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Typed functional language
Programming Computable Functions (PCF), or Programming with Computable Functions, or Programming language for Computable Functions, is a programming language
Programming Computable Functions
Programming_Computable_Functions
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
Deductive system for computable functions by Dana Scott
Logic for Computable Functions (LCF), theorem proving logic by Robin Milner. Programming Computable Functions (PCF), small theoretical programming language
Logic_of_Computable_Functions
1970s automated theorem prover
foundation of logic of computable functions previously proposed by Dana Scott. Work on the LCF system introduced the general-purpose programming language ML to
Logic for Computable Functions
Logic_for_Computable_Functions
Programming language
by LOOP-programs is a proper subset of computable functions (and thus a proper subset of the functions computable by WHILE and GOTO programs). The LOOP
LOOP_(programming_language)
Real number that can be computed within arbitrary precision
the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel
Computable_number
Branch of computer science
class of programming languages now known as function-level programming languages. In 1977, Gordon Plotkin introduces Programming Computable Functions, an abstract
Programming_language_theory
Sequence of program instructions invokable by other software
features. Some programming languages, such as COBOL and BASIC, make a distinction between functions that return a value (typically called "functions") and those
Function (computer programming)
Function_(computer_programming)
Topics referred to by the same term
correlation Polymer-clad fiber, a type of optical fiber Programming Computable Functions, a functional programming language Physical Constraints File, a file format
PCF
One of several equivalent definitions of a computable function
recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in
General_recursive_function
Quickly growing function
total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates
Ackermann_function
Function computable with bounded loops
closely with our intuition of what a computable function must be. Certainly the initial functions are intuitively computable (in their very simplicity), and
Primitive_recursive_function
Ability of a computing system to simulate Turing machines
abstract machine or programming language): Turing completeness A computational system that can compute every Turing-computable function is called Turing-complete
Turing_completeness
Study of computable functions and Turing degrees
with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability
Computability_theory
C standard library header file
operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. The C++ standard library
C_mathematical_functions
Executing several computations during overlapping time periods
pattern Concurrent computing Concurrent object-oriented programming Construction and Analysis of Distributed Processes (CADP) D (programming language) Dining
Concurrent_computing
Study of mathematical analysis seen through computability theory
of any computable function. The differentiation operator over real-valued functions is not computable, but over complex functions is computable. The latter
Computable_analysis
Turing machine that halts for any input
theorem shows that the functions computable by machines that always halt do not include extensions of all partial computable functions, which implies the
Decider_(Turing_machine)
Use of functions that call themselves
recursion into programming. John McCarthy took the first steps by creating the programming language LISP in 1960. In his paper Recursive Functions of Symbolic
Recursion_(computer_science)
General-purpose programming language
general-purpose programming language that emphasizes performance, type safety, concurrency, and memory safety. Rust supports multiple programming paradigms
Rust_(programming_language)
Programming language for statistics
R is a programming language for statistical computing and data visualization. It has been widely adopted in the fields of data mining, bioinformatics,
R_(programming_language)
Concept in theoretical computer science
the functions S(n) and Σ(n) eventually become larger than any computable function and are hence noncomputable. This has implications in computability theory
Busy_beaver
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
Problem in computer science
computable relies on the following constructs (or their equivalents): computable subprograms (the program that computes f is a subprogram in program e)
Halting_problem
Theorem in computability theory
In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions
Kleene's_recursion_theorem
Rules out assigning to arbitrary functions their computational complexity
complexity of computable functions. Each computable function has an infinite number of different program representations in a given programming language.
Blum's_speedup_theorem
General-purpose programming language
programming languages, with C compilers available for practically all modern computer architectures and operating systems. The book The C Programming
C_(programming_language)
Measure of required computing power
necessary for a computer or computer program to function. Compute is commonly defined as the amount of computing power or computational resources required
Compute_(machine_learning)
Computer programming paradigm
computer science, function-level programming is one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical
Function-level_programming
Instructions a computer can execute
artificial intelligence. Object-oriented programming is a programming method to execute operations (functions) on objects. The basic idea is to group the
Computer_program
Topics referred to by the same term
function may refer to: Recursive function (programming), a function which references itself General recursive function, a computable partial function
Recursive_function
Concept in computability theory
of all partial computable functions. Such enumerations are formally called computable numberings of the partial computable functions. An arbitrary numbering
Admissible_numbering
Ordinal-indexed family of rapidly increasing functions
a total function. If the fundamental sequences are computable (e.g., as in the Wainer hierarchy), then every fα is a total computable function. In the
Fast-growing_hierarchy
Systems programming language
Mojo is a programming language for Linux and macOS. It is a system programming language with semantics inspired by Rust such as static typing and a borrow
Mojo_(programming_language)
Programming paradigm in which many processes are executed simultaneously
have brought parallel computing to desktop computers. Thus parallelization of serial programs has become a mainstream programming task. In 2012 quad-core
Parallel_computing
Functional programming language for arrays
symbols instead of APL symbols. APL (named after the book A Programming Language) is a programming language developed in the 1960s by Kenneth E. Iverson. Its
APL_(programming_language)
to model programming language concepts such as function types. It turns out that restricting expression to the set of computable functions is not sufficient
Function_type
Software programming optimization technique
support that make it easy for the programmer to memoize a function, and others memoize certain functions by default. Memoization has also been used in other
Memoization
Programming paradigm based on applying and composing functions
functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm
Functional_programming
Function whose job is only to call another subroutine
computation. Wrapper functions simplify writing computer programs by abstracting the details of a subroutine's implementation. Wrapper functions are a means of
Wrapper_function
Function definition that is not bound to an identifier
and anonymous functions are often referred to as lambdas or lambda abstractions. Anonymous functions have been a feature of programming languages since
Anonymous_function
Cloud computing model
anti-pattern that can occur in serverless architectures when functions (e.g., AWS Lambda, Azure functions) excessively invoke each other in fragmented chains,
Serverless_computing
American computer scientist (1935–2013)
it one of the main objects of semantic research, along with Programming Computable Functions (PCF) and ML. He was an editor of journals such as the Communications
John_C._Reynolds
Computational software program
3000 functions contributed as Resource Functions. In addition to the Wolfram Function Repository, there is a Wolfram Data Repository with computable data
Wolfram_Mathematica
Method to solve optimization problems
Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique
Linear_programming
Function with variable number of arguments
a variable number of arguments. Support for variadic functions differs widely among programming languages. There are many mathematical and logical operations
Variadic_function
Mathematical-logic system
usual for such a proof, computable means computable by any model of computation that is Turing complete. In fact computability can itself be defined via
Lambda_calculus
Theorem in computability theory
finite-state programs, not to Turing-complete languages. Let φ {\displaystyle \varphi } be an admissible numbering of the partial computable functions, and let
Rice's_theorem
Thesis on the nature of computability
definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil
Church–Turing_thesis
Mathematical theory
probability to any computable theory. Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
Parallel computing platform: GPGPU libraries and application programming interface
heterogeneous computing. It offers several programming models: HIP (GPU-kernel-based programming), OpenMP (directive-based programming), and OpenCL. ROCm
ROCm
Ability to solve a problem by an effective procedure
Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are
Computability
Generalization of Rice's theorem
that when a semi-decidable property of partial computable functions is true on a certain partial function, one can extract a finite subfunction such that
Rice–Shapiro_theorem
Overview of and topical guide to computer programming
computer programming: Computer programming – process that leads from an original formulation of a computing problem to executable computer programs. Programming
Outline of computer programming
Outline_of_computer_programming
Programming language
November 10, 2021. "C Library Functions". GeeksforGeeks. July 18, 2021. "C Programming Tutorial". cprogramming.com. C programming language at Wikipedia's sister
Outline of the C programming language
Outline_of_the_C_programming_language
Variable that represents an argument to a function
In computer programming, a parameter, or formal argument, is a variable that represents an argument to a function call. A function's signature defines
Parameter (computer programming)
Parameter_(computer_programming)
Programming language with hardware abstraction
high-level programming language is a programming language with strong abstraction from the details of the computer. In contrast to low-level programming languages
High-level programming language
High-level_programming_language
Design pattern in functional programming to build generic types
with some form of the Maybe type, there are functions that aid in their use such as composing monadic functions with each other and testing if a Maybe contains
Monad (functional programming)
Monad_(functional_programming)
Arctangent function with two arguments
It is used by IEEE-754, C mathematical functions, Mathcad, and most programming languages. Some programming languages supports an optional parameter
Atan2
Halting probability of a random computer program
universal computable function. Such a function, intuitively, represents a program in a programming language with the property that no valid program can be
Chaitin's_constant
Placeholder variables in programming
variables in computer programming or computer-related documentation. They have been used to name entities such as variables, functions, and commands whose
Foobar
Using one interface or symbol with regards to multiple different types
the first programming language to implement it. Christopher Strachey chose the term ad hoc polymorphism to refer to polymorphic functions that can be
Polymorphism (computer science)
Polymorphism_(computer_science)
Technique for creating lexically scoped first class functions
in 1970 as a language feature in the PAL programming language to support lexically scoped first-class functions. Peter Landin defined the term closure in
Closure (computer programming)
Closure_(computer_programming)
General-purpose programming language
type, structured programming (Fortran 77), array programming, modular programming, generic programming (Fortran 90), parallel computing (Fortran 95), object-oriented
Fortran
Organizing code into modules
Modular programming is a programming paradigm that emphasizes organizing the functions of a codebase into independent modules, each providing an aspect
Modular_programming
Type of computing function
functions and memory functions are related in that both involve extensive memory access, but a distinction exists between the two. Memory functions use
Memory-bound_function
Association of one output to each input
a theory that defines computable functions without using set theory, and is the theoretical background of functional programming. It consists of terms
Function_(mathematics)
Programming language close to hardware
A low-level programming language is a programming language that provides little or no abstraction from a computer's instruction set architecture, memory
Low-level programming language
Low-level_programming_language
reversible programming language written at Caltech in 1982. The operational semantics of the language were formally specified, together with a program inverter
Janus (reversible computing programming language)
Janus_(reversible_computing_programming_language)
Numerical computing environment and programming language
multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data
MATLAB
Models of computation
a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computable in the Church–Turing sense. Technically
Hypercomputation
Programming language environment
Numbers in the Ch Programming Language". Scientific Programming: 76–106. Cheng, Harry (1993). "Scientific Computing in the Ch Programming Language". Scientific
Ch_(computer_programming)
Self-replicating program
hash functions and are considered a conceptual relative of quines rather than a type of quine in the strict programming sense. Computer programming portal
Quine_(computing)
Common way to code a relatively small construct
In programming and in code, an idiom describes a commonly-used way to code a relatively small construct in a particular programming context (i.e. programming
Programming_idiom
System with multiple networked computers
mobility – Process in distributed computing Dataflow programming – Computer programming paradigm Decentralized computing – Distribution of jobs across different
Distributed_computing
Programming paradigm
Tacit programming, also called point-free style, is a programming paradigm in which function definitions do not identify the arguments (or "points") on
Tacit_programming
Programming language
"Codewalk: First-Class Functions in Go". Go supports first class functions, higher-order functions, user-defined function types, function literals, closures
Go_(programming_language)
Free graphics library
Processing uses the Java programming language, with added simplifications such as added classes and aliased mathematical functions and operations. It also
Processing
Style of computer programming
Generic programming is a style of computer programming in which algorithms are written in terms of data types to-be-specified-later that are then instantiated
Generic_programming
Programming language
result, he went on to develop the meta language for his Logic for Computable Functions, a language that would only allow the writer to construct valid proofs
OCaml
Axioms in computational complexity theory
are functions that are arbitrarily high in complexity class: for any total computable f {\displaystyle f} , there exists total computable functions not
Blum_axioms
Programming paradigm
In computing, aspect-oriented programming (AOP) is a programming paradigm that aims to increase modularity by allowing the separation of cross-cutting
Aspect-oriented_programming
General-purpose programming language
collection. Python supports multiple programming paradigms but with an emphasis on object-oriented programming and dynamic typing. Guido van Rossum began
Python_(programming_language)
Library of C programs
The C date and time functions are a group of functions in the standard library of the C programming language implementing date and time manipulation operations
C_date_and_time_functions
Programming language
specified for function arguments and function return values. Functions in Hack are thus annotated with types like the following: // Hack functions are annotated
Hack_(programming_language)
Statistical programming language
features, such as the transition from macros to functions and how functions can be passed to other functions (such as apply). Many other changes to the S
S_(programming_language)
history of programming languages spans from documentation of early mechanical computers to modern tools for software development. Early programming languages
History of programming languages
History_of_programming_languages
Software that provides access that hides details
function of some variable) and higher-order functions (parameters are functions). Modern members of the Lisp programming language family such as Clojure, Scheme
Abstraction (computer science)
Abstraction_(computer_science)
Continuous function whose value increases to infinity
of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated
Barrier_function
Interface to call functions from other programming languages
A foreign function interface (FFI) is a mechanism by which a program written in one programming language can call interoperable routines or make use of
Foreign_function_interface
Measure of algorithmic complexity
2^{*}} be a computable function mapping finite binary strings to binary strings. It is a universal function if, and only if, for any computable f : 2 ∗ →
Kolmogorov_complexity
functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions
List of mathematical functions
List_of_mathematical_functions
Formalism in computer science
explicit recursion combinators, such as Plotkin's "Programming language for Computable Functions" (PCF), are not normalizing, but they are not intended
Typed_lambda_calculus
Language for controlling a computer
classify a language used in computing that is not considered a programming language.[citation needed] Some regard a programming language as a theoretical
Programming_language
General-purpose functional programming language
ML is a modern dialect of ML, the language used in the Logic for Computable Functions (LCF) theorem-proving project. It is distinctive among widely used
Standard_ML
Computation model defining an abstract machine
level text; most of Chapter XIII "Computable functions" is on Turing machine proofs of computability of recursive functions, etc. Knuth, Donald E. (1973)
Turing_machine
Function that is tied to a particular instance or class
C++ a method is known as a member function. C++ also has the concept of virtual functions which are member functions that can be overridden in derived
Method_(computer_programming)
Form of type polymorphism
context" are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation
Subtyping
Connection between computers or programs
An application programming interface (API) is a connection between computers or between computer programs. It is a type of software interface, offering
API
Concept in computer programming
function). In object-oriented programming, global data is defined in the scope of a class and can be private, making it accessible only to functions of
Reentrancy_(computing)
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PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
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