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Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
How To Compute Antiderivatives
, 1995
"... oped by Lebesgue (see appendix for details). By proving that at least one of these techniques would always succeed, the process could be continued until the definite integral over all possible intervals was obtained. At this point, the antiderivative F (x) = R x 0 f(x) dx (up to a constant) beco ..."
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oped by Lebesgue (see appendix for details). By proving that at least one of these techniques would always succeed, the process could be continued until the definite integral over all possible intervals was obtained. At this point, the antiderivative F (x) = R x 0 f(x) dx (up to a constant) becomes apparent. The trouble with Denjoy's procedure is that it needs to be continued transfinitely and, in fact, may require arbitrarily large countable ordinals to complete. He called his process "totalization". The question was immediately raised (for example in Lusin's thesis) as to whether such use of transfinite numbers was really necessary. Could perhaps a di#erent approach avoid these countable ordinals (or at least arbitrarily large ones) and still recover the primitive? Received March 15, 1995. Research supported by the National Science Foundation. The author would like to thank
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"... CHRIS FREILING This is not about the symbolic manipulation of functions so popular these days. Rather it is about the more abstract, but infinitely less practical, problem of the primitive. Simply stated: ..."
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CHRIS FREILING This is not about the symbolic manipulation of functions so popular these days. Rather it is about the more abstract, but infinitely less practical, problem of the primitive. Simply stated: