Future directions in declarative programming

This blog has been around for a while now, and as time has gone on some of my opinions and views have changed. One thing that has remained the same is that I have always had a mind focused on logic. Everything to do with logic interests me. I don't know why this is, some of us just have a mind focused on logic I suppose.

As a logician, I have tried to seek out a wide variety of tools of logical reasoning: logic programming, horn clauses, set theory, predicate logic, ontologies, lattices and formal concept analysis, categorical logic and topoi, etc. As I have done all this research and thinking about logic I've felt there is a mismatch between functional programming and the techniques I use. My primary problem then has been how do we solve this mismatch between functional programming and logic?

Problem: functional programming is not logical enough

Solution 1: integrate functional and logic programming in to a single language

Solution 2: embrace functional programming but make it more logical by developing a new logic of functions

When I first encountered topos theory, I thought that solution 1 would be the way to go. We would simply take existing logical and functional programming techniques and use topoi as a unifying bridge between them. The result would be a unified multi-paradigm declarative language with topos theory as its core.

The idea of unifying functional and logical programming is rather obvious and it fits with the common practice of multi-paradigm programming. The problem with the approach of throwing everything and the kitchen sink into a language is its indecisive. The multi-paradigm approach is too fence sitting and it fails to committ to one thing or another.

It occurs to me in developing the toposic structure theory of computations (2023) that we can just develop new logical techniques for handling functions to get our 'logic fix' that way, all without leaving functional programming for another paradigm. Practical work in modern logic uses categoric logic and topos theory. Therefore, this new logic of functional programming will have to be developed using categorical logic and the topos of functions.

What should the future trend in declarative programming be? It should be towards more and better functional programming. We can make things more functional by developing them in the functional languages: Clojure, F#, Haskell, etc and we can make these existing functional languages better. Instead of the multi-paradigm concept, functional programming should come first.

Previously:
The future of declarative programming

References:
[1] Hartmanis, J., & Stearns, R. E. (1966). Algebraic structure theory of sequential machines.

[2] Bernier, J. (2023). Toposic structure theory of computations.