Initiality, induction, and computability
Algebraic methods in semantics
Handbook of theoretical computer science (vol. B)
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
Theoretical Computer Science
Swinging types = functions + relations + transition systems
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Final Data Types and Their Specification
ACM Transactions on Programming Languages and Systems (TOPLAS)
Abstract data types and software validation
Communications of the ACM
Algebraic Foundations of Systems Specification
Algebraic Foundations of Systems Specification
Compiling language definitions: the ASF+SDF compiler
ACM Transactions on Programming Languages and Systems (TOPLAS)
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
Deriving Incremental Implementations from Algebraic
AMAST '91 Proceedings of the Second International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Invariants, Bisimulations and the Correctness of Coalgebraic Refinements
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Initial algebra and final coalgebra semantics for concurrency.
Initial algebra and final coalgebra semantics for concurrency.
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
Mathematical Structures in Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
The rewriting logic semantics project
Theoretical Computer Science
Adjoint folds and unfolds: or: scything through the thicket of morphisms
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
CEFP'09 Proceedings of the Third summer school conference on Central European functional programming school
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The increasing application of notions and results from category theory, especially from algebra and coalgebra, has revealed that any formal software or hardware model is constructor- or destructor-based, a white-box or a black-box model. A highly-structured system may involve both constructor- and destructor-based components. The two model classes and the respective ways of developing them and reasoning about them are dual to each other. Roughly said, algebras generalize the modeling with context-free grammars, word languages and structural induction, while coalgebras generalize the modeling with automata, Kripke structures, streams, process trees and all other state- or object-oriented formalisms. We summarize the basic concepts of co/algebra and illustrate them at a couple of signatures including those used in language or compiler construction like regular expressions or acceptors.