Proceedings of a tutorial and workshop on Category theory and computer programming
Algebraic methods in semantics
A mathematical approach to nondeterminism in data types
ACM Transactions on Programming Languages and Systems (TOPLAS)
Information and Computation
Partiality, cartesian closedness, and toposes
Information and Computation
Nondeterministic algebraic specifications and nonconfluent term rewriting
Journal of Logic Programming
A complete calculus for the multialgebraic and functional semantics of nondeterminism
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
Categories of relational structures
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
A View on Implementing Processes: Categories of Circuits
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Relating Two Categorial Models of Term Rewriting
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Equational Reasoning with Two-Dimensional Diagrams
Term Rewriting, French Spring School of Theoretical Computer Science, Advanced Course
MPC '95 Mathematics of Program Construction
Algebraic Graph Derivations for Graphical Calculi
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Term Graph Syntax for Multi-Algebras
Term Graph Syntax for Multi-Algebras
Premonoidal categories and notions of computation
Mathematical Structures in Computer Science
The HASCASL prologue: categorical syntax and semantics of the partial λ-calculus
Theoretical Computer Science
A Note on an Old-Fashioned Algebra for (Disconnected) Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
Unitary Theories, Unitary Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
Control-Flow semantics for assembly-level data-flow graphs
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
Hi-index | 5.23 |
Multi-algebras allow for the modelling of nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature Σ as cartesian functors from the algebraic theory over Σ to Set. We introduce two different notions of theory over a signature, both having a structure weaker than cartesian, and we consider functors from them to Rel or Pfn, the categories of sets and relations or partial functions, respectively.Next we discuss how the functorial presentation provides guidelines when choosing syntactical notions for a class of algebras, and as an application we argue that the natural generalization of usual terms are "conditioned terms" for partial algebras, and "term graphs" for multi-algebras.