In
mathematical logic and
type theory, the
?-cube is a framework for exploring the axes of refinement in
Coquand's
calculus of constructions, starting from the
simply typed lambda calculus as the vertex of a cube placed at the origin, and the calculus of constructions (higher order dependently-typed polymorphic lambda calculus) as its diametric opposite vertex. Each axis of the cube represents a new form of abstraction
All eight calculi include the most basic form of abstraction, terms depending on terms, ordinary functions as in the simply-typed lambda calculus.
All eight calculi are strongly normalizing.
The idea of the cube is due to the mathematician Henk Barendregt (1991).
