 pages, 9 figures. This is the journal version of the paper published at AIS

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto