Cubical Higher Type Theory as a Programming Language | Existential Type

]]>Actually, the contemporary functional languages are still of von Neumann, i.e. with additional lazy evaluation (term reduction to normal form). This means, the computation on higher type objects are done there in a symbolic way.

The original idea of Backus was “programs as mathematical objects”, where the objects (like functionals) are not represented by names (terms) in computations.

Although symbolic computations make sense (like algebraic calculations), and the computations on higher order object can be done (via some equations) if they are evaluated to the primitive types, the intuition behind the functionals is that they are *objects* that can be constructed as concrete structures.

Such objects may be envisioned as programmable integrated circuits (FPGAs).

This may break the current paradigm in IT that only symbolic computations (term rewriting) can be done on higher order objects.

It seems that the hardware technology is still far from making possible to break the paradigm.

By the way, human brain is non-von Neumann. The recent advances in Neurobiology may shed some light on how non symbolic computations can be done, google

R. Douglas Fields. Glial Regulation of the Neuronal Connectome through Local and Long-Distant Communication.