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The curiously recurring template pattern (CRTP) is an idiom, originally in C++, in which a class X derives from a class template instantiation using X itself as a template argument. [1] More generally it is known as F-bound polymorphism , and it is a form of F -bounded quantification .
For example, the first few terms of this series are 1, 5, 16, 45, 121, 320, 841, 2205 .... [4] (The same equation holds for any unimodular hyperbolic toral automorphism if the eigenvalues are replaced.) Γ is ergodic and mixing, Γ is an Anosov diffeomorphism and in particular it is structurally stable.
Models And Counter-Examples (Mace) is a model finder. [1] Most automated theorem provers try to perform a proof by refutation on the clause normal form of the proof problem, by showing that the combination of axioms and negated conjecture can never be simultaneously true, i.e. does not have a model. A model finder such as Mace, on the other ...
Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr.. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties.
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The counter machine models go by a number of different names that may help to distinguish them by their peculiarities. In the following the instruction "JZDEC ( r )" is a compound instruction that tests to see if a register r is empty; if so then jump to instruction I z, else if not then DECrement the contents of r:
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More interesting results are obtained by applying the Y combinator to functions of two or more variables. The additional variables may be used as a counter, or index. The resulting function behaves like a while or a for loop in an imperative language. Used in this way, the Y combinator implements simple recursion. The lambda calculus does not ...