Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter ...

We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of ...

Lambda-calculus and type theory form a foundational framework in computer science and mathematical logic, offering a formal approach to modelling computation and reasoning about programs. At its core, ...