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Total Functional Programming
Total 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. Restrictions 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. # Every function must be a total (as opposed to partial) function. That is, it must have a definition for everything inside its domain. #* There are several possible ways to extend commonly used partial functions such as division to be total: choosing an arbitrary result for inputs on which the function is normally undefined (such as \forall x \in \mathbb. x \div 0 = 0 for division); adding another argument to specify the result for those inputs; or exclud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Programming
In 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. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner. Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming which treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lazy Evaluation
In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed ( non-strict evaluation) and which also avoids repeated evaluations (sharing). The benefits of lazy evaluation include: * The ability to define control flow (structures) as abstractions instead of primitives. * The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms. * The ability to define partially-defined data structures where some elements are errors. This allows for rapid prototyping. Lazy evaluation is often combined with memoization, as described in Jon Bentley's ''Writing Efficient Programs''. After a function's value is computed for that parameter or set of parameters, the result is stored in a lookup table that is indexed by the values of those parameters; the next time the function is called, the table is consulted to determine whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Paradigms
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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Termination Analysis
In computer science, termination analysis is program analysis which attempts to determine whether the evaluation of a given program halts for ''each'' input. This means to determine whether the input program computes a ''total'' function. It is closely related to the halting problem, which is to determine whether a given program halts for a ''given'' input and which is undecidable. The termination analysis is even more difficult than the Halting problem: the termination 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 machine is a total Turing machine, and this problem is at level \Pi^0_2 of the arithmetical hierarchy and thus is strictly more difficult than the Halting problem. Now as the question whether a computable function is total is not semi-decidable, each ''sound'' termination analyzer (i.e. an affirmative answer is never given for a non-terminating program) is '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Constructions
In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. It can serve as both a typed programming language and as constructive foundation for mathematics. For this second reason, the CoC and its variants have been the basis for Coq and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction), and the predicative calculus of inductive constructions (which removes some impredicativity). General traits The CoC is a higher-order typed lambda calculus, initially developed by Thierry Coquand. It is well known for being at the top of Barendregt's lambda cube. It is possible within CoC to define functions from terms to terms, as well as terms to types, types to types, and types to terms. The CoC is strongly normalizing, and hence consistent. Usage The CoC has been developed alongs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin-Löf Type Theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types. Design Martin-Löf designed the type theory on the principles of mathematical constructivism. Constructivism requires any existence proof to contain a "witness". So, any proof of "there exists a prime greater than 1000" must identify a specific number that is both prime and greater than 1000. Intuitionistic type theory accomplished this design goal by internalizing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System F
System F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML. It was discovered independently by logician Jean-Yves Girard (1972) and computer scientist John C. Reynolds Whereas simply typed lambda calculus has variables ranging over terms, and binders for them, System F additionally has variables ranging over ''types'', and binders for them. As an example, the fact that the identity function can have any type of the form ''A'' → ''A'' would be formalized in System F as the judgement :\vdash \Lambda\alpha. \lambda x^\alpha.x: \forall\alpha.\alpha \to \alpha where \alpha is a type variable. The upper-case \Lambda is traditionally used to denote type-level functions, as opposed to the lower-ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Turner (computer Scientist)
David A. Turner (born 26 January 1946) is a British computer scientist. He is best known for designing and implementing three programming languages, including the first for functional programming based on lazy evaluation, combinator graph reduction, and polymorphic types: SASL (1972), Kent Recursive Calculator (KRC) (1981), and the commercially supported Miranda (1985). Miranda had a strong influence on the later Haskell. He has a Doctor of Philosophy (D.Phil.) from the University of Oxford. He has held professorships at Queen Mary College, London, University of Texas at Austin and the University of Kent at Canterbury, where he has spent most of his career and retains the title of Emeritus Professor of Computation. He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charity (programming Language)
Charity may refer to: Common meanings * Charitable organization or charity, a non-profit organization whose primary objectives are philanthropy and social well-being of persons * Charity (practice), the practice of being benevolent, giving and sharing * Charity (Christian virtue), the Christian religious concept of unlimited love and kindness Places * Charity, Guyana, a small township * Charity, Missouri, a community in the United States * Mount Charity, Antarctica * Charity Glacier, Livingston Island, Antarctica * Charity Island (Tasmania), Australia * Charity Creek, Sydney, Australia * Charity Lake, British Columbia, Canada * Charity Island (Michigan), United States Arts and entertainment * ''Charity'' (play), an 1874 play by W. S. Gilbert * ''Charity'' (novel), third in the ''Faith, Hope, Charity'' espionage trilogy of novels by Len Deighton * "Charity" (''Dilbert'' episode) * "Charity" (''Malcolm in the Middle'' episode) * "Charity", a 1912 Cole Porter song - see List o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epigram (programming Language)
Epigram is a functional programming language with dependent types, and the integrated development environment (IDE) usually packaged with the language. Epigram's type system is strong enough to express program specifications. The goal is to support a smooth transition from ordinary programming to integrated programs and proofs whose correctness can be checked and certified by the compiler. Epigram exploits the ''Curry–Howard correspondence'', also termed the ''propositions as types principle'', and is based on intuitionistic type theory. The Epigram prototype was implemented by Conor McBride based on joint work with James McKinna. Its development is continued by the Epigram group in Nottingham, Durham, St Andrews, and Royal Holloway, University of London in the United Kingdom (UK). The current experimental implementation of the Epigram system is freely available together with a user manual, a tutorial and some background material. The system has been used under Linux, Window ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dependent Types
In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations. Two common examples of dependent types are ''dependent functions'' and ''dependent pairs''. The return type of a dependent function may depend on the ''value'' (not just type) of one of its arguments. For instance, a function that takes a positive integer n may return an array of length n, where the array length is part of the type of the array. (Note that this is different from polymorphism and generic programming, both of which include the type as an argument.) A dependent pair may have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corecursion
In computer science, corecursion is a type of operation that is dual to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data. A similar but distinct concept is '' generative recursion'' which may lack a definite "direction" inherent in corecursion and recursion. Where recursion allows programs to operate on arbitrarily complex data, so long as they can be reduced to simple data (base cases), corecursion allows programs to produce arbitrarily complex and potentially infinite data structures, such as streams, so long as it can be produced from simple data (base cases) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |