Results 1 
5 of
5
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. Isabelle is ..."
Abstract

Cited by 422 (47 self)
 Add to MetaCart
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 ...
Categorical Logic
 A CHAPTER IN THE FORTHCOMING VOLUME VI OF HANDBOOK OF LOGIC IN COMPUTER SCIENCE
, 1995
"... ..."
New Foundations for Fixpoint Computations
, 1990
"... This paper introduces a new higherorder typed constructive predicate logic for fixpoint computations, which exploits the categorical semantics of computations introduced by Moggi [8] and contains a strong version of MartinLof's `iteration type' [11]. The type system enforces a separation of comput ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
This paper introduces a new higherorder typed constructive predicate logic for fixpoint computations, which exploits the categorical semantics of computations introduced by Moggi [8] and contains a strong version of MartinLof's `iteration type' [11]. The type system enforces a separation of computations from values. The logic contains a novel form of fixpoint induction and can express partial and total correctness statements about evaluation of computations to values. The constructive nature of the logic is witnessed by strong metalogical properties which are proved using a categorytheoretic version of the `logical relations' method. 1 Computation types It is well known that primitive recursion at higher types can be given a categorical characterisation in terms of Lawvere's concept of natural number object [6]. We show that a similar characterisation can be given for general recursion via fixpoint operators of higher types, in terms of a new conceptthat of a fixpoint object in ...
A Preliminary User's Manual for Isabelle
"... The theorem prover Isabelle and several of its objectlogics are described. Where ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The theorem prover Isabelle and several of its objectlogics are described. Where
New Foundations for Fixpoint Computations
"... This paper introduces a new higherorder typed constructive predicate logic for fixpoint computations, which exploits the categorical semantics of computations introduced by Moggi [8] and contains a strong version of MartinLof’s ‘iteration type ’ [ll]. The type system enforces a separation of compu ..."
Abstract
 Add to MetaCart
This paper introduces a new higherorder typed constructive predicate logic for fixpoint computations, which exploits the categorical semantics of computations introduced by Moggi [8] and contains a strong version of MartinLof’s ‘iteration type ’ [ll]. The type system enforces a separation of computations from values. The logic contains a novel form of fixpoint induction and can express partial and total correctness statements about evaluation of computations to values. The constructive nature of the logic is witnessed by strong metalogical properties which are proved using a categorytheoretic version of the ‘logical relations ’ method. 1 Computation types It is well known that primitive recursion at higher types can be given a categorical characterisation in terms of Lawvere’s concept of natural number object [6]. We show that a similar characterisation can be given for general recursion via fixpoint operators of higher types, in terms of a new conceptthat of a fixpoint object in a suitably