In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different...
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(LF), a pure lambda calculus with dependent types. Based on work by Berardi on pure type systems, Henk Barendregt proposed the Lambda cube to systematize...
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Dependent type (section Systems of the lambda cube)
to types, for example). The lambda cube is generalized further by pure type systems. The system λ Π {\displaystyle \lambda \Pi } of pure first order dependent...
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typed lambda calculus with types as first-class values These formal systems are extensions of lambda calculus that are not in the lambda cube: Binary...
86 KB (11,551 words) - 21:24, 5 October 2024
System F (redirect from Second order lambda calculus)
(also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism...
18 KB (2,531 words) - 11:58, 10 August 2024
Coq and Lean. The lambda cube was not a new type theory but a categorization of existing type theories. The eight corners of the cube included some existing...
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Pure type system (redirect from L-cube)
cube of constructive logics akin to the lambda cube (these specifications are non-dependent). A modification of this cube was later called the L-cube...
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Calculus of constructions (category Lambda calculus)
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...
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(physics), theory organizing subatomic baryons and mesons into octets Lambda cube Octal, base-8 number system Octant (solid geometry) Octave (poetry) Octetra...
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Type theory (section Lambda terms)
combinatory logic others defined in the lambda cube (also known as pure type systems) others under the name typed lambda calculus Homotopy type theory explores...
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Curry–Howard isomorphism Calculus of constructions Constructivist analysis Lambda cube System F Introduction to topos theory LF (logical framework) Computability...
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frequently studied impredicative typed λ-calculi are based on those of the lambda cube, especially System F. In 1985, Luca Cardelli and Peter Wegner recognized...
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System U (category Lambda calculus)
Sørensen, Morten Heine; Urzyczyn, Paweł (2006). "Pure type systems and the lambda cube". Lectures on the Curry–Howard isomorphism. Elsevier. doi:10.1016/S0049-237X(06)80015-7...
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{\displaystyle \lambda \leq \kappa } , the space I λ {\displaystyle I^{\lambda }} is embeddable in I κ {\displaystyle I^{\kappa }} . The Tychonoff cube I κ {\displaystyle...
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polymorphism have been considered in the literature, the most famous being the lambda cube of Henk Barendregt. The intersection of logic and type theory is a vast...
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= jit(cube) # apply the cube and jit_cube functions to the same data for speed comparison cube(x) jit_cube(x) The computation time for jit_cube (line...
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Mogensen–Scott encoding (category Lambda calculus)
the lambda calculus. Church encoding performs a similar function. The data and operators form a mathematical structure which is embedded in the lambda calculus...
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^{\text{Hencky}}&=-{\frac {\ln \lambda _{\text{trans}}}{\ln \lambda _{\text{axial}}}}\\[6pt]\nu ^{\text{Biot}}&={\frac {1-\lambda _{\text{trans}}}{\lambda _{\text{axial}}-1}}\\[6pt]\nu...
33 KB (4,418 words) - 22:05, 2 October 2024
B T λ 4 , {\displaystyle B_{\lambda }(T)={\frac {2ck_{\text{B}}T}{\lambda ^{4}}},} where B λ {\displaystyle B_{\lambda }} is the spectral radiance (the...
11 KB (1,842 words) - 09:46, 3 November 2023
dyadic cubes are a collection of cubes in Rn of different sizes or scales such that the set of cubes of each scale partition Rn and each cube in one scale...
8 KB (1,264 words) - 23:59, 10 May 2024
{\displaystyle G=\left\{\lambda ,{\frac {1}{1-\lambda }},{\frac {\lambda -1}{\lambda }},{\frac {1}{\lambda }},{\frac {\lambda }{\lambda -1}},1-\lambda \right\}\subset...
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of the compensation for the risk borne in investment the α-conversion in lambda calculus the independence number of a graph a placeholder for ordinal numbers...
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, b ) = ( λ a , λ b ) , {\displaystyle \lambda (a,b)=(\lambda a,\lambda b),} where λ {\displaystyle \lambda } is any real number. A simple basis of this...
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combinatorially equivalent to one of five types: the rhombohedron (including the cube), hexagonal prism, truncated octahedron, rhombic dodecahedron, and the rhombo-hexagonal...
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{\displaystyle \lambda (x^{3}+y^{3}+z^{3})+\mu xyz=0.} Each curve in the family is determined by a pair of parameter values ( λ , μ {\displaystyle \lambda ,\mu }...
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polytopes, of which there are only three in six dimensions: the 6-simplex, 6-cube, and 6-orthoplex. A wider family are the uniform 6-polytopes, constructed...
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{\displaystyle \lambda ={\frac {l}{L}}} The extension ratio λ is related to the engineering strain e by e = λ − 1 {\displaystyle e=\lambda -1} This equation...
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measures are modified or omitted. The Lebesgue measure λ {\displaystyle \lambda } on the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is locally...
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defined by recursively composing type constructors. For example, simply typed lambda calculus can be seen as a language with a single non-basic type constructor—the...
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examples of a massless Bose gas with a linear dispersion relation. For a cube of side-length L {\displaystyle L} , the resonating modes of the sonic disturbances...
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