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A computer is an imperative machine. Its CPU reads a list of instructions and performs one operation after another, with each operation modifying the state of its registers and memory. But that doesn’t mean we always have to write our computer programs as imperative step-by-step recipes; imperative programs are often too low-level and overspecified, which is why we're generally terrible at writing them.

One interesting alternative is declarative programming, where we focus on describing a problem instead of listing exactly what steps to take to solve it. That idea’s been around for a long time but has recently begun to reappear everywhere.

In this article I want to encourage you to think outside of your normal programming habits. I’ll present a more abstract and declarative style called relational programming, and show you how to implement a minimal relational language in Ruby.

This article is based on a talk I gave at Joy of Coding 2015 and the London Ruby User Group . The video of the talk is below, and the Stride Rite Hudsen Boys Leather Sandals Black RxEfUQ68N
are also available. All the Ruby code is Tamaris Black Women’s Ballet Flat Pink Pink 510 WDfgocg
, and James Coglan has ported it to ES6, Haskell and Python .

Contents

I recently read a good rant in an article called “ Aerosoles Womens NU Day SlipOn Loafer Black Leather 5RJ3ZzcPn
”. The term “von Neumann style” refers to programming languages whose design reflects the way a computer actually works: they have variables to represent memory locations, assignment statements to write to those locations, loops and branches to control the Gabor 81250 Womens Court Shoes Rot eTgAU
, and so on.

These languages encourage us to do what Bret Victor calls “ playing computer ” — spending a lot of time thinking about how computers work, and adapting our ideas to compensate. The article is an angry explanation of why this is a terribly restrictive way of writing programs, and a call to think more broadly and creatively about how we can express ideas as code.

I found it very persuasive, but unfortunately the rant was written in 1978, by John Backus , the designer of FORTRAN . John Backus died in 2007, and a lot of his complaints are still valid today. So his rant wasn’t a total success; it was influential, but perhaps not as much as it could have been. We’re still stuck with mostly “von Neumann style” languages that talk about state and assignment and memory and stuff — computer things, not idea things.

I want to continue that rant and ask you to consider the possibility of finding different ways of explaining ourselves to computers.

I’ll begin by briefly mentioning a few different programming paradigms. The first is unstructured programming. An example of unstructured programming is assembly language: programs consist of a linear sequence of instructions interrupted by the occasional jump. A programmer in an unstructured language can ask the computer to perform one instruction after another, and to conditionally go to a different place in the program.

Packaging build : the main focus here is packaging binaries/testing for dashboard submissions. The repository is usually simpler, and most logic for layout is in the CMake build system. In this case downloading tarballs and source trees is taken care of by CMake, and virtually all source code (outside of the superbuild repository) is contained in the build tree. This generally assures that the build tree will be clean, but means it is hard to use this to develop code in actively, for this reason it tends to be complementary to some other developer build instructions.

Packaging build

The Tomviz superbuild is a good example of this, which is derived from an earlier version of the ParaView superbuild . You will often need to copy SHAs for the projects from source trees tested locally to ‘versions.cmake’ in the case of Tomviz (as well as release tarballs referenced above), and once pushed these will be built by the builders. In both of these cases the superbuild actually contains the CPack packaging code, whereas in the case of Open Chemistry the individual software repositories contain the code for packaging. These contain all instructions for building the installers created on demand, or offered as part of a release.

Dependency build : a third kind of superbuild I have seen more recently is what I call the dependency build. This usually follows the pattern of a packaging build, and is normally also a packaging build with a second mode where it builds everything but the project being targeted by the superbuild. So in CMB’s superbuild there is a concept of a developer mode where it builds everything but the actual project. It may then write some config file or similar to help the developer’s build find the dependencies that were built for them.

Dependency build

Most superbuild projects use a common installation prefix, or a set of prefixes, to install build artifacts in. In Titan I think we started with one prefix per external project, but later moved to a common prefix for all projects. In Open Chemistry we use a common prefix for all projects, named ‘prefix’ at the top level of the build tree. The single common prefix can be very useful as you can simply add CMAKE_PREFIX_PATH to reference that prefix, and have projects favor anything found in there, this path can also be populated with a list.

The major disadvantage of this approach is that the prefix can become dirty over time, having multiple versions installed, and stale files causing issues. This is also an issue that arises with build trees in general, and starting from a clean build directory is often the best solution to avoid this. It also means that you cannot separate out different dependencies that were built and installed, but superbuilds are usually developed to support one (or a small number of) project(s).

When we get into the mindset of developing the superbuild a question that comes up is whether we should build everything from source. Conceptually that is the best/simplest approach, but it is also the one that will lead to the longest possible build times. After spending quite some time thinking about this for Titan, later Open Chemistry and Tomviz I have come to the conclusion that it depends…

Data-driven approach
An example training set for four visual categories. In practice we may have thousands of categories and hundreds of thousands of images for each category.

The image classification pipeline . We’ve seen that the task in Image Classification is to take an array of pixels that represents a single image and assign a label to it. Our complete pipeline can be formalized as follows:

The image classification pipeline Input: Learning: Evaluation:

As our first approach, we will develop what we call a Nearest Neighbor Classifier . This classifier has nothing to do with Convolutional Neural Networks and it is very rarely used in practice, but it will allow us to get an idea about the basic approach to an image classification problem.

Nearest Neighbor Classifier

Example image classification dataset: CIFAR-10. One popular toy image classification dataset is the Alma en Pena Sandals and Slippers for Women Colour Grey Brand Model Sandals and Slippers for Women V18541 Grey Grey yxNmnA1
. This dataset consists of 60,000 tiny images that are 32 pixels high and wide. Each image is labeled with one of 10 classes (for example “airplane, automobile, bird, etc” ). These 60,000 images are partitioned into a training set of 50,000 images and a test set of 10,000 images. In the image below you can see 10 random example images from each one of the 10 classes:

Example image classification dataset: CIFAR-10.
Left: Example images from the CIFAR-10 dataset . Right: first column shows a few test images and next to each we show the top 10 nearest neighbors in the training set according to pixel-wise difference.

Suppose now that we are given the CIFAR-10 training set of 50,000 images (5,000 images for every one of the labels), and we wish to label the remaining 10,000. The nearest neighbor classifier will take a test image, compare it to every single one of the training images, and predict the label of the closest training image. In the image above and on the right you can see an example result of such a procedure for 10 example test images. Notice that in only about 3 out of 10 examples an image of the same class is retrieved, while in the other 7 examples this is not the case. For example, in the 8th row the nearest training image to the horse head is a red car, presumably due to the strong black background. As a result, this image of a horse would in this case be mislabeled as a car.

You may have noticed that we left unspecified the details of exactly how we compare two images, which in this case are just two blocks of 32 x 32 x 3. One of the simplest possibilities is to compare the images pixel by pixel and add up all the differences. In other words, given two images and representing them as vectors I 1 , I 2 , a reasonable choice for comparing them might be the L1 distance :

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