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Dependently-Typed Formalisation of Relation-Algebraic Abstractions

  • Wolfram Kahl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6663)

Abstract

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.

Keywords

Dependently typed programming algebras as data allegories of relational algebra morphisms nested algebras 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wolfram Kahl
    • 1
  1. 1.McMaster UniversityHamiltonCanada

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