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.
In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed and which also avoids repeated evaluations.
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 computer science, syntactic sugar is syntax within a programming language that is designed to make things easier to read or to express. It makes the language "sweeter" for human use: things can be expressed more clearly, more concisely, or in an alternative style that some may prefer. Syntactic sugar is usually a shorthand for a common operation that could also be expressed in an alternate, more verbose, form: The programmer has a choice of whether to use the shorter form or the longer form, but will usually use the shorter form since it is shorter and easier to type and read.
In combinatory logic for computer science, a fixed-point combinator, is a higher-order function that returns some fixed point of its argument function, if one exists.
In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow.
In type theory, a typing rule is an inference rule that describes how a type system assigns a type to a syntactic construction. These rules may be applied by the type system to determine if a program is well-typed and what type expressions have. A prototypical example of the use of typing rules is in defining type inference in the simply typed lambda calculus, which is the internal language of Cartesian closed categories.
Peter John Landin was a British computer scientist. He was one of the first to realise that the lambda calculus could be used to model a programming language, an insight that is essential to the development of both functional programming and denotational semantics.
David A. Turner was a British computer scientist. He is best known for designing and implementing three programming languages, including the first for functional programming based on lazy evaluation, combinator graph reduction, and polymorphic types: SASL (1972), Kent Recursive Calculator (KRC) (1981), and the commercially supported Miranda (1985).
In computer science, a programming language is said to have first-class functions if it treats functions as first-class citizens. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structures. Some programming language theorists require support for anonymous functions as well. In languages with first-class functions, the names of functions do not have any special status; they are treated like ordinary variables with a function type. The term was coined by Christopher Strachey in the context of "functions as first-class citizens" in the mid-1960s.
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.
In functional programming, a generalized algebraic data type is a generalization of parametric algebraic data types.
In computer science, polymorphic recursion refers to a recursive parametrically polymorphic function where the type parameter changes with each recursive invocation made, instead of staying constant. Type inference for polymorphic recursion is equivalent to semi-unification and therefore undecidable and requires the use of a semi-algorithm or programmer-supplied type annotations.
This article describes the features in the programming language Haskell.
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.
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.
