In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different...

(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...

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...

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...

(also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism...

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...

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...

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...

(physics), theory organizing subatomic baryons and mesons into octets Lambda cube Octal, base-8 number system Octant (solid geometry) Octave (poetry) Octetra...

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...

Curry–Howard isomorphism Calculus of constructions Constructivist analysis Lambda cube System F Introduction to topos theory LF (logical framework) Computability...

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...

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...

{\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...

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...

= 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...

the lambda calculus. Church encoding performs a similar function. The data and operators form a mathematical structure which is embedded in the lambda calculus...

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...

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...

{\displaystyle G=\left\{\lambda ,{\frac {1}{1-\lambda }},{\frac {\lambda -1}{\lambda }},{\frac {1}{\lambda }},{\frac {\lambda }{\lambda -1}},1-\lambda \right\}\subset...

^{\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...

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...

, 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...

combinatorially equivalent to one of five types: the rhombohedron (including the cube), hexagonal prism, truncated octahedron, rhombic dodecahedron, and the rhombo-hexagonal...

{\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 }...

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...

{\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...

measures are modified or omitted. The Lebesgue measure λ {\displaystyle \lambda } on the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is locally...

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...

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...