[Iris-Club] pre-wp's definition: s, s1, and s2
Lars Birkedal
birkedal at cs.au.dk
Sun Aug 21 09:03:50 CEST 2016
Dear Jeehon,
The fixed point is unique, see 5.10 in the tutorial notes:
http://cs.au.dk/~abizjak/documents/publications/categorical-logic-tutorial-notes.pdf
Best,
Lars.
On 20 Aug 2016, at 16:22, Jeehoon Kang <jeehoon.kang at sf.snu.ac.kr<mailto:jeehoon.kang at sf.snu.ac.kr>> wrote:
Another point is that, "wp is defined as the fixed-point of a contractive function," but I am not sure there is "the" fixed-point. Previously in the documentation it is only said that a contractive function has "a" fixed-point.
- Is it indeed "the" fixed-point"?
- If not, in what sense a chosen fixed-point is canonical?
Thank you,
Jeehoon
2016-08-20 23:02 GMT+09:00 Jeehoon Kang <jeehoon.kang at sf.snu.ac.kr<mailto:jeehoon.kang at sf.snu.ac.kr>>:
I think I almost understand `pre-wp` ;-) But I still cannot understand the use of step-index: may I ask what is the intuition behind requiring `m+1 \in ...` for the value case? I think I understand why you required `m in ...` in the reduction case, since there is actually a step. But for the value case, I am not sure why it is necessary to demand `m+1 \in ...`. Why `m \in ...` is not enough?
Thank you,
Jeehoon
2016-08-19 21:14 GMT+09:00 Ralf Jung <jung at mpi-sws.org<mailto:jung at mpi-sws.org>>:
Hi,
> But I am still confused of the definition of `pre-wp`.. In the 2nd
> line, `s` should have the type ∆(Val), mandated by `ϕ(s)`; and yet at
> the same time `s` should have the type Res, from `s · rf`. May I ask if
> what am I missing here?
Right, that should have been ϕ(v)(s). Then things hopefully make sense...
Kind regards,
Ralf
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Seoul National University<http://www.snu.ac.kr/>
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Jeehoon Kang (Ph.D. student)<http://sf.snu.ac.kr/jeehoon.kang>
Software Foundations Laboratory<http://sf.snu.ac.kr/>
Seoul National University<http://www.snu.ac.kr/>
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