The ABC approach written about her seems good to me, but I still think of this as abstraction. I get that this is a 'zero' or 'low cost' abstraction but it's still an abstraction. Don't want to be overly nit picky so going to leave it there.
The name includes the word "Algebraic". What is the meaning? Usually this means you are defining certain operations on symbols. In a very broad sense, all programming is that, sure, but -- is something more meant, or is the word really just there for prestige?
The general approach sounds like it has potential. Though it wouldn't mix with "modern" C++.
I'd guess that 'algebraic' refers to the emphasis on composability: you create new procedures by composing existing procedures (forming a free monoid), as opposed to creating procedures via a 'telescoping' structure of encapsulation. Perhaps it is further meant to imply associativity in some sense.