Philip Wadler's Essence of Functional Programming
I spent several weeks in 2012 playing around with this, without getting very far. I was haunted by that phrase "text processing algorithm that passes information both from left to right and right to left". Later I realised that it might be an algorithm for matching regular expressions with back-references.
See Philip Wadler, The essence of functional programming.
Here's a good talk by Emily Riehl on the maths behind the ideas. I wonder if the question at 30:10 is referring to the problem of composing interpreters which Wadler says in that paper is not solved. For example, can we compose two computational effects into one interpreter, to get a computation of maybe-lists? That might be useful in the "passing the state backwards" interpreter.
42:24 It sounds like that's the way forward, if not actually the solution!
See also Bartosz Milewski - Category Theory for Programmers and Freeman Dyson on Richard Feynman and QED.
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