Categories, types, and structures: an introduction to category theory for the working computer scientist
Interaction categories and the foundations of typed concurrent programming
Proceedings of the NATO Advanced Study Institute on Deductive program design
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Programmed graph replacement systems
Handbook of graph grammars and computing by graph transformation
Graph grammars with node-label controlled rewriting and embedding
Proceedings of the 2nd International Workshop on Graph-Grammars and Their Application to Computer Science
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Semantic Analysis of Matrix Structures
ICDAR '05 Proceedings of the Eighth International Conference on Document Analysis and Recognition
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Proving properties about lists using containers
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Matrix approach to graph transformation: matching and sequences
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Rewriting measurement-based quantum computations with generalised flow
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
On the confluence of the graphic calculus with penrose diagrams (i)
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Equivalence checking of quantum protocols
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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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 reasoning about compact closed categories. 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.