Re: [isabelle] Executing real numbers as approximating functions



Am 08.08.2012 um 22:01 schrieb Brian Huffman:

> On Wed, Aug 8, 2012 at 9:47 PM, Florian Haftmann
> <florian.haftmann at informatik.tu-muenchen.de> wrote:
>> once I have heard about a formalisation to execute real numbers as
>> approximating functions, i.e. where each real number r is implemented
>> using a function
>> 
>>  R :: nat => float
>> 
>> such that R n equals r approximated to the n-th digit (or something
>> similar).
>> 
>> Can somebody give me a reference for that?
> 
> Russell O'Connor has implemented a similar representation of the
> computable reals in Coq:

Section 4 of Johannes's PLMMS '09 paper [1] states that Harrison's Ph.D. thesis [2] has something like that (with "nat => int"), but I couldn't find it in the thesis (cf. Sects. 2.3 to 2.7). The "positional expansion" of 2.4 seems the most closely related, but from what I understand it yields one digit at a time, not an approximation. Maybe Johannes can expand on this.

[1] http://home.in.tum.de/~hoelzl/documents/hoelzl09realinequalities.pdf
[2] http://taha.e.twiki.net/twiki/pub/Teaching/617References_Fall09/Theorem-Proving-with-the-Real-Numbers.pdf

Jasmin






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