Email Gateway (Aug 19 2022 at 14:28): Email Gateway (Aug 19 2022 at 14:28):From: yongjian Li <lyj238@ios.ac.cn>
Dear experts:
I read line 2404 in Determinats.thy, which is listed as follows:
definition trace :: "'a::semiring_1^'n^'n ⇒ 'a"
where "trace A = setsum (λi. ((A$i)$i)) (UNIV::'n set)"
I can guess A is of type 'a matrix, returns a result with type 'a. (informally)
This is the first time I meet the type cat operator ^, can some experts
interpret it?
Or simply point me which tutorial material I should read .
regards!
Yongjian Li
Associate Research Professor, Ph.D
State Key Laboratory of Computer Science
Institute of Software, Chinese Academy of Sciences
Beijing, China
Tel: (+86)10 6266 1645
Email:lyj238@ios.ac.cn
Homepage: http://lcs.ios.ac.cn/~lyj238
Email Gateway (Aug 19 2022 at 14:28):From: Lawrence Paulson <lp15@cam.ac.uk>
This is a way of representing an N-dimensional vector space as a type, even though higher-order logic does not have dependent types. The idea is to represent the number N by a type having that many elements.
John Harrison invented this idea, and his exposition is still the best:
http://link.springer.com/article/10.1007%2Fs10817-012-9250-9
Larry Paulson
Last updated: Nov 21 2024 at 12:39 UTC