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Proof Generation in the Touchstone Theorem Prover
 In Proceedings of the International Conference on Automated Deduction
, 2000
"... . The ability of a theorem prover to generate explicit derivations for the theorems it proves has major benets for the testing and maintenance of the prover. It also eliminates the need to trust the correctness of the prover at the expense of trusting a much simpler proof checker. However, it is ..."
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. The ability of a theorem prover to generate explicit derivations for the theorems it proves has major benets for the testing and maintenance of the prover. It also eliminates the need to trust the correctness of the prover at the expense of trusting a much simpler proof checker. However, it is not always obvious how to generate explicit proofs in a theorem prover that uses decision procedures whose operation does not directly model the axiomatization of the underlying theories. In this paper we describe the modications that are necessary to support proof generation in a congruenceclosure decision procedure for equality and in a Simplexbased decision procedure for linear arithmetic. Both of these decision procedures have been integrated using a modied NelsonOppen cooperation mechanism in the Touchstone theorem prover, which we use to produce proofcarrying code. Our experience with designing and implementing Touchstone is that proof generation has a relatively low c...
A thread of HOL development
 Computer Journal
"... The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evoluti ..."
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The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evolution of certain important features available in a recent implementation. We also illustrate how the module system of Standard ML provided security and modularity in the construction of the HOL kernel, as well as serving in a separate capacity as a useful representation medium for persistent, hierarchical logical theories.
Binary Decision Diagrams as a HOL Derived
"... jrh�cl.cam.ac.uk Binary Decision Diagrams �BDDs � are a representation for Boolean formulas which makes many operations � in particular tautology�checking � surprisingly e�cient in important practical cases. In contrast to such custom decision procedures � the HOL theorem prover expands all proofs o ..."
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jrh�cl.cam.ac.uk Binary Decision Diagrams �BDDs � are a representation for Boolean formulas which makes many operations � in particular tautology�checking � surprisingly e�cient in important practical cases. In contrast to such custom decision procedures � the HOL theorem prover expands all proofs out to a sequence of extremely simple primitive inferences. In this paper we describe how the BDD algorithm may be adapted to comply with such strictures � helping us to understand the strengths and limitations of the HOL approach. 1. BINARY DECISION DIAGRAMS There are many ways to test whether a Boolean expres� sion is a tautology �i.e. true for all truth assignments of the variables it involves� � such as the use of truth tables or transformation to conjunctive normal form. However � the problem of tautology checking is co�NP complete � in fact the complementary operation of test�