[Haskell-cafe] Vectors, vector spaces and type-level Haskell

[Branimir Maksimovic]

> On 04.10.2021., at 09:55, Stuart Hungerford <stuart.hungerford at gmail.com> wrote:
> 
> On Mon, Oct 4, 2021 at 6:45 PM Branimir Maksimovic
> <branimir.maksimovic at gmail.com <mailto:branimir.maksimovic at gmail.com>> wrote:
> 
>> On 04.10.2021., at 09:38, Stuart Hungerford <stuart.hungerford at gmail.com> wrote:
>> 
>> On Mon, 4 Oct 2021 at 4:25 pm, Branimir Maksimovic <branimir.maksimovic at gmail.com> wrote:
>>> 
>>> 2d vector space is generated by two base vectors, if, which are orthogonal,
>>> that is normalised. They generate any other vector in that space.
>> 
>> Yes, so I would be looking to somehow tie  the 2 basis vectors back to a 2D vector space. Or indeed n basis vectors to an n-vector space.
>> 
>> 
>> Space is generated by base vectors, think in that way…
>> With vector addition and scalar multiplication you get third vector.
>> so dimension is number of different directions of base vectors.
>> So, easy...
> 
> Thanks Branimir I appreciate you taking the time to reply to what
> could be a silly question. Perhaps I haven't explained what I'm
> looking for very well.
> 
> I know about the vector and scalar operations the vector space
> inherits from the underlying abelian group and field of scalars.
> Including the basis of linearly independent vectors that generates all
> vectors in the space.
> 
> What I'd like to do is use the Haskell type system to encode those
> operations so I can't--for example--use a two dimensional and three
> dimensional vector in the same operation, or "ask" a vector what its
> "ambient" vector space is and have those operations checked at compile
> time.
> 
> I've avoided learning about type-level programming in Haskell so far,
> but it may be time to delve deeper...
> 
> Thanks again,
> 
> Stu
Well vector is tuple 3d space 3 tuples of 3 elements each representing
3 directions in 3d space eg.
Types can be anything, but same, so you could represent
with a 3 lists also. i dunno what you mean by type checking?
You have type checking already.

Greets, Branimir (and thanks)

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