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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
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
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
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
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)
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
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
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
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
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
Programming language
computable by LOOP-programs is a proper subset of computable functions (and thus a subset of the computable by WHILE and GOTO program functions). The LOOP language
LOOP_(programming_language)
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
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
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
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
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
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
Computer programming paradigm
science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical
Function-level_programming
Concept in theoretical computer science
fact, both the functions Σ(n) and S(n) eventually become larger than any computable function. This has implications in computability theory, the halting
Busy_beaver
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)
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
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
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)
Mathematical-logic system based on functions
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
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
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
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
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
Executing several computations during overlapping time periods
waiting for all other computations to complete. Concurrent computing is a form of modular programming. In its paradigm an overall computation is factored into
Concurrent_computing
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)
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
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
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
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
Intermediate language
received the 2025 Alonzo Church Award for his work on CBPV. Programming Computable Functions Kavvos, G. A.; Morehouse, Edward; Licata, Daniel R.; Danner
Call-by-push-value
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
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
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
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)
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
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)
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
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
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)
General-purpose programming language
general-purpose programming language which emphasizes performance, type safety, concurrency, and memory safety. Rust supports multiple programming paradigms
Rust_(programming_language)
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
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
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
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)
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
Academic subfield of computer science
Walter A. Carnielli (2000). Computability: Computable Functions, Logic, and the Foundations of Mathematics, with Computability: A Timeline (2nd ed.). Wadsworth/Thomson
Theory_of_computation
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
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
Dynamic programming language
not all functions are generic functions. In Julia, Dylan, and Fortress, extensibility is the default, and the system's built-in functions are all generic
Julia_(programming_language)
Variable that represents an argument to a function
by a programming language. Evaluation strategy defines the semantics for how parameters can be declared and how arguments are passed to a function. Generally
Parameter (computer programming)
Parameter_(computer_programming)
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
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 (programming language theory)
Polymorphism_(programming_language_theory)
High-level computer programming conceptualization
languages and logic programming. Functional programming is a subset of declarative programming. Programs written using this paradigm use functions, blocks of code
Programming_paradigm
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)
Concept in computer science
computable functions" (Plotkin 1977). Programming Computable Functions is used by (Mitchell 1996). It is also referred to as Programming with Computable Functions
Let_expression
polynomial-time computable functions (FP) have received much attention and possess several implicit representations. Jones defined a programming language that
Implicit computational complexity
Implicit_computational_complexity
Concept in computer science
large amounts of "garbage" history. RTMs compute precisely the set of injective (one-to-one) computable functions. They are not strictly universal in the
Reversible_computing
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
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)
Proprietary language for AI accelerators
proprietary programming language based on Python available for Linux and macOS. Mojo aims to combine the usability of a high-level programming language,
Mojo_(programming_language)
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
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
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
Solving an optimization problem with a quadratic objective function
quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context
Quadratic_programming
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
General-purpose programming language
type, structured programming (Fortran 77), array programming, modular programming, generic programming (Fortran 90), parallel computing (Fortran 95), object-oriented
Fortran
Ordered listing of items in collection
arbitrary function with domain ω and only countably many computable functions. A specific example of a set with an enumeration but not a computable enumeration
Enumeration
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
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
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
Study of mathematical algorithms for optimization problems
convex programming. Fractional programming studies optimization of ratios of two nonlinear functions. The special class of concave fractional programs can
Mathematical_optimization
Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be
Computable_topology
Point in a computer program where instruction-execution begins
programming languages, the entry point is in a runtime library, a set of support functions for the language. The library code initializes the program
Entry_point
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)
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
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)
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)
Process to create executable computer programs
procedures, by writing code in one or more programming languages. Programmers typically use high-level programming languages that are more easily intelligible
Computer_programming
Determination of whether a given program halts for each input
analysis in the model of Turing machines as the model of programs implementing computable functions would have the goal of deciding whether a given Turing
Termination_analysis
Type of subroutine
anonymous functions into other programming languages has made this capability widely available. Thunks are useful in object-oriented programming platforms
Thunk
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)
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
Procedural, imperative computer programming language
PL/I (Programming Language One, pronounced /piː ɛl wʌn/ and sometimes written PL/1) is a procedural, imperative computer programming language initially
PL/I
Function that takes one or more functions as an input or that outputs a function
Combinatory logic Function-level programming Functional programming Kappa calculus - a formalism for functions which excludes higher-order functions Strategy pattern
Higher-order_function
C standard library header file
operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. Different C standards
C_mathematical_functions
Programming paradigm based on modeling the logic of a computation
In computer science, declarative programming is a programming paradigm that expresses the logic of a computation without fully describing its control flow
Declarative_programming
Computer program that translates code from one programming language to another
A translator or programming language processor is a computer program that converts the programming instructions written in human convenient form into machine
Translator_(computing)
mathematical functions such as the square root and the common logarithm (for use in multiplication and division), and the trigonometric functions. By the time
History_of_computing
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 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)
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
Programmable machine that processes data
capable of computing anything that is computable by executing instructions (program) stored on tape, allowing the machine to be programmable. The fundamental
Computer
Inverse functions of sin, cos, tan, etc.
trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions, under
Inverse trigonometric functions
Inverse_trigonometric_functions
Subfield of mathematics
also called computability theory, studies the properties of computable functions and the Turing degrees, which divide the uncomputable functions into sets
Mathematical_logic
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
Girl/Female
Indian
Sacred, Pure, Comparable to the ganges, Another name for Durga, ***, Another name for Durga
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Boy/Male
Muslim
Similar. Comparable.
Boy/Male
Arabic, Australian, Muslim
Similar; Comparable; One who Warns
Girl/Female
Tamil
Sacred, Pure, Comparable to the ganges, Another name for Durga, ***, Another name for Durga
Boy/Male
Afghan, Arabic, Celebrity, German, Indian, Muslim, Sindhi
Observer; Supervisor; Little; Insignificant; Warner; Similar; Comparable; Another Name for the Quran; One who Preaches
Girl/Female
Tamil
Sacred, Pure, Comparable to the ganges, Another name for Durga, ***, Another name for Durga
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Boy/Male
Muslim
Similar. Comparable.
Girl/Female
Indian
Sacred, Pure, Comparable to the ganges, Another name for Durga, ***, Another name for Durga
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
Boy/Male
Hindu
Daughter God
Girl/Female
Hindu, Indian
Puppet
Female
Polish
Polish form of Russian Roza, RÓŻA means "rose."
Boy/Male
Arabic, Muslim
Light of the Prophet Muhammad
Girl/Female
Hindu, Indian
Sight
Boy/Male
Tamil
Lightning
Girl/Female
Arabic, French, Indian, Muslim, Sindhi
Branches of a Tree
Boy/Male
Indian, Punjabi, Sikh
Beauteous Union with God
Girl/Female
Hindu
Artistic or Goddess Parvati
Girl/Female
Danish, German, Greek, Latin
Pearl
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
PROGRAMMING COMPUTABLE-FUNCTIONS
n.
The quality of being imputable; imputableness.
a.
Not commutable; not capable of being exchanged with, or substituted for, another.
a.
Not compliable; not conformable.
a.
Correspondent; conformable; hence, comparable.
a.
Suitable; consistent.
n.
The quality of being commutable.
a.
Capable of being attributed; ascribable; imputable.
a.
Capable of bending or yielding; apt to yield; compliant.
a.
Compatible; suitable; consistent.
a.
Capable of being commuted or interchanged.
a.
Comparable.
adv.
In a compatible manner.
a.
That may be confuted.
a.
Such as can be, or is liable to be, combated; as, combatable foes, evils, or arguments.
a.
Not computable.
a.
Capable of existing in harmony; congruous; suitable; not repugnant; -- usually followed by with.
a.
Capable of being computed, numbered, or reckoned.
n.
The quality of being commutable; interchangeableness.
a.
Not confutable.
n.
Quality of being imputable.