In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess (PR) capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power.
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling. As power consumption by computers has become a concern in recent years, parallel computing has become the dominant paradigm in computer architecture, mainly in the form of multi-core processors.
In functional programming, a monad is a structure that combines program fragments (functions) and wraps their return values in a type with additional computation. In addition to defining a wrapping monadic type, monads define two operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type. General-purpose languages use monads to reduce boilerplate code needed for common operations. Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effects.
In computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjan's 1986 article.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set. Alternative names are switching function, used especially in older computer science literature, and truth function, used in logic. Boolean functions are the subject of Boolean algebra and switching theory.
In computer science, array programming refers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings.
NESL is a parallel programming language developed at Carnegie Mellon by the SCandAL project and released in 1993. It integrates various ideas from parallel algorithms, functional programming, and array programming languages.
A bit array is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores kw bits, where w is the number of bits in the unit of storage, such as a byte or word, and k is some nonnegative integer. If w does not divide the number of bits to be stored, some space is wasted due to internal fragmentation.
In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning the results in a collection of the same type. It is often called apply-to-all when considered in functional form.
In computer science, the prefix sum, cumulative sum, inclusive scan, or simply scan of a sequence of numbers x0, x1, x2, ... is a second sequence of numbers y0, y1, y2, ..., the sums of prefixes of the input sequence:
Data parallelism is parallelization across multiple processors in parallel computing environments. It focuses on distributing the data across different nodes, which operate on the data in parallel. It can be applied on regular data structures like arrays and matrices by working on each element in parallel. It contrasts to task parallelism as another form of parallelism.
In computing, algorithmic skeletons, or parallelism patterns, are a high-level parallel programming model for parallel and distributed computing.
In computer science, partial application refers to the process of fixing a number of arguments of a function, producing another function of smaller arity. Given a function , we might fix the first argument, producing a function of type . Evaluation of this function might be represented as . Note that the result of partial function application in this case is a function that takes two arguments. Partial application is sometimes incorrectly called currying, which is a related, but distinct concept.
In machine learning and data mining, a string kernel is a kernel function that operates on strings, i.e. finite sequences of symbols that need not be of the same length. String kernels can be intuitively understood as functions measuring the similarity of pairs of strings: the more similar two strings a and b are, the higher the value of a string kernel K(a, b) will be.
A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis.
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks. A line search along the coordinate direction can be performed at the current iterate to determine the appropriate step size. Coordinate descent is applicable in both differentiable and derivative-free contexts.
SequenceL is a general purpose functional programming language and auto-parallelizing compiler and tool set, whose primary design objectives are performance on multi-core processor hardware, ease of programming, platform portability/optimization, and code clarity and readability. Its main advantage is that it can be used to write straightforward code that automatically takes full advantage of all the processing power available, without programmers needing to be concerned with identifying parallelisms, specifying vectorization, avoiding race conditions, and other challenges of manual directive-based programming approaches such as OpenMP.
In parallel computing, work stealing is a scheduling strategy for multithreaded computer programs. It solves the problem of executing a dynamically multithreaded computation, one that can "spawn" new threads of execution, on a statically multithreaded computer, with a fixed number of processors. It does so efficiently in terms of execution time, memory usage, and inter-processor communication.
Futhark is a multi-paradigm, high-level, functional, data parallel, array programming language. It is a dialect of the language ML, originally developed at UCPH Department of Computer Science (DIKU) as part of the HIPERFIT project. It focuses on enabling data parallel programs written in a functional style to be executed with high performance on massively parallel hardware, especially graphics processing units (GPUs). Futhark is strongly inspired by NESL, and its implementation uses a variant of the flattening transformation, but imposes constraints on how parallelism can be expressed in order to enable more aggressive compiler optimisations. In particular, irregular nested data parallelism is not supported. It is free and open-source software released under an ISC license.
