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The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 433 (47 self)
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Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment. Higherorder logic has several practical advantages over other metalogics. Many proof techniques are known, such as Huet's higherorder unification procedure. Key words: higherorder logic, higherorder unification, Isabelle, LCF, logical frameworks, metareasoning, natural deduction Contents 1 History and overview 2 2 The metalogic M 4 2.1 Syntax of the metalogic ......................... 4 2.2 ...
The Theory of Classification, Part 1: Perspectives on Type Compatibility
 MayJune 2002
, 2002
"... This is the first article in a regular series on objectoriented type theory, aimed specifically at nontheoreticians. The objectoriented notion of classification has for long been a fascinating issue for type theory, chiefly because no other programming paradigm has so sought to establish systemat ..."
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Cited by 6 (4 self)
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This is the first article in a regular series on objectoriented type theory, aimed specifically at nontheoreticians. The objectoriented notion of classification has for long been a fascinating issue for type theory, chiefly because no other programming paradigm has so sought to establish systematic sets of relationships between all of its types. Over
A Preliminary User's Manual for Isabelle
"... The theorem prover Isabelle and several of its objectlogics are described. Where ..."
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Cited by 1 (0 self)
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The theorem prover Isabelle and several of its objectlogics are described. Where