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Knowledge Archives in Theorema: A LogicInternal Approach
"... Abstract. Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching la ..."
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Abstract. Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces and specifying the domains of categories and functors as namespaces with variable operations. All these constructs are logicinternal in the sense that they have a natural translation to higherorder logic so that certain aspects of Mathematical Knowledge Management can be realized in the object logic itself. There are a variety of operations on archives, though in this paper we can only sketch a few of them: knowledge retrieval and theory exploration, merging and splitting, insertion and translation to predicate logic.
KAT and PHL in Coq
"... In this article we describe an implementation of Kleene algebra with tests (KAT) in the Coq theorem prover. KAT is an equational system that has been successfully applied in program verification and, in particular, it subsumes the propositional Hoare logic (PHL). We also present an PHL encoding in K ..."
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In this article we describe an implementation of Kleene algebra with tests (KAT) in the Coq theorem prover. KAT is an equational system that has been successfully applied in program verification and, in particular, it subsumes the propositional Hoare logic (PHL). We also present an PHL encoding in KAT, by deriving its deduction rules as theorems of KAT. Some examples of simple program's formal correctness are given. This work is part of a study of the feasibility of using KAT in the automatic production of certificates in the context of (sourcelevel) ProofCarryingCode (PCC).
Mathematical Knowledge Archives in Theorema
"... Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambigu ..."
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Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces, addressing the domains of categories and functors as namespaces with variable opera− tions. All constructs are logic–internal in the sense that they have a natural translation to higher–order logic so that �mathematical knowledge management � can be treated by the object logic itself. 1