About: We prove Chen and Grätzer’s construction theorem for Stone algebras in Isabelle/HOL. The development requires extensive reasoning about algebraic structures in addition to reasoning in algebraic structures. We present an approach for this using classes and locales with implicit carriers. This involves using function liftings to implement some aspects of dependent types and using embeddings of algebras to inherit theorems. We also formalise a theory of filters based on partial orders.   Goto Sponge  NotDistinct  Permalink

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  • We prove Chen and Grätzer’s construction theorem for Stone algebras in Isabelle/HOL. The development requires extensive reasoning about algebraic structures in addition to reasoning in algebraic structures. We present an approach for this using classes and locales with implicit carriers. This involves using function liftings to implement some aspects of dependent types and using embeddings of algebras to inherit theorems. We also formalise a theory of filters based on partial orders.
Subject
  • Mathematical structures
  • Abstract algebra
  • Smoked food
  • Algebraic structures
  • Free theorem provers
  • Proof assistants
  • Software using the BSD license
  • Beer in Poland
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