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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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Cited by 11 (7 self)
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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.
An Irrational Construction of R from Z
"... This paper reports on a construction of the real numbers in the ProofPower implementation of the HOL logic. Since the original construction was implemented, some major improvements to the ideas have been discovered. The improvements involve some entertaining mathematics: it turns out that the De ..."
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Cited by 1 (0 self)
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This paper reports on a construction of the real numbers in the ProofPower implementation of the HOL logic. Since the original construction was implemented, some major improvements to the ideas have been discovered. The improvements involve some entertaining mathematics: it turns out that the Dedekind cuts provide many routes one can travel to get from the ring of integers, Z, to the eld of real numbers, R.
1.1 Automated Theorem Proving Background
"... Abstract. This paper reports on a construction of the real numbers in the ProofPower implementation of the HOL logic. Since the original construction was implemented, some major improvements to the ideas have been discovered. The improvements involve some entertaining mathematics: it turns out that ..."
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Abstract. This paper reports on a construction of the real numbers in the ProofPower implementation of the HOL logic. Since the original construction was implemented, some major improvements to the ideas have been discovered. The improvements involve some entertaining mathematics: it turns out that the Dedekind cuts provide many routes one can travel to get from the ring of integers, Z, to the field of real numbers, R. The traditional stopover on the way is the field of rational numbers, Q. This paper shows that going via certain rings of algebraic numbers can provide a pleasant alternative to the more welltrodden track.