Ever published?

[saulshanabrook]

Did this paper ever get published? I can't find it anywhere besides this Github repo. Very interesting work!

[womenflyplanes]

No, but I could put it on Arxiv.

On Sun, Apr 22, 2018 at 10:16 PM, Saul Shanabrook notifications@github.com wrote:

Did this paper ever get published? I can't find it anywhere besides this Github repo. Very interesting work!

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[womenflyplanes]

If you are familiar with the topic and feel like reviewing I could then put that on the arxiv for others to see. Lenore

[saulshanabrook]

I have just been reading of MoA, but am not that familiar. I am interested because I am working on a series of array representation and computation libraries, called xnd. I am looking to see if some mathematical underpinnings could be helpful to lay out how the computation part is structured. Right now, we are mostly using the strides and broadcasting system of NumPy.

I don't know if you have seen it, but there is also a very recent paper called "Modeling of languages for tensor manipulation" by @normanrink that seems to touch on similar themes (from my little understanding of type theory).

[womenflyplanes]

Thanks for replying. I’ll check these out and perhaps we could talk after that.

On Mon, May 21, 2018 at 4:34 PM Saul Shanabrook notifications@github.com wrote:

I have just been reading of MoA, but am not that familiar. I am interested because I am working on a series of array representation and computation libraries, called xnd https://xnd.io/. I am looking to see if some mathematical underpinnings could be helpful to lay out how the computation part is structured. Right now, we are mostly using the strides and broadcasting system of NumPy.

I don't know if you have seen it, but there is also a very recent paper called "Modeling of languages for tensor manipulation" https://arxiv.org/abs/1801.08771 by @normanrink https://github.com/normanrink that seems to touch on similar themes (from my little understanding of type theory).

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[womenflyplanes]

I just checked the reference and they indeed have similar goals. They reference SPIRAL and Milner's work. SPIRAL is indeed very nice, as is Milner's work. I worked with a colleague to describe MoA using Milner's paradigm. https://www.researchgate.net/publication/220458692_Parallel_Functional_Programming_with_Arrays We did not exploit the power of Psi Reduction nor Dimension Lifting, areas of great importance to automation of MoA, a Universal Algebra, ubiquitous semantically, in most languages. i'd love to help you achieve similar optimizations. Lenore

On Mon, May 21, 2018 at 4:34 PM, Saul Shanabrook notifications@github.com wrote:

I have just been reading of MoA, but am not that familiar. I am interested because I am working on a series of array representation and computation libraries, called xnd https://xnd.io/. I am looking to see if some mathematical underpinnings could be helpful to lay out how the computation part is structured. Right now, we are mostly using the strides and broadcasting system of NumPy.

I don't know if you have seen it, but there is also a very recent paper called "Modeling of languages for tensor manipulation" https://arxiv.org/abs/1801.08771 by @normanrink https://github.com/normanrink that seems to touch on similar themes (from my little understanding of type theory).

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[womenflyplanes]

Re Spiral, as they say in one of their talks, ... must find the correct patterns to substitute... in Psi reduction, everything reduces to normal forms based in indexing and shapes. Why MoA and Psi Calculus can do that no other tensor algebra can due is compose any algorithm, not just single algorithms, AND handle the important boundary conditions, without doing something else, for scalars and empty arrays.

On Mon, May 21, 2018 at 10:38 PM, Lenore Mullin lenore.mullin@gmail.com wrote:

I just checked the reference and they indeed have similar goals. They reference SPIRAL and Milner's work. SPIRAL is indeed very nice, as is Milner's work. I worked with a colleague to describe MoA using Milner's paradigm. https://www.researchgate.net/publication/220458692_Parallel_Functional_ Programming_with_Arrays We did not exploit the power of Psi Reduction nor Dimension Lifting, areas of great importance to automation of MoA, a Universal Algebra, ubiquitous semantically, in most languages. i'd love to help you achieve similar optimizations. Lenore

On Mon, May 21, 2018 at 4:34 PM, Saul Shanabrook <notifications@github.com

wrote:

I have just been reading of MoA, but am not that familiar. I am interested because I am working on a series of array representation and computation libraries, called xnd https://xnd.io/. I am looking to see if some mathematical underpinnings could be helpful to lay out how the computation part is structured. Right now, we are mostly using the strides and broadcasting system of NumPy.

I don't know if you have seen it, but there is also a very recent paper called "Modeling of languages for tensor manipulation" https://arxiv.org/abs/1801.08771 by @normanrink https://github.com/normanrink that seems to touch on similar themes (from my little understanding of type theory).

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[womenflyplanes]

Finally, One must always have the identity (iota ( rho Xi) ) psi Xi equiv Xi

That is, from the shape of any array, Xi, get all coordinates, then index the array. This should be true for any array from 0-dimensional i.e. scalars, to n-dimensional. Note: The shape of a scalar is the empty vector.

On Mon, May 21, 2018 at 10:41 PM, Lenore Mullin lenore.mullin@gmail.com wrote:

Re Spiral, as they say in one of their talks, ... must find the correct patterns to substitute... in Psi reduction, everything reduces to normal forms based in indexing and shapes. Why MoA and Psi Calculus can do that no other tensor algebra can due is compose any algorithm, not just single algorithms, AND handle the important boundary conditions, without doing something else, for scalars and empty arrays.

On Mon, May 21, 2018 at 10:38 PM, Lenore Mullin lenore.mullin@gmail.com wrote:

I just checked the reference and they indeed have similar goals. They reference SPIRAL and Milner's work. SPIRAL is indeed very nice, as is Milner's work. I worked with a colleague to describe MoA using Milner's paradigm. https://www.researchgate.net/publication/220458692_Parallel_ Functional_Programming_with_Arrays We did not exploit the power of Psi Reduction nor Dimension Lifting, areas of great importance to automation of MoA, a Universal Algebra, ubiquitous semantically, in most languages. i'd love to help you achieve similar optimizations. Lenore

On Mon, May 21, 2018 at 4:34 PM, Saul Shanabrook < notifications@github.com> wrote:

I have just been reading of MoA, but am not that familiar. I am interested because I am working on a series of array representation and computation libraries, called xnd https://xnd.io/. I am looking to see if some mathematical underpinnings could be helpful to lay out how the computation part is structured. Right now, we are mostly using the strides and broadcasting system of NumPy.

I don't know if you have seen it, but there is also a very recent paper called "Modeling of languages for tensor manipulation" https://arxiv.org/abs/1801.08771 by @normanrink https://github.com/normanrink that seems to touch on similar themes (from my little understanding of type theory).

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

Thanks for the reference. I scanned the paper and it looks very applicable, but I will need to write out some code to get an intuitive sense for what it's saying. Are there any simple implementations of these concepts I could look at as well?

[womenflyplanes]

No implementations on the paper I referenced. You'll have to work out a few examples. Re, Psi reduction, i have many papers(algorithms) that can help you. Let me know if you want to Skype or Hangout, e.g., Often a few conversations help colleagues to see how simple and elegant the theory is.

The psi function is with shape, iota , and gamma are you need to build the algebra. Do you have my dissertation? Conformal Computing on the ArXiv is another good reference. Lenore

On Mon, May 21, 2018 at 10:52 PM, Saul Shanabrook notifications@github.com wrote:

Thanks for the reference. I scanned the paper and it looks very applicable, but I will need to write out some code to get an intuitive sense for what it's saying. Are there any simple implementations of these concepts I could look at as well?

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[womenflyplanes]

Saul, I just Googled you. Perhaps we should talk about a paper where we have a mutual interest. You know my interests. If not, my interests go from theory, to software and hardware, given a theoretical mathematical description, targeting optimal, verifiable, software or hardware with any input language and any output language. No matter what your professional goals, more papers published help your cause. Lenore

On Tue, May 22, 2018 at 6:57 AM, Lenore Mullin lenore.mullin@gmail.com wrote:

No implementations on the paper I referenced. You'll have to work out a few examples. Re, Psi reduction, i have many papers(algorithms) that can help you. Let me know if you want to Skype or Hangout, e.g., Often a few conversations help colleagues to see how simple and elegant the theory is.

The psi function is with shape, iota , and gamma are you need to build the algebra. Do you have my dissertation? Conformal Computing on the ArXiv is another good reference. Lenore

On Mon, May 21, 2018 at 10:52 PM, Saul Shanabrook < notifications@github.com> wrote:

Thanks for the reference. I scanned the paper and it looks very applicable, but I will need to write out some code to get an intuitive sense for what it's saying. Are there any simple implementations of these concepts I could look at as well?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/josefs/MoA-ARRAYS/issues/1#issuecomment-390846527, or mute the thread https://github.com/notifications/unsubscribe-auth/AGsmlA5-x_Hp7_gyZsdmig4fxCKuxaDBks5t031_gaJpZM4TfJVt .

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

I think a hangout would be great. Are you around tomorrow before 4pm EST? Maybe in the morning? @teoliphant and I have been talking a lot today about different ways of creating abstractions for the NumPy API that support people running computation on different array backends, like sparse or compressed arrays. So we would love to talk about how these theories could possibly help to serve as a good abstraction level.

If tomorrow doesn't work, we could also do Saturday.

[womenflyplanes]

Unfortunately, I can not do tomorrow unless it is after 5PM. Saturday works. What time?

On Wed, May 23, 2018 at 10:45 PM, Saul Shanabrook notifications@github.com wrote:

I think a hangout would be great. Are you around tomorrow before 4pm EST? Maybe in the morning? @teoliphant https://github.com/teoliphant and I have been talking a lot today about different ways of creating abstractions for the NumPy API that support people running computation on different array backends, like sparse or compressed arrays. So we would love to talk about how these theories could possibly help to serve as a good abstraction level.

If tomorrow doesn't work, we could also do Saturday.

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[saulshanabrook]

Earlier is better for us on saturday. like 11am EST? What works for you?

[womenflyplanes]

11 AM EST Is good. Send me hangout request.

On Thu, May 24, 2018 at 12:24 AM Saul Shanabrook notifications@github.com wrote:

Earlier is better for us on saturday. like 11am EST? What works for you?

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[womenflyplanes]

Something I am very interested isL Identifying an enhanced subset of Python that has the MoA Algebra so that we can perform provable optimizations mechanically. That is, what are the syntactic expressions that have the same semantic meaning as the MoA algebra. Do you keep shapes around to play with? I have many questions for you guys also. I would like to use Python to express not only tensor algorithms but algorithms that can be transformed to idealized hardware starting with an FPGA. Many hardware choices going from simulation to synthesis and the ONF must express it. Lenore

On Thu, May 24, 2018 at 6:46 AM, Lenore Mullin lenore.mullin@gmail.com wrote:

11 AM EST Is good. Send me hangout request.

On Thu, May 24, 2018 at 12:24 AM Saul Shanabrook notifications@github.com wrote:

Earlier is better for us on saturday. like 11am EST? What works for you?

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

I sent you a calendar invite with a call attached.

Identifying an enhanced subset of Python that has the MoA Algebra so that we can perform provable optimizations mechanically. That is, what are the syntactic expressions that have the same semantic meaning as the MoA algebra.

Yes exactly, that is what we are interested in as well. Right now, we are using compiling some code to LLVM, using Numba, but we are interested in adding a layer, so that different array backends can be written for different hardware/different implementations (i.e. sparse arrays).

The other things we were wondering is if MoA can support arrays that are not contiguous, that have different stride lengths. Like in NumPy, you can selected every other element, and this just changes the strides:

In [1]: import numpy as np

In [2]: x = np.arange(10)

In [3]: x
Out[3]: array([0, 2, 4, 6, 8])

In [4]: x.strides
Out[4]: (8,)

In [5]: y = x[::2]

In [6]: y.strides
Out[6]: (16,)

In [7]: y
Out[7]: array([0, 2, 4, 6, 8])

It wouldn't necessarily have to work just like this, but it's helpful for someone to be able to do this type of indexing with copying the array.

[womenflyplanes]

Any composition of indexing with shapes is Possible because regular sparseness has patterns on shapes also and for random sparseness we can have and array of indices indexing the array.

On Thu, May 24, 2018 at 10:39 AM Saul Shanabrook notifications@github.com wrote:

I sent you a calendar invite with a call attached.

Identifying an enhanced subset of Python that has the MoA Algebra so that we can perform provable optimizations mechanically. That is, what are the syntactic expressions that have the same semantic meaning as the MoA algebra.

Yes exactly, that is what we are interested in as well. Right now, we are using compiling some code to LLVM, using Numba http://numba.pydata.org/numba-doc/latest/user/overview.html, but we are interested in adding a layer, so that different array backends can be written for different hardware/different implementations (i.e. sparse arrays).

The other things we were wondering is if MoA can support arrays that are not contiguous, that have different stride lengths. Like in NumPy, you can selected every other element, and this just changes the strides:

In [1]: import numpy as np

In [2]: x = np.arange(10)

In [3]: x Out[3]: array([0, 2, 4, 6, 8])

In [4]: x.strides Out[4]: (8,)

In [5]: y = x[::2]

In [6]: y.strides Out[6]: (16,)

In [7]: y Out[7]: array([0, 2, 4, 6, 8])

It wouldn't necessarily have to work just like this, but it's helpful for someone to be able to do this type of indexing with copying the array.

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[womenflyplanes]

I am glad we have similar goals. I look forward to our hangout on Saturday.

On Thu, May 24, 2018 at 10:45 AM Lenore Mullin lenore.mullin@gmail.com wrote:

Any composition of indexing with shapes is Possible because regular sparseness has patterns on shapes also and for random sparseness we can have and array of indices indexing the array.

On Thu, May 24, 2018 at 10:39 AM Saul Shanabrook notifications@github.com wrote:

I sent you a calendar invite with a call attached.

Identifying an enhanced subset of Python that has the MoA Algebra so that we can perform provable optimizations mechanically. That is, what are the syntactic expressions that have the same semantic meaning as the MoA algebra.

Yes exactly, that is what we are interested in as well. Right now, we are using compiling some code to LLVM, using Numba http://numba.pydata.org/numba-doc/latest/user/overview.html, but we are interested in adding a layer, so that different array backends can be written for different hardware/different implementations (i.e. sparse arrays).

The other things we were wondering is if MoA can support arrays that are not contiguous, that have different stride lengths. Like in NumPy, you can selected every other element, and this just changes the strides:

In [1]: import numpy as np

In [2]: x = np.arange(10)

In [3]: x Out[3]: array([0, 2, 4, 6, 8])

In [4]: x.strides Out[4]: (8,)

In [5]: y = x[::2]

In [6]: y.strides Out[6]: (16,)

In [7]: y Out[7]: array([0, 2, 4, 6, 8])

It wouldn't necessarily have to work just like this, but it's helpful for someone to be able to do this type of indexing with copying the array.

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

It was really great to talk to you yesterday. You mentioned hand compiling vs automated compiling of these expressions. Do you have a source that goes over how the automatic compilation would work for some simple operations like indexing, reshaping, napping, and reducing? I wanna see if I can get a more viseral sense of how these things could work in Python.

[womenflyplanes]

I do. I'll have to get it from UA. I have lots of stuff on various compilers. I'll try to get to that today, otherwise tomorrow. BTW, did you get the photo I sent? Lenore

On Sun, May 27, 2018 at 12:53 PM, Saul Shanabrook notifications@github.com wrote:

It was really great to talk to you yesterday. You mentioned hand compiling vs automated compiling of these expressions. Do you have a source that goes over how the automatic compilation would work for some simple operations like indexing, reshaping, napping, and reducing? I wanna see if I can get a more viseral sense of how these things could work in Python.

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

Thanks! No rush on that.

I don't think I did. You can email it to me at s.shanabrook@gmail.com

[womenflyplanes]

I’ll send again now. Please forward to Travis.

On Sun, May 27, 2018 at 1:02 PM Saul Shanabrook notifications@github.com wrote:

Thanks! No rush on that.

I don't think I did. You can email it to me at s.shanabrook@gmail.com

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[womenflyplanes]

Here is a doc related to the compiler. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.54.4307&rep=rep1&type=pdf

On Sun, May 27, 2018 at 12:53 PM, Saul Shanabrook notifications@github.com wrote:

It was really great to talk to you yesterday. You mentioned hand compiling vs automated compiling of these expressions. Do you have a source that goes over how the automatic compilation would work for some simple operations like indexing, reshaping, napping, and reducing? I wanna see if I can get a more viseral sense of how these things could work in Python.

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[womenflyplanes]

Saul, If we decide to NOT use Omega, ie Mullin’s reshspe-transpose conjecture , this grammar and compiler should be ok. Let me know if you were able to recompile the compiler I sent you. Lenore

On Sun, May 27, 2018 at 3:13 PM Lenore Mullin lenore.mullin@gmail.com wrote:

Here is a doc related to the compiler.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.54.4307&rep=rep1&type=pdf

On Sun, May 27, 2018 at 12:53 PM, Saul Shanabrook < notifications@github.com> wrote:

It was really great to talk to you yesterday. You mentioned hand compiling vs automated compiling of these expressions. Do you have a source that goes over how the automatic compilation would work for some simple operations like indexing, reshaping, napping, and reducing? I wanna see if I can get a more viseral sense of how these things could work in Python.

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/josefs/MoA-ARRAYS/issues/1#issuecomment-392347004, or mute the thread https://github.com/notifications/unsubscribe-auth/AGsmlAPB5Nd3e8WTFIUa2nID4ZkD8vJDks5t2tokgaJpZM4TfJVt .

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[saulshanabrook]

Thanks for the code and docs. I haven't tried compiling them yet, but I have been looking through the various documents there and the examples. I understand the general outline of the compilation, where you wanna end up with forms that just relate the final indexing to indexing on existing arrays with computation. The reduction example was very helpful to see how this plays out.

Is there an example there for for doing aggregates? Like finding the minimum, sum, or the index of the minimum? Do you need the omega operator to perform those?

[womenflyplanes]

No, omega is not needed for t hem. Hence, examples should work. I don't know what is there. The compiler was done over 20 years ago.

On Tue, May 29, 2018 at 1:12 AM, Saul Shanabrook notifications@github.com wrote:

Thanks for the code and docs. I haven't tried compiling them yet, but I have been looking through the various documents there and the examples. I understand the general outline of the compilation, where you wanna end up with forms that just relate the final indexing to indexing on existing arrays with computation. The reduction example was very helpful to see how this plays out.

Is there an example there for for doing aggregates? Like finding the minimum, sum, or the index of the minimum? Do you need the omega operator to perform those?

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-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein

[womenflyplanes]

The best thing to do is to compile the compiler and make up examples if they don't exist. If I remember correctly, examples exist for all functions and operators.

On Tue, May 29, 2018 at 1:12 AM, Saul Shanabrook notifications@github.com wrote:

Thanks for the code and docs. I haven't tried compiling them yet, but I have been looking through the various documents there and the examples. I understand the general outline of the compilation, where you wanna end up with forms that just relate the final indexing to indexing on existing arrays with computation. The reduction example was very helpful to see how this plays out.

Is there an example there for for doing aggregates? Like finding the minimum, sum, or the index of the minimum? Do you need the omega operator to perform those?

— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/josefs/MoA-ARRAYS/issues/1#issuecomment-392654762, or mute the thread https://github.com/notifications/unsubscribe-auth/AGsmlGma5vCVCuMj0VBhihplT6Yxa5-Eks5t3NjBgaJpZM4TfJVt .

-- "Great spirits have always encountered violent opposition from mediocre minds" - Albert Einstein