Applicative Programming Language
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Applicative Programming Language
In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative. The semantics of applicative languages are based on beta reduction of terms, and Side effect such as mutation of state are not permitted. Lisp and ML are applicative programming languages. See also * Applicative universal grammar * Function-level programming In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming. In his 1977 Turin ... References {{Reflist Programming language classification Applicative computing systems ...
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Applicative Functor
In functional programming, an applicative functor, or an applicative for short, is an intermediate structure between functors and monads. In category theory they are calleclosed monoidal functors Applicative functors allow for functorial computations to be sequenced (unlike plain functors), but don't allow using results from prior computations in the definition of subsequent ones (unlike monads). Applicative functors are the programming equivalent of lax monoidal functors with tensorial strength in category theory. Applicative functors were introduced in 2008 by Conor McBride and Ross Paterson in their paper ''Applicative programming with effects''. Applicative functors first appeared as a library feature in Haskell, but have since spread to other languages such as Idris, Agda, OCaml, Scala, and F#. Glasgow Haskell, Idris, and F# offer language features designed to ease programming with applicative functors. In Haskell, applicative functors are implemented in the Applicativ ...
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Programming Paradigm
A programming paradigm is a relatively high-level way to conceptualize and structure the implementation of a computer program. A programming language can be classified as supporting one or more paradigms. Paradigms are separated along and described by different dimensions of programming. Some paradigms are about implications of the execution model, such as allowing Side effect (computer science), side effects, or whether the sequence of operations is defined by the execution model. Other paradigms are about the way code is organized, such as grouping into units that include both state and behavior. Yet others are about Syntax (programming languages), syntax and Formal grammar, grammar. Some common programming paradigms include (shown in hierarchical relationship): * imperative programming, Imperative code directly controls Control flow, execution flow and state change, explicit statements that change a program state ** procedural programming, procedural organized as function (c ...
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Function (computer Science)
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-defined interface and behavior and can be invoked multiple times. Callable units provide a powerful programming tool. The primary purpose is to allow for the decomposition of a large and/or complicated problem into chunks that have relatively low cognitive load and to assign the chunks meaningful names (unless they are anonymous). Judicious application can reduce the cost of developing and maintaining software, while increasing its quality and reliability. Callable units are present at multiple levels of abstraction in the programming environment. For example, a programmer may write a function in source code that is compiled to machine code that implements similar semantics. There is a callable unit in the source code and an associated one in the machine code, but they are different kinds of callable units with different impl ...
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Argument (computer Science)
In computer programming, a parameter, a.k.a. formal argument, is a variable that represents an argument, a.k.a. actual argument, a.k.a. actual parameter, to a subroutine call.. A function's signature defines its parameters. A call invocation involves evaluating each argument expression of a call and associating the result with the corresponding parameter. For example, consider subroutine def add(x, y): return x + y. Variables x and y are parameters. For call add(2, 3), the expressions 2 and 3 are arguments. For call add(a+1, b+2), the arguments are a+1 and b+2. Parameter passing is defined by a programming language. Evaluation strategy defines the semantics for how parameters can be declared and how arguments are passed to a subroutine. Generally, with call by value, a parameter acts like a new, local variable initialized to the value of the argument. If the argument is a variable, the subroutine cannot modify the argument state because the parameter is a copy. With call by ref ...
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Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), 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 Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, d ...
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Concatenative Languages
A concatenative programming language is a point-free computer programming language in which all expressions denote functions, and the juxtaposition of expressions denotes function composition. Concatenative programming replaces function application, which is common in other programming styles, with function composition as the default way to build subroutines. Example For example, a nesting of operations in an applicative language like the following: baz(bar(foo(x))) ...is written in a concatenative language as a sequence of functions: x foo bar baz Functions and procedures written in concatenative style are not value level, i.e. they typically do not represent the data structures they operate on with explicit names or identifiers. Instead they are function levela function is defined as a pipeline, or a sequence of operations that take parameters from an implicit data structure upon which all functions operate, and return the function results to that shared structure so ...
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Semantics (computer Science)
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs. Semantics describes the processes a computer follows when executing a program in that specific language. This can be done by describing the relationship between the input and output of a program, or giving an explanation of how the program will be executed on a certain platform, thereby creating a model of computation. History In 1967, Robert W. Floyd published the paper ''Assigning meanings to programs''; his chief aim was "a rigorous standard for proofs about computer programs, including proofs of correctness, equivalence, and termination". Floyd further wrote: A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It mu ...
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Beta Reduction
In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computation based on function abstraction and application using variable Name binding, binding and Substitution (algebra), substitution. Untyped lambda calculus, the topic of this article, is a universal machine, a model of computation that can be used to simulate any Turing machine (and vice versa). 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 #History, logically consistent, and documented it in 1940. Lambda calculus consists of constructing #Lambda terms, lambda terms and performing #Reduction, reduction operations on them. A term is defined as any valid lambda calculus expression. In the simplest form of lambda calculus, terms are built using only the following rules: # x: A #validLambdaVar, variable is a character or string representing a pa ...
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Side Effect (computer Science)
In computer science, an operation, function or expression is said to have a side effect if it has any observable effect other than its primary effect of reading the value of its arguments and returning a value to the invoker of the operation. Example side effects include modifying a non-local variable, a static local variable or a mutable argument passed by reference; raising errors or exceptions; performing I/O; or calling other functions with side-effects. In the presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly used to produce side effects, to update a system's state. By contrast ...
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State (computer Science)
In information technology and computer science, a system is described as stateful if it is designed to remember preceding events or user interactions; the remembered information is called the state of the system. The set of states a system can occupy is known as its state space. In a discrete system, the state space is countable and often finite. The system's internal behaviour or interaction with its environment consists of separately occurring individual actions or events, such as accepting input or producing output, that may or may not cause the system to change its state. Examples of such systems are digital logic circuits and components, automata and formal language, computer programs, and computers. The output of a digital circuit or deterministic computer program at any time is completely determined by its current inputs and its state. Digital logic circuit state Digital logic circuits can be divided into two types: combinational logic, whose output signals a ...
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Lisp Programming Language
Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized Polish notation#Explanation, 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 Programming language dialect, dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme (programming language), Scheme, Racket (programming language), Racket, and Clojure. Lisp was originally created as a practical mathematical notation for computer programs, influenced by (though not originally derived from) the notation of Alonzo Church's lambda calculus. It quickly became a favored programming language for artificial intelligence (AI) research. As one of the earliest programming languages, Lisp pioneered many ideas in computer science, includ ...
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ML Programming Language
ML (Meta Language) is a general-purpose, high-level, functional programming language. It is known for its use of the polymorphic Hindley–Milner type system, which automatically assigns the data types of most expressions without requiring explicit type annotations (type inference), and ensures type safety; there is a formal proof that a well-typed ML program does not cause runtime type errors. ML provides pattern matching for function arguments, garbage collection, imperative programming, call-by-value and currying. While a general-purpose programming language, ML is used heavily in programming language research and is one of the few languages to be completely specified and verified using formal semantics. Its types and pattern matching make it well-suited and commonly used to operate on other formal languages, such as in compiler writing, automated theorem proving, and formal verification. Overview Features of ML include a call-by-value evaluation strategy, first-class fu ...
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