They didn't coin the term paramorphism. Lambert Marteens did in 1992 [0]. It's an extension of the concept of catamorphisms. These terms were invented by people knowledgeable about category theory [1].
I also disagree with the notion that they aren't really doing math. It's very straightforward to derive programs by proving other properties of these recursive combinators. I would recommend reading A tutorial on the universality and expressiveness of fold [1] as an example of this; folds are catamorphisms, which is why I bring it up.
> They didn't coin the term paramorphism. Lambert Marteens did in 1992
I literally linked that paper.
> It's very straightforward to derive programs by proving other properties of these recursive combinators.
Cool they don't do that. There's a word for being obliquely related: allusion.
It's amazing how much benefit of the doubt CS people get. In math you either prove a theorem/lemma by writing it out in full or you... have nothing. In CS people tell nice stories, draw cool diagrams, write down random formulae and everyone is just hmm yes brilliant.
> they're alluding to math[1] but they're not doing math.
So they're applying the math somebody else already put together? It isn't clear what your opinion is. Are you saying it's not valid if it's not math?
Let's judge the paper by what they say they did in the abstract.
> We show that synthesizing recursive functional programs using a class of primitive recursive combinators is both simpler and solves more benchmarks from the literature than previously proposed approaches.
It sounds like their proposed metrics are subjective ("simpler") or data-oriented ("solves more ... than previously").
> Our method synthesizes paramorphisms, a class of programs that includes the most common recursive programming patterns on algebraic data types.
They're applying a pre-existing concept ("paramorphisms") to a problem domain where (it is implied) it either has not been applied before, or with a new spin.
> The crux of our approach is to split the synthesis problem into two parts: a multi-hole template that fixes the recursive structure, and a search for non-recursive program fragments to fill the template holes.
They give a novel (,it is implied) structural model for solving their problem using their chosen concept as their key contribution to the study of this problem. It is indirectly suggested that factoring the recursive and non-recursive parts apart allows them to be handled more effectively individually.
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Regarding your specific complaints: I do not see any immediate need for new math. Nor are they inventing new words, at least in the title or abstract. You may have legitimate concerns about general academic practice, but if you're going to levy those criticisms at this paper, you could do your arguments better justice than with a drive-by.
You did; I overlooked that. I don't know why you're implying the authors invented the term and made up the combinator just now, then.
> Cool they don't do that.
Their program is basically doing an automated version of what Graham Hutton did in that paper, except they rewrite functions using para instead of fold.
Edit:
> It's amazing how much benefit of the doubt CS people get. In math you either prove a theorem/lemma by writing it out in full or you... have nothing. In CS people tell nice stories, draw cool diagrams, write down random formulae and everyone is just hmm yes brilliant.
You seem to have a chip on your shoulder. I don't know why you're telling me this.
I also disagree with the notion that they aren't really doing math. It's very straightforward to derive programs by proving other properties of these recursive combinators. I would recommend reading A tutorial on the universality and expressiveness of fold [1] as an example of this; folds are catamorphisms, which is why I bring it up.
[0]: https://www.researchgate.net/publication/256269748_Paramorph...
[1]: https://www.cambridge.org/core/journals/journal-of-functiona...