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In functional programming, continuation-passing style (CPS) is a style of programming in which control is passed explicitly in the form of a continuation. This is contrasted with direct style, which is the usual style of programming. Gerald Jay Sussman and Guy L. Steele, Jr. coined the phrase in AI Memo 349 (1975), which sets out the first version of the Scheme programming language.John C. Reynolds gives a detailed account of the numerous discoveries of continuations.

A function written in continuation-passing style takes an extra argument: an explicit "continuation"; i.e., a function of one argument. When the CPS function has computed its result value, it "returns" it by calling the continuation function with this value as the argument. That means that when invoking a CPS function, the calling function is required to supply a procedure to be invoked with the subroutine's "return" value. Expressing code in this form makes a number of things explicit which are implicit in direct style. These include: procedure returns, which become apparent as calls to a continuation; intermediate values, which are all given names; order of argument evaluation, which is made explicit; and tail calls, which simply call a procedure with the same continuation, unmodified, that was passed to the caller.

Programs can be automatically transformed from direct style to CPS. Functional and logic compilers often use CPS as an intermediate representation where a compiler for an imperative or procedural programming language would use static single assignment form (SSA). SSA is formally equivalent to a subset of CPS (excluding non-local control flow, which does not occur when CPS is used as intermediate representation). Functional compilers can also use A-normal form (ANF) (but only for languages requiring eager evaluation), rather than with 'thunks' (described in the examples below) in CPS. CPS is used more frequently by compilers than by programmers as a local or global style.

In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space ${\displaystyle \Omega }$ on which a sensible kernel function (measuring similarity between elements of ${\displaystyle \Omega }$) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in ${\displaystyle \mathbb {R} ^{d}}$, discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song , Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in.

The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings.

Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages:

1. Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables
2. Intermediate density estimation is not needed
3. Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel)
4. If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations
5. Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven.
6. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods

Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms.

An anti-pattern is a common response to a recurring problem that is usually ineffective and risks being highly counterproductive. The term, coined in 1995 by Andrew Koenig, was inspired by a book, Design Patterns, which highlights a number of design patterns in software development that its authors considered to be highly reliable and effective.

The term was popularized three years later by the book AntiPatterns, which extended its use beyond the field of software design to refer informally to any commonly reinvented but bad solution to a problem. Examples include analysis paralysis, cargo cult programming, death march, groupthink and vendor lock-in.

Unums (universal numbers) are a family of number formats and arithmetic for implementing real numbers on a computer, proposed by John L. Gustafson in 2015. They are designed as an alternative to the ubiquitous IEEE 754 floating-point standard. The latest version is known as posits.

In computer science, the maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers. Formally, the task is to find indices ${\displaystyle i}$ and ${\displaystyle j}$ with ${\displaystyle 1\leq i\leq j\leq n}$, such that the sum

${\displaystyle \sum _{x=i}^{j}A[x]}$

is as large as possible. (Some formulations of the problem also allow the empty subarray to be considered; by convention, the sum of all values of the empty subarray is zero.) Each number in the input array A could be positive, negative, or zero.

For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6.

Some properties of this problem are:

1. If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
2. If the array contains all non-positive numbers, then a solution is any subarray of size 1 containing the maximal value of the array (or the empty subarray, if it is permitted).
3. Several different sub-arrays may have the same maximum sum.

This problem can be solved using several different algorithmic techniques, including brute force, divide and conquer, dynamic programming, and reduction to shortest paths.

A cross compiler is a compiler capable of creating executable code for a platform other than the one on which the compiler is running. For example, a compiler that runs on a PC but generates code that runs on Android devices is a cross compiler.

A cross compiler is useful to compile code for multiple platforms from one development host. Direct compilation on the target platform might be infeasible, for example on embedded systems with limited computing resources.

Cross compilers are distinct from source-to-source compilers. A cross compiler is for cross-platform software generation of machine code, while a source-to-source compiler translates from one coding language to another in text code. Both are programming tools.

Cargo cult programming is a style of computer programming characterized by the ritual inclusion of code or program structures that serve no real purpose. Cargo cult programming is symptomatic of a programmer not understanding either a bug they were attempting to solve or the apparent solution (compare shotgun debugging, deep magic). The term cargo cult programmer may apply when an unskilled or novice computer programmer (or one inexperienced with the problem at hand) copies some program code from one place to another with little understanding of how it works or whether it is required.

Cargo cult programming can also refer to the practice of applying a design pattern or coding style blindly without understanding the reasons behind that design principle. Examples being adding unnecessary comments to self-explanatory code, overzealous adherence to the conventions of a programming paradigm, or adding deletion code for objects that garbage collection automatically collect.

Obsessive and redundant checks for null values or testing whether a collection is empty before iterating its values may be a sign of cargo cult programming. Such obsessive checks make the code less readable, and often prevent the output of proper error messages, obscuring the real cause of a misbehaving program.

Ruby is an interpreted, high-level, general-purpose programming language which supports multiple programming paradigms. It was designed with an emphasis on programming productivity and simplicity. In Ruby, everything is an object, including primitive data types. It was developed in the mid-1990s by Yukihiro "Matz" Matsumoto in Japan.

Ruby is dynamically typed and uses garbage collection and just-in-time compilation. It supports multiple programming paradigms, including procedural, object-oriented, and functional programming. According to the creator, Ruby was influenced by Perl, Smalltalk, Eiffel, Ada, BASIC, Java and Lisp.

The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of dynamic programming to compare biological sequences. The algorithm was developed by Saul B. Needleman and Christian D. Wunsch and published in 1970. The algorithm essentially divides a large problem (e.g. the full sequence) into a series of smaller problems, and it uses the solutions to the smaller problems to find an optimal solution to the larger problem. It is also sometimes referred to as the optimal matching algorithm and the global alignment technique. The Needleman–Wunsch algorithm is still widely used for optimal global alignment, particularly when the quality of the global alignment is of the utmost importance. The algorithm assigns a score to every possible alignment, and the purpose of the algorithm is to find all possible alignments having the highest score.

Pearson hashing is a hash function designed for fast execution on processors with 8-bit registers. Given an input consisting of any number of bytes, it produces as output a single byte that is strongly dependent on every byte of the input. Its implementation requires only a few instructions, plus a 256-byte lookup table containing a permutation of the values 0 through 255.

This hash function is a CBC-MAC that uses an 8-bit substitution cipher implemented via the substitution table. An 8-bit cipher has negligible cryptographic security, so the Pearson hash function is not cryptographically strong, but it is useful for implementing hash tables or as a data integrity check code, for which purposes it offers these benefits:

• It is extremely simple.
• It executes quickly on resource-limited processors.
• There is no simple class of inputs for which collisions (identical outputs) are especially likely.
• Given a small, privileged set of inputs (e.g., reserved words for a compiler), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.
• Two input strings differing by exactly one character never collide. E.g., applying the algorithm on the strings ABC and AEC will never produce the same value.

One of its drawbacks when compared with other hashing algorithms designed for 8-bit processors is the suggested 256 byte lookup table, which can be prohibitively large for a small microcontroller with a program memory size on the order of hundreds of bytes. A workaround to this is to use a simple permutation function instead of a table stored in program memory. However, using a too simple function, such as T[i] = 255-i, partly defeats the usability as a hash function as anagrams will result in the same hash value; using a too complex function, on the other hand, will affect speed negatively. Using a function rather than a table also allows extending the block size. Such functions naturally have to be bijective, like their table variants.

The algorithm can be described by the following pseudocode, which computes the hash of message C using the permutation table T:

algorithm pearson hashing is
    h := 0

    for each c in C loop
        h := T[ h xor c ]
    end loop

    return h

The hash variable (h) may be initialized differently, e.g. to the length of the data (C) modulo 256; this particular choice is used in the Python implementation example below.