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Polymorphic Recursion
In computer science, polymorphic recursion (also referred to as Milner– Mycroft typability or the Milner–Mycroft calculus) refers to a recursive parametrically polymorphic function where the type parameter changes with each recursive invocation made, instead of staying constant. Type inference for polymorphic recursion is equivalent to semi-unification and therefore undecidable and requires the use of a semi-algorithm or programmer-supplied type annotations. Example Nested datatypes Consider the following nested datatype: data Nested a = a :<: (Nested , Epsilon infixr 5 :<: nested = 1 :<: ,3,4:<: 5,6 ,9 :<: Epsilon
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ...
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Polymorphism (computer Science)
In programming language theory and type theory, polymorphism is the provision of a single interface (computing), interface to entities of different Data type, types or the use of a single symbol to represent multiple different types.: "Polymorphic types are types whose operations are applicable to values of more than one type." The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. The most commonly recognized major classes of polymorphism are: * ''Ad hoc polymorphism'': defines a common interface for an arbitrary set of individually specified types. * ''Parametric polymorphism'': not specifying concrete types and instead use abstract symbols that can substitute for any type. * ''Subtyping'' (also called ''subtype polymorphism'' or ''inclusion polymorphism''): when a name denotes instances of many different classes related by some common superclass. History Interest in polymorphic type systems developed significa ...
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University Of Munich
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operation. Originally established in Ingolstadt in 1472 by Duke Ludwig IX of Bavaria-Landshut, the university was moved in 1800 to Landshut by King Maximilian I of Bavaria when the city was threatened by the French, before being relocated to its present-day location in Munich in 1826 by King Ludwig I of Bavaria. In 1802, the university was officially named Ludwig-Maximilians-Universität by King Maximilian I of Bavaria in honor of himself and Ludwig IX. LMU is currently the second-largest university in Germany in terms of student population; in the 2018/19 winter semester, the university had a total of 51,606 matriculated students. Of these, 9,424 were freshmen while international students totalled 8,875 or approximately 17% of the student pop ...
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Electronic Notes In Theoretical Computer Science
''Electronic Notes in Theoretical Computer Science'' is an electronic computer science journal published by Elsevier, started in 1995. Its issues include many post-proceedings for workshops, etc. The journal is abstracted and indexed in Scopus and Science Citation Index The Science Citation Index Expanded – previously entitled Science Citation Index – is a citation index originally produced by the Institute for Scientific Information (ISI) and created by Eugene Garfield. It was officially launched in 1964 .... Electronic Notes in Theoretical Computer Science has been discontinued as of 2021. References Computer science journals Elsevier academic journals Publications established in 1995 {{comp-sci-theory-stub ...
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Lambert Meertens
Lambert Guillaume Louis Théodore Meertens or L.G.L.T. Meertens (born 10 May 1944, in Amsterdam) is a Dutch computer scientist and professor. , he is a researcher at the Kestrel Institute, a nonprofit computer science research center in Palo Alto's Stanford Research Park. Life and career As a student at the Ignatius Gymnasium in Amsterdam, Meertens designed a computer with Kees Koster, a classmate. In the 1960s, Meertens applied affix grammars to the description and composition of music, and obtained a special prize from the jury at the 1968 International Federation for Information Processing (IFIP) Congress in Edinburgh for his computer-generated string quartet, Quartet No. 1 in C major for 2 violins, viola and violoncello, based on the first non- context-free affix grammar. The string quartet was published in 1968, as ''Mathematical Centre Report MR 96''. Meertens was one of the editors of the Revised ALGOL 68 Report. He was the originator and one of the designers of the p ...
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Richard Bird (computer Scientist)
Richard Simpson Bird (4 February 1943 – 4 April 2022) was a Supernumerary Fellow of Computation at Lincoln College, University of Oxford, in Oxford England, and former director of the Oxford University Computing Laboratory (now the Department of Computer Science, University of Oxford). Bird's research interests lay in algorithm design and functional programming, and he was known as a regular contributor to the ''Journal of Functional Programming'' and the author of ''Introduction to Functional Programming using Haskell'' and other books. His name is associated with the Bird–Meertens formalism, a calculus for deriving programs from specifications in a functional programming style. Formerly, Bird was at the University of Reading. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the programming languages ALGOL 60 and ALGOL 68 ALGOL 68 (s ...
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ACM Transactions On Programming Languages And Systems
The ''ACM Transactions on Programming Languages and Systems'' (''TOPLAS'') is a bimonthly, open access, peer-reviewed scientific journal on the topic of programming languages published by the Association for Computing Machinery. Background Published since 1979, the journal's scope includes programming language design, implementation, and semantics of programming languages, compilers and interpreters, run-time systems, storage allocation and garbage collection, and formal specification, testing, and verification of software. It is indexed in Scopus and SCImago. The editor-in-chief is Andrew Myers (Cornell University). According to the ''Journal Citation Reports'', the journal had a 2020 impact factor of 0.410. References External links * TOPLASat ACM Digital Library TOPLASat DBLP Computer science journals English-language journals Publications established in 1979 Bimonthly journals Transactions on Programming Languages and Systems The ''ACM Transactions on Program ...
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Higher-ranked Polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism. Parametrically polymorphic definitions are ''uniform'': they behave identically regardless of the type they are instantiated at. In contrast, ad hoc polymorphic definitions are given a distinct definition for each type. Thus, ad hoc polymorphism can generally only support a limited number of such distinct types, since a separate implementation has to be provided for each type. Basic definition It is possible to write functions that do not depend on the types of their arguments. For example, the identity function \mathsf ...
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Tower Of Hanoi
The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: # Only one disk may be moved at a time. # Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. # No disk may be placed on top of a disk that is smaller than it. With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2''n'' − 1, where ''n'' is the number of disks. Origins The puzzle was introduced to the Wes ...
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Class (computer Programming)
In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name for the default constructor of the class (a subroutine that creates objects), and as the type of objects generated by instantiating the class; these distinct concepts are easily conflated. Although, to the point of conflation, one could argue that is a feature inherent in a language because of its polymorphic nature and why these languages are so powerful, dynamic and adaptable for use compared to languages without polymorphism present. Thus they can model dynamic systems (i.e. the real world, machine learning, AI) more easily. When an object is created by a constructor of the class, the resulting object is called an instance of the class, and the member variable ...
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Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally develo ...
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