1. 10
  1.  

  2. 2

    “As far as I can tell, any modulo-based addition is a monoid, but while, say, modulo 37 addition probably doesn’t have any practical application, modulo 360 addition does, because it’s how you do angular addition. “

    Yes, modulo-based addition would be a monoid.

    A group, is a monoid that has inverses for every element.

    Modulo-based addition is a group (under addition), so it is a monoid. It has stronger properties than a monoid needs (it has inverse, it is a cyclic group).

    “..Parameter Object/tuple isomorphism # The third isomorphism that I claim exists is the one between Parameter Objects and tuples. If, however, we assume that the two above isomorphisms hold, then this third isomorphism exists as well. I know from my copy of Conceptual Mathematics that isomorphisms are transitive. If you can translate from Parameter Object to argument list, and from argument list to tuple, then you can translate from Parameter Object to tuple; and vice versa. Thus, I’m not going to use more words on this isomorphism. … “

    Hmm… so I am struggling with this assertion… I guess tuples and list of arguments can be used ‘in the same way’. But I am not sure this makes the two objects mathematically isomorphic. Although, I could be mis-interpreting the assertion.

    1. 2

      I liked the pictures in the profunctor articles. They chose C♯ for their presentation language, which might be a little verbose for teaching.

      1. 1

        I’m unfamiliar with Mark Seemann, his writing or his credibility, can someone vouch for him in terms of using the massive article series he linked to as solid reference material? Given the intriguing nature of this post I’m considering reading his “Code That Fits in Your Head” book, but am also curious as to whether that is good.

        1. 1

          Given the intriguing nature of this post I’m considering reading his “Code That Fits in Your Head” book, but am also curious as to whether that is good.

          Well, there’s one way to find out – but it will cost you upwards of $40 or a quick web search for reviews.