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Author here.

Chapter 2 of my dissertation covers a lot about the syntax of Dyna https://matthewfl.com/papers/mfl-dissertation.pdf

As refset said in the other comment, In Dyna, terms return values like a function in a functional programming language. Hence, when you write

  word(I)
this returns the value defined by the `word` function. E.g.

  word(0) = "Hello".
This is different from typical logic programming languages like Prolog in that if you write

  foo(X, bar(Y))
then you are "calling" the term `foo`, but then `bar` ends up being a structured-term that gets unified with the second argument of `foo`. Prolog provides this shortcut as "calling" `bar` doesn't make sense in this case, as `bar` only would return the value `true`, which isn't particularly useful.

In Dyna, we provide square brackets to create structured-terms as both calling the term "bar" and creating the structured-term bar can be useful. E.g. the Prolog expression `foo(X, bar(Y))` would be equivalent to the dyna `foo(X, bar[Y])`.

For the aggregator `max=`, this is looping over the different possible values on the right-hand-side and selecting the value that is the max. Hence in

  phrase(X,I,K) max= phrase(Y,I,K) \* rule(X,Y).
this is looping over the variable `Y` and selecting the one that is maximal. Using `max=` on

  phrase(X,I,I+1) max= rule(X, word(I)).
is done because we want all of the right-hand-sides to use the same aggregator so that we can aggregate between different rules that contribute to `phrase/3`.


Thanks! Honesty: I don't know if I have the time to read a dissertation (or two, or three, judging from the references on the article above). I will try to make some time because Dyna looks interesting.

Regarding 'max=' I guess then phrase/3 is calculating... the string of words I with maximum probability? Which IIUC is bound to Y? If so, that's cool. I've done that with DCGs in the past, but the functional syntax makes it ... look more like a function :)

>> E.g. the Prolog expression `foo(X, bar(Y))` would be equivalent to the dyna `foo(X, bar[Y])`.

I'm guessing that's for convenience? I think it's not rare for functional languages to have a "quoting" (?) mechanism like that?

Edit: Might be a good idea to add an example that also shows a program's output, alongside its source code.




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