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...

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...

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

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...

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...

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...

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

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...

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

{\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...

= 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...

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...

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

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...

^{\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...

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...

{\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 }...

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

, 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...

Functor (disambiguation). In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming...

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...