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Combinatory Logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. In mathematics Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic. While the expressive power of combinatory logic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinational Logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has ''memory'' while combinational logic does not. Combinational logic is used in computer circuits to perform Boolean algebra on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an arithmetic logic unit, or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as half adders, full adders, half subtractors, full subtractors, multiplexers, demultiplexers, encoders and decoders are also made by using combin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quine 1960 1966 , in philosophy of mathematics
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Quine may refer to: * Quine (surname), people with the surname ''Quine'' * Willard Van Orman Quine, the philosopher, or things named after him: ** Quine (computing), a program that produces its source code as output ** Quine–McCluskey algorithm, an algorithm used for logic minimization ** Quine's paradox, in logic ** Duhem–Quine thesis, in philosophy of science ** Quine–Putnam indispensability argument The Quine–Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. It was named after the phil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-strict Programming Language
A strict programming language is a programming language which employs a strict programming paradigm, allowing only strict functions (functions whose parameters must be evaluated completely before they may be called) to be defined by the user. A non-strict programming language allows the user to define non-strict functions, and hence may allow lazy evaluation. Examples Nearly all programming languages in common use today are strict. Examples include C#, Java, Perl (all versions, i.e. through version 5 and version 7), Python, Ruby, Common Lisp, and ML. Some strict programming languages include features that mimic laziness. Raku, formerly known as Perl 6, has lazy lists. Python has generator functions. Julia provides a macro system to build non-strict functions, as does Scheme. Examples for non-strict languages are Haskell, Miranda, and Clean. Explanation In most non-strict languages the non-strictness extends to data constructors. This allows conceptually infinite data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Variables And Bound Variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable, in contrast, is a variable that has been ''bound'' to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents Mathematical proof, proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as Recursive data type, inductively-defined data structures such as list (computer science), lists, boxed lists, or Tree (data structure), trees, which are constructed according to the axioms and rule of inference, rules of inference of the logical system. Consequently, proof theory is syntax (logic), syntactic in nature, in contrast to model theory, which is Formal semantics (logic), semantic in nature. Some of the major areas of proof theory include structural proof theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation
Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An especially well-known discipline of the study of computation is computer science. Physical process of Computation Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers. This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing. An even more radical point of view, pancomputationalism (inaudible word), is the postulate of digital physics that argues that the evolution of the universe is itself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dana Scott
Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California. His work on automata theory earned him the Turing Award in 1976, while his collaborative work with Christopher Strachey in the 1970s laid the foundations of modern approaches to the semantics of programming languages. He has worked also on modal logic, topology, and category theory. Early career He received his B.A. in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph.D. thesis on ''Convergent Sequences of Complete Theories'' under the supervision of Alonzo Church while at Princeton, and defended his thesis in 1958. Solomon Feferman (2005) writes of this period: After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960. In 1959, he pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henk Barendregt
Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) is a Dutch logician, known for his work in lambda calculus and type theory. Life and work Barendregt studied mathematical logic at Utrecht University, obtaining his master's degree in 1968 and his PhD in 1971, both ''cum laude'', under Dirk van Dalen and Georg Kreisel. After a postdoctoral position at Stanford University, he taught at Utrecht University. Since 1986, Barendregt has taught at Radboud University Nijmegen, where he now holds the Chair of Foundations of Mathematics and Computer Science. His research group works on Constructive Interactive Mathematics. He is also Adjunct Professor at Carnegie Mellon University, Pittsburgh, USA. He has been a visiting scholar at Darmstadt, ETH Zürich, Siena, and Kyoto. Barendregt was elected a member of Academia Europaea in 1992. In 1997 Barendregt was elected member of the Royal Netherlands Academy of Arts and Sciences. On 6 February 2003 Barendregt was awarded the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belgium
Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to the southwest, and the North Sea to the northwest. It covers an area of and has a population of more than 11.5 million, making it the 22nd most densely populated country in the world and the 6th most densely populated country in Europe, with a density of . Belgium is part of an area known as the Low Countries, historically a somewhat larger region than the Benelux group of states, as it also included parts of northern France. The capital and largest city is Brussels; other major cities are Antwerp, Ghent, Charleroi, Liège, Bruges, Namur, and Leuven. Belgium is a sovereign state and a federal constitutional monarchy with a parliamentary system. Its institutional organization is complex and is structured on both regional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Feys
Robert Feys (19 December 1889 – 13 April 1961) was a Belgian logician and philosopher, who worked at the University of Leuven (Belgium).De Raeymaeker, Louis.In memoriam le chanoine Robert Feys" ''Revue Philosophique de Louvain'' 59.62 (1961): 371-374. Feys was born in Mechelen, and received his PhD in 1909 from the Institute of Philosophy, University of Leuven. In 1913 he was appointed Professor at the Université Saint-Louis, Brussels. But due to the War he enlisted in the Army. In 1919 he was appointed Professor at the Institute St. Gertrude in Nivelles. In 1929 he returned to the Université Saint-Louis, Brussels, and in 1944 he was appointed Professor at the University of Leuven. In 1958 Feys and Haskell B. Curry devised the type inference algorithm for the simply typed lambda calculus The simply typed lambda calculus (\lambda^\to), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor (\to) that builds function types. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
