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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 471 (49 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 ...
Natural Deduction as HigherOrder Resolution
 Journal of Logic Programming
, 1986
"... An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause. ..."
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Cited by 61 (11 self)
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An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause.
Constructing Recursion Operators in Intuitionistic Type Theory
 Journal of Symbolic Computation
, 1984
"... MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are for ..."
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Cited by 22 (5 self)
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MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are formally derived for a large class of wellfounded relations. Included are < on natural numbers, and relations formed by inverse images, addition, multiplication, and exponentiation of other relations. The constructions are given in full detail to allow their use in theorem provers for Type Theory, such as Nuprl. The theory is compared with work in the field of ordinal recursion over higher types.
Proving termination of normalization functions for conditional expressions
 Journal of Automated Reasoning
, 1986
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~ 1989 Kluwer Academic Publishers. Printed in the Netherlands. The Foundation of a Generic Theorem Prover
, 1988
"... Abstract. 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 metahlogic (or 'logical framework') in which the objectlogics are form ..."
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Abstract. 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 metahlogic (or 'logical framework') in which the objectlogics are formalized. Isabelle is now based on higherorder logic a precise and wellunderstood foundation. Examples illustrate the use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown to be 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