> Here is a stack machine that [instead of addition] implements subtraction, based on the mode assignment i/o/i [without changing the code already used for addition]. (You might have heard people claim that logic programs can be "run backwards"; this is one thing that can mean.)
k >> plus 0 _ P |----> k << P
k >> plus (s N) _ (s P) |----> k; _ >> plus N _ P
k; _ << P |----> k << P
So if you're confused because of the slightly unusual notation, here's the same thing in Prolog syntax:
% "Sum is the sum of S1 and S2"
plus(S1, S2, Sum) :- Sum is S1 + S2.
% "What is the sum of 3 and 5?"
?- plus(3, 5, S).
% Answer: S = 8
% "Is 10 the sum of 3 and 5"
?- plus(3, 5, 10).
% Answer: fail
% "What's the difference between 3 and 10?"
?- plus(3, X, 10).
% throws an error
It doesn't work this way in general because the Prolog is/2 predicate can only be used in one direction to evaluate the term on the right hand side where must all variable must be bound to a number in context. The article mentions Peano arithmetic as one finite/incomplete axiomatisation of natural numbers but doesn't elaborate on it.
Thanks. I thought it was interesting choosing arithmetic instead of some other relation because multimodal arithmetic (via CLP) is more of a PhD thesis than a blog post. Other relations might've been easier to demonstrate a general query.
What I couldn't tell from the article was if the author somehow achieved a multimodal arithmetic relation without needing CLP using a stack machine. That would be a neat technique.
> I've recently been curious about the abstract machines implied by this process for other kinds of programs.
Olivier Danvy's "Rational Reconstruction of the SECD Machine" [0] explores the idea of this transformation as well, but frames it as a relationship between operational and denotational semantics:
> This deconstruction–reconstruction is actually interesting in itself because it provides a bridge between small-step operational semantics (in the form of an abstract machine) and denotational semantics (in the form of a compositional evaluation function)
His work on (de/re)functionalization is super interesting.
> Here is a stack machine that [instead of addition] implements subtraction, based on the mode assignment i/o/i [without changing the code already used for addition]. (You might have heard people claim that logic programs can be "run backwards"; this is one thing that can mean.)
So if you're confused because of the slightly unusual notation, here's the same thing in Prolog syntax: It doesn't work this way in general because the Prolog is/2 predicate can only be used in one direction to evaluate the term on the right hand side where must all variable must be bound to a number in context. The article mentions Peano arithmetic as one finite/incomplete axiomatisation of natural numbers but doesn't elaborate on it.Thanks. I thought it was interesting choosing arithmetic instead of some other relation because multimodal arithmetic (via CLP) is more of a PhD thesis than a blog post. Other relations might've been easier to demonstrate a general query.
What I couldn't tell from the article was if the author somehow achieved a multimodal arithmetic relation without needing CLP using a stack machine. That would be a neat technique.
> I've recently been curious about the abstract machines implied by this process for other kinds of programs.
Olivier Danvy's "Rational Reconstruction of the SECD Machine" [0] explores the idea of this transformation as well, but frames it as a relationship between operational and denotational semantics:
> This deconstruction–reconstruction is actually interesting in itself because it provides a bridge between small-step operational semantics (in the form of an abstract machine) and denotational semantics (in the form of a compositional evaluation function)
His work on (de/re)functionalization is super interesting.
[0]: https://link.springer.com/chapter/10.1007/11431664_4
[dead]