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 effects 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 Turing A ... 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. 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 as well, including 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 Applicative type class. Definition In Haskell, an applic ...
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Programming Paradigm
Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, such as allowing side effects, or whether the sequence of operations is defined by the execution model. Other paradigms are concerned mainly with the way that code is organized, such as grouping a code into units along with the state that is modified by the code. Yet others are concerned mainly with the style of syntax and grammar. Common programming paradigms include: * imperative in which the programmer instructs the machine how to change its state, ** procedural which groups instructions into procedures, ** object-oriented which groups instructions with the part of the state they operate on, * declarative in which the programmer merely declares properties of the desired result, but not how to compute it ** functional in which the de ...
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Function (computer Science)
In computer programming, a function or subroutine is a sequence of program instructions that performs a specific task, packaged as a unit. This unit can then be used in programs wherever that particular task should be performed. Functions may be defined within programs, or separately in libraries that can be used by many programs. In different programming languages, a function may be called a routine, subprogram, subroutine, method, or procedure. Technically, these terms all have different definitions, and the nomenclature varies from language to language. The generic umbrella term ''callable unit'' is sometimes used. A function is often coded so that it can be started several times and from several places during one execution of the program, including from other functions, and then branch back (''return'') to the next instruction after the ''call'', once the function's task is done. The idea of a subroutine was initially conceived by John Mauchly during his work on ENIAC, ...
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Argument (computer Science)
In computer programming, a parameter or a formal argument is a special kind of variable used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called ''actual arguments'' or ''actual parameters'') with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters. Unlike ''argument'' in usual mathematical usage, the ''argument'' in computer science is the actual input expression passed/supplied to a function, procedure, or routine in the invocation/call statement, whereas the ''parameter'' is the variable inside the implementation of the subroutine. For example, if one defines the add subroutine as def add(x, y): return x + y, then x, y are paramet ...
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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, ...
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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 sequence of operations in an applicative language like the following: y = foo(x) z = bar(y) w = baz(z) ...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 s ...
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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. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation. History In 1967, Robert W. Floyd publishes the paper ''Assigning meanings to programs''; his chief aim is "a rigorous standard for proofs about computer programs, including proofs of correctness, equivalence, and termination". Floyd further writes: A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It must specify which of the phrases in a syntactically correct program represent commands, and what conditions ...
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Beta Reduction
Lambda 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. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\la ...
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Side Effects
In medicine, a side effect is an effect, whether therapeutic or adverse, that is secondary to the one intended; although the term is predominantly employed to describe adverse effects, it can also apply to beneficial, but unintended, consequences of the use of a drug. Developing drugs is a complicated process, because no two people are exactly the same, so even drugs that have virtually no side effects, might be difficult for some people. Also, it is difficult to make a drug that targets one part of the body but that does not affect other parts, the fact that increases the risk of side effects in the untargeted parts. Occasionally, drugs are prescribed or procedures performed specifically for their side effects; in that case, said side effect ceases to be a side effect and is now an intended effect. For instance, X-rays were historically (and are currently) used as an imaging technique; the discovery of their oncolytic capability led to their employ in radiotherapy (ablation of ...
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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 are dependen ...
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Lisp Programming Language
Lisp (historically LISP) is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation. Originally specified in 1960, Lisp 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. 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, including tree data structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and the read†...
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ML Programming Language
ML (Meta Language) is a General purpose programming language, general-purpose functional programming language. It is known for its use of the polymorphic Hindley–Milner type system, which automatically assigns the data type, types of most Expression (programming), expressions without requiring explicit type annotations, and ensures type safetythere 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 (computer science), garbage collection, imperative programming, call-by-value and currying. It is used heavily in programming language research and is one of the few languages to be completely specified and verified using Formal semantics of programming languages, 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 Featur ...
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