RALL: Machine-supported proofs for relation algebra

  • David von Oheimb
  • Thomas F. Gritzner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1249)


We present a theorem proving system for abstract relation algebra called RALL (=Relation-Algebraic Language and Logic), based on the generic theorem prover Isabelle. On the one hand, the system is an advanced case study for Isabelle/HOL, and on the other hand, a quite mature proof assistant for research on the relational calculus. RALL is able to deal with the full language of heterogeneous relation algebra including higher-order operators and domain constructions, and checks the type-correctness of all formulas involved. It offers both an interactive proof facility, with special support for substitutions and estimations, and an experimental automatic prover. The automatic proof method exploits an isomorphism between relation-algebraic and predicate-logical formulas, relying on the classical universal-algebraic concepts of atom structures and complex algebras.


Relation algebra Isabelle interactive and automatic theorem proving atom structure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • David von Oheimb
    • 1
  • Thomas F. Gritzner
    • 2
  1. 1.Fakultät für InformatikTechnische Universität MünchenMünchenGermany
  2. 2.Universität der Bundeswehr MünchenNeubibergGermany

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