# Re: [isabelle] a line of type definition

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
On 15 May 2014, at 10:43, yongjian Li <lyj238 at ios.ac.cn> wrote:
> 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!
>

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