Wolfram Kahl

Relational methods in computer science

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Relational and algebraic methods in computer science

This book constitutes the proceedings of the 14th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2014 held in Marienstatt, Germany, in April/May 2014. The 25 revised full papers presented were carefully selected from 37 submissions. The papers are structured in specific fields on concurrent Kleene algebras and related formalisms, reasoning about computations and programs, heterogeneous and categorical approaches, applications of relational and algebraic methods and developments related to modal logics and lattices.

Calculational Relation-Algebraic Proofs in Isabelle/Isar

We propose a collection of theories in the proof assistant Isabelle/Isar that support calculational reasoning in and about heterogeneous relational algebras and Kleene algebras.

A Relation-Algebraic Approach to Graph Structure Transformation

Graph transformation is a rapidly expanding field of research, motivated by a wide range of applications.

Relational treatment of term graphs with bound variables

We show how and why it makes sense to use a relational formalisation instead of the usual functional one in the treatment of term graphs. Special attention is paid to term graphs with bound variables, that have, to our knowledge, never been formalised with such a generality before. Besides the novel treatment of term graphs themselves, we present an innovative relational homomorphism concept that for the first time allows to consider terms, resp. term trees as a special case of term graphs and still have the full power of (second-order) substitution available.

Dependently-typed formalisation of relation-algebraic abstractions

We present a formalisation in the dependently-typed programming language Agda2 of basic category and allegory theory, and of generalised algebras where function symbols are interpreted in a parameter category. We use this nestable algebra construction as the basis for nestable category and allegory constructions, ultimately aiming at a formalised foundation of the algebraic approach to graph transformation, which uses constructions in categories of graph structures considered as unary algebras. The features of Agda permit strongly-typed programming with these nested algebras and with relational homomorphisms between them in a natural mathematical style and with remarkable ease, far beyond what can be achieved even in Haskell.

Relational matching for graphical calculi of relations

Abstract In this paper we extend an earlier approach to graphical relation calculi towards relational matching, thus allowing proofs with fewer auxiliary steps and concentrating more on the essential proof ideas. For facilitating the formal argument we introduce hierarchical relational diagrams as an intermediate structure and employ more of the algebraic graph rewriting repertoire for defining relational rewriting of these hierarchical diagrams.

Amalgamating pushout and pullback graph transformation in collagories

The relation-algebraic approach to graph transformation replaces the universal category-theoretic characterisations of pushout and pullbacks with the local characterisations of tabulations and co-tabulations. The theory of collagories is a weak axiomatisation of relationalgebraic operations that closely corresponds to adhesive categories. We show how to amalgamate double-pushout and double-pullback rewriting steps into a fused rewriting concept where rules can contain subgraph variables in a natural and flexible way, and rewriting can delete or duplicate the matched instances of such variables.

Control-Flow semantics for assembly-level data-flow graphs

As part of a larger project, we have built a declarative assembly language that enables us to specify multiple code paths to compute particular quantities, giving the instruction scheduler more flexibility in balancing execution resources for superscalar execution. Since the key design points for this language are to only describe data flow, have built-in facilities for redundancies, and still have code that looks like assembler, by virtue of consisting mainly of assembly instructions, we are basing the theoretical foundations on data-flow graph theory, and have to accommodate also relational aspects. Using functorial semantics into a Kleene category of “hyper-paths”, we formally capture the data-flow-with-choice aspects of this language and its implementation, providing also the framework for the necessary correctness proofs.

Refinement and Development of Programs from Relational Specifications

Abstract These tutorial notes present an overview of specification and refinement concepts and methods that are based on relations.