Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Enhancing the NUPRL proof development system and applying it to computational abstract algebra
Algebra of programming
Heterogeneous relation algebra
Relational methods in computer science
Algebraic approaches to graph transformation. Part I: basic concepts and double pushout approach
Handbook of graph grammars and computing by graph transformation
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Proof, language, and interaction
Constructive Category Theory (No. 1)
Proceedings on Mathematical Foundations of Computer Science
Universal Algebra in Type Theory
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Journal of Functional Programming
ACM Transactions on Computational Logic (TOCL)
Algebra of Programming Using Dependent Types
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
An Optimized Cell BE Special Function Library Generated by Coconut
IEEE Transactions on Computers
Domain and Antidomain Semigroups
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Collagories for Relational Adhesive Rewriting
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Amalgamating pushout and pullback graph transformation in collagories
ICGT'10 Proceedings of the 5th international conference on Graph transformations
Integrating an automated theorem prover into agda
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Towards certifiable implementation of graph transformation via relation categories
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
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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.