Lambda calculusLambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It 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. Lambda calculus consists of constructing lambda terms and performing reduction operations on them.
Lambda liftingLambda lifting is a meta-process that restructures a computer program so that functions are defined independently of each other in a global scope. An individual "lift" transforms a local function into a global function. It is a two step process, consisting of; Eliminating free variables in the function by adding parameters. Moving functions from a restricted scope to broader or global scope. The term "lambda lifting" was first introduced by Thomas Johnsson around 1982 and was historically considered as a mechanism for implementing functional programming languages.
Let expressionIn computer science, a "let" expression associates a function definition with a restricted scope. The "let" expression may also be defined in mathematics, where it associates a Boolean condition with a restricted scope. The "let" expression may be considered as a lambda abstraction applied to a value. Within mathematics, a let expression may also be considered as a conjunction of expressions, within an existential quantifier which restricts the scope of the variable.
History of PythonPython (programming language) The programming language Python was conceived in the late 1980s, and its implementation was started in December 1989 by Guido van Rossum at CWI in the Netherlands as a successor to ABC capable of exception handling and interfacing with the Amoeba operating system. Van Rossum is Python's principal author, and his continuing central role in deciding the direction of Python is reflected in the title given to him by the Python community, Benevolent Dictator for Life (BDFL).
Python syntax and semanticsThe syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java. However, there are some definite differences between the languages. It supports multiple programming paradigms, including structured, object-oriented programming, and functional programming, and boasts a dynamic type system and automatic memory management.
Higher-order abstract syntaxIn computer science, higher-order abstract syntax (abbreviated HOAS) is a technique for the representation of abstract syntax trees for languages with variable binders. An abstract syntax is abstract because it is represented by mathematical objects that have certain structure by their very nature. For instance, in first-order abstract syntax (FOAS) trees, as commonly used in compilers, the tree structure implies the subexpression relation, meaning that no parentheses are required to disambiguate programs (as they are, in the concrete syntax).
Typed lambda calculusA typed lambda calculus is a typed formalism that uses the lambda-symbol () to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.
Anonymous functionIn computer programming, an anonymous function (function literal, lambda abstraction, lambda function, lambda expression or block) is a function definition that is not bound to an identifier. Anonymous functions are often arguments being passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only used once, or a limited number of times, an anonymous function may be syntactically lighter than using a named function.
Simply typed lambda calculusThe simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor () that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus. The term simple type is also used to refer extensions of the simply typed lambda calculus such as products, coproducts or natural numbers (System T) or even full recursion (like PCF).
Functional programmingIn 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 functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.
Filter (higher-order function)In functional programming, filter is a higher-order function that processes a data structure (usually a list) in some order to produce a new data structure containing exactly those elements of the original data structure for which a given predicate returns the boolean value true. In Haskell, the code example filter even [1..10] evaluates to the list 2, 4, ..., 10 by applying the predicate even to every element of the list of integers 1, 2, ...
Total functional programmingTotal functional programming (also known as strong functional programming, to be contrasted with ordinary, or weak functional programming) is a programming paradigm that restricts the range of programs to those that are provably terminating. Termination is guaranteed by the following restrictions: A restricted form of recursion, which operates only upon 'reduced' forms of its arguments, such as Walther recursion, substructural recursion, or "strongly normalizing" as proven by abstract interpretation of code.
Pierre de RonsardPierre de Ronsard (pjɛʁ də ʁɔ̃saʁ; 11 September 1524 – 27 December 1585) was a French poet or, as his own generation in France called him, a "prince of poets". Ronsard was born at Manoir de la Possonnière in the village of Couture-sur-Loir, Vendômois. His father served Francis I as maître d'hôtel du roi. Ronsard received an education at home before attending the College of Navarre in Paris at age nine. He later travelled extensively, including visits to Scotland, Flanders, and Holland.
Set (abstract data type)In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
List (abstract data type)In computer science, a list or sequence is an abstract data type that represents a finite number of ordered values, where the same value may occur more than once. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence; the (potentially) infinite analog of a list is a stream. Lists are a basic example of containers, as they contain other values. If the same value occurs multiple times, each occurrence is considered a distinct item.
PoetryPoetry (a term derived from the Greek word poiesis, "making"), also called verse, is a form of literature that uses aesthetic and often rhythmic qualities of language − such as phonaesthetics, sound symbolism, and metre − to evoke meanings in addition to, or in place of, a prosaic ostensible meaning. A poem is a literary composition, written by a poet, using this principle. Poetry has a long and varied history, evolving differentially across the globe.
Python (programming language)Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library.
Higher-order functionIn mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function as its result. All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function.
Ruby (programming language)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.
String (computer science)In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. String may also denote more general arrays or other sequence (or list) data types and structures.
