PIMS-ULethbridge PIMS Distinguished Visitor Series: Fairouz Kamareddine

Historically functions have been treated as a kind of meta-object. This all changed with the work of Frege, Russell and Church. Furthermore, the challenges of the paradoxes led to the formalisation of type theory by Russell. Since, functions and types have gone through a long process of evolution through various degrees of abstraction, construction and evaluation making both functions and types first class citizens as far away from meta-level as possible. In this talk, I argue that desirable properties of the historic lower order approach (decidability, easiness of calculations) can be maintained without losing the flexibility of the higher-order aspects. I argue that the low level approach is still worthwhile for many exact disciplines.