Lawrence C. Paulson. Set theory for veri cation: II. induction and recursion. Journal of Automated Reasoning, 15(2):167-215, 1995. Home/Search Document Not in Database Summary Related Articles Check |
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Ordinal Arithmetic: A Case Study for Rippling in a Higher.. - Dennis, Smaill (Correct)
....we consider some options for further work (x6) 2 Ordinal Arithmetic: A Higher Order Family of Problems First we present the background to the problem area. Traditionally the theory of ordinals is presented within set theory; a machine checked presentation following this route is given in [17]. We instead present a computationally more direct theory of ordinals in which to reason. Ordinals can be thought of as (equivalence classes of) well ordered linear orders. As such they are a generalisation of the usual natural numbers. We work with so called ordinal notations, as in [14] this ....
....and lemmas shown in this section. We feel it demonstrates the possible applications for higher order proof planning systems in the ordinal domain. 6 Related and Further Work Di erent mechanisations of reasoning about ordinals and cardinals have been carried out previously. For example, Paulson [17] introduces ordinals in the course of a development of set theory. While providing the foundational assurance of a development from rst principles, this work assumes a fair amount of user interaction in building up proofs. A further development in this style is in [18] Closer in spirit to our ....
L.C. Paulson. Set theory for verication: II. induction and recursion. Journal of Automated Reasoning, 15:353-389, 1995.
Structuring Metatheory on Inductive Definitions - Basin, Matthews (2000) (1 citation) (Correct)
....de nitions in FS 0 support structured metatheoretic development. Our approach, based on parameterizing possible extensions is also possible in other metatheories that support similar kinds of inductive de nitions. Possible alternative candidates include constructive type theories [3] set theory [14] or higher order logic [6] We have also carried out a development similar to the one sketched in this paper using a theory of inductive de nitions based on the Knaster Tarski Theorem in Isabelle s theory of higher order logic [12] The di erences were minor. What follows is a snapshot from this ....
L. C. Paulson. Set theory for verication: II. Induction and recursion. J. Auto. Reas., 15:167-215, 1995.
Scoped Metatheorems - Basin, al. (1998) (Correct)
....to formalize and prove some variant of the Knaster Tarski xedpoint theorem, e.g. higher logic or set theory, is an alternative possible starting point for a theory of inductive de nitions. In particular, theorem provers like the HOL system [5] and Isabelle (which implements both HOL [11] and ZF [12]) provide such logics. These logics form the basis of packages that provide users with syntactic support for formalizing inductive de nitions from which the package automatically constructs and derives the corresponding induction principles. In terms of the Knaster Tarski theorem, an inductive de ....
L. C. Paulson. Set theory for verication: II. Induction and recursion. J. Auto. Reas., 15:167-215, 1995.
Solving for Set Variables in Higher-Order Theorem Proving - Brown (Correct)
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Lawrence C. Paulson. Set theory for veri cation: II. induction and recursion. Journal of Automated Reasoning, 15(2):167-215, 1995.
Motivation and Long Term Objectives - My Research Concerns (Correct)
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L. C. Paulson. Set theory for veri cation: II. induction and recursion. J. Automated Reasoning, 15:167-215, 1995.
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