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:

Larry Paulson

On 15 May 2014, at 10:43, yongjian Li <lyj238 at> wrote:

> Dear experts:
>  I read line 2404 in Determinats.thy, which is listed as follows:
> definition trace :: "'a::semiring_1^'n^'n &#8658; '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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