In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program.
Lisp is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation. Originally specified in the late 1950s, it is the second-oldest high-level programming language still in common use, after Fortran. Lisp has changed since its early days, and many dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme, Racket, and Clojure.
Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. In 1936, Church found a formulation which was logically consistent, and documented it in 1940.
Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.
In computability theory, a system of data-manipulation rules is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine. This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete.
In programming languages, a closure, also lexical closure or function closure, is a technique for implementing lexically scoped name binding in a language with first-class functions. Operationally, a closure is a record storing a function together with an environment. The environment is a mapping associating each free variable of the function with the value or reference to which the name was bound when the closure was created. Unlike a plain function, a closure allows the function to access those captured variables through the closure's copies of their values or references, even when the function is invoked outside their scope.
In computer programming, CAR (car) and CDR (cdr) are primitive operations on cons cells introduced in the Lisp programming language. A cons cell is composed of two pointers; the car operation extracts the first pointer, and the cdr operation extracts the second.
In computer programming, cons is a fundamental function in most dialects of the Lisp programming language. consconstructs memory objects which hold two values or pointers to two values. These objects are referred to as (cons) cells, conses, non-atomic s-expressions ("NATSes"), or (cons) pairs. In Lisp jargon, the expression "to cons x onto y" means to construct a new object with (cons xy). The resulting pair has a left half, referred to as the car, and a right half, referred to as the cdr.
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
In computer science, a continuation is an abstract representation of the control state of a computer program. A continuation implements (reifies) the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process's execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment. Continuations are useful for encoding other control mechanisms in programming languages such as exceptions, generators, coroutines, and so on.
A timer or countdown timer is a type of clock that starts from a specified time duration and stops upon reaching 00:00. An example of a simple timer is an hourglass. Commonly, a timer triggers an alarm when it ends. A timer can be implemented through hardware or software. Stopwatches operate in the opposite direction, upwards from 00:00, measuring elapsed time since a given time instant. Time switches are timers that control an electric switch.
In computer programming, a callback is a function that is stored as data and designed to be called by another function – often back to the original abstraction layer.
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.
In the Scheme computer programming language, the procedure call-with-current-continuation, abbreviated call/cc, is used as a control flow operator. It has been adopted by several other programming languages.
Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including mathematics, software engineering, and linguistics. There are a number of academic conferences and journals in the area.
In computing, a meta-circular evaluator (MCE) or meta-circular interpreter (MCI) is an interpreter which defines each feature of the interpreted language using a similar facility of the interpreter's host language. For example, interpreting a lambda application may be implemented using function application. Meta-circular evaluation is most prominent in the context of Lisp. A self-interpreter is a meta-circular interpreter where the interpreted language is nearly identical to the host language; the two terms are often used synonymously.
A counter machine or counter automaton is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the most primitive of the four types of register machines. A counter machine comprises a set of one or more unbounded registers, each of which can hold a single non-negative integer, and a list of arithmetic and control instructions for the machine to follow. The counter machine is typically used in the process of designing parallel algorithms in relation to the mutual exclusion principle. When used in this manner, the counter machine is used to model the discrete time-steps of a computational system in relation to memory accesses. By modeling computations in relation to the memory accesses for each respective computational step, parallel algorithms may be designed in such a matter to avoid interlocking, the simultaneous writing operation by two threads to the same memory address.
The history of the programming language Scheme begins with the development of earlier members of the Lisp family of languages during the second half of the twentieth century. During the design and development period of Scheme, language designers Guy L. Steele and Gerald Jay Sussman released an influential series of Massachusetts Institute of Technology (MIT) AI Memos known as the Lambda Papers (1975–1980). This resulted in the growth of popularity in the language and the era of standardization from 1990 onward. Much of the history of Scheme has been documented by the developers themselves.
In computer science and computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. At a more detailed level, the description may include the instruction set architecture design, microarchitecture design, logic design, and implementation.
A CEK Machine is an abstract machine invented by Matthias Felleisen and Daniel P. Friedman that implements left-to-right call by value. It is generally implemented as an interpreter for functional programming languages, but can also be used to implement simple imperative programming languages. A state in a CEK machine includes a control statement, environment and continuation. The control statement is the term being evaluated at that moment, the environment is (usually) a map from variable names to values, and the continuation stores another state, or a special halt case. It is a simplified form of another abstract machine called the SECD machine.
