Missing Applicative instance

[shoooe]

Sounds like a Matrix a is a perfect fit for an Applicative (and possibly even Monad) instance. Data.Vector also has such instances, and given that the former is implemented in terms of the latter, the actual implementation of these instances should be trivial.

What am I missing?

[octopuscabbage]

Applicative I can see, although it would have to be a partial function because it will only work on matricies of the same dimensions.

I don't see a monad instance because how would one concatenate matricies in a sane way.

[hherman1]

I'd say >> ~ Tensor Product,

As far as concatenation

Monoid a => Monoid (Matrix a)
Pointwise mappend

[octopuscabbage]

I'd say >> ~ Tensor Product,

I'm not familiar with that operation so I can't really say if that makes sense or not.

Monoid a => Monoid (Matrix a)
Pointwise mappend

makes sense, for different sized matrices we could just <> mempty.

[hherman1]

http://www.sharetechnote.com/image/EngMath_TensorProduct_01.png

Similar to how list does >>, but makes sense in 2D

[octopuscabbage]

What happens if the matrices are differently sized? Would they just be mempty?

[octopuscabbage]

I plan to at least write the monoid instance in a few minutes and the tensor product if I can figure it out.

[hherman1]

its a_ii * B, dimensions dont matter for tensor

On Wed, Jan 20, 2016 at 3:52 PM, Chris Denniston notifications@github.com
wrote:

I plan to at least write the monoid instance in a few minutes and the
tensor product if I can figure it out.

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Reply to this email directly or view it on GitHub
#17 (comment).

[octopuscabbage]

ohh i see that now

[octopuscabbage]

The problem being that applicative is a requirement for monad. Maybe we can work backwards from <*> being ap?

[octopuscabbage]

would applicative just be tensor multiplication but instead of multiplication be function application?

[shoooe]

I guess we can close this now, right?

[octopuscabbage]

I suppose once the PR gets merged but we should probably take our commentary there.

[Daniel-Diaz]

Closing this. See #27