Lambda cube

Common card · No. 438943

In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between terms and types. Here, "dependency" refers to the capacity of a term or type to bind a term or type. The respective dimensions of the λ-cube correspond to: x-axis ( → {\displaystyle \rightarrow } ): types that can depend on terms, corresponding to dependent types. y-axis ( ↑ {\displaystyle \uparrow } ): terms that can depend on types, corresponding to polymorphism. z-axis ( ↗ {\displaystyle \nearrow } ): types that can depend on other types, corresponding to (binding) type operators. The different ways to combine these three dimensions yield...

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