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

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...

(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...

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...

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...

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...

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...

to identify the allowed logical conversions from one type to another. Lambda cube Logical hexagon Square of opposition Triangle of opposition Hans Reichenbach...

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...

Lambda cube Logical cube Square of opposition Triangle of opposition N-opposition theory logical hexagon Moretti, Alessio. "The oppositional cube (or...

{\displaystyle s(A)=\emptyset } ). Boole's syllogistic Free logic Lambda cube Logical cube Logical hexagon Triangle of opposition Per The Traditional Square...

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...

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

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...

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...

triangle of contraries and Sir William Hamilton’s subcontraries. Lambda cube Logical cube Logical hexagon Square of opposition Bazhanov, Valentin (January...

= 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...

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...

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...

^{\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...

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

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...

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

dependence of the heat capacity of solids, which is proportional to the cube of temperature – the Debye T 3 law. Similarly to the Einstein photoelectron...

{3}{2}}{\frac {\lambda _{x}^{4}+\lambda _{y}^{4}+\lambda _{z}^{4}}{(\lambda _{x}^{2}+\lambda _{y}^{2}+\lambda _{z}^{2})^{2}}}-{\frac {1}{2}}}...

and only if λ ( n ) = φ ( n ) , {\displaystyle \lambda (n)=\varphi (n),} where λ {\displaystyle \lambda } and φ {\displaystyle \varphi } are respectively...