4 ms·

Really? Category theory (when applied to FP) is basically the theory of function composition. I would think this point of view is huge in academia due to the pr

Really? Category theory (when applied to FP) is basically the theory of function composition. I would think this point of view is huge in academia due to the prevalence of CT among academia and FP. >with the divergence between compositional and applicative languages being almost completely absent. Most FP languages have facilities to do both anyway. And the isomorphisms between the two concepts are small in distance so it doesn't matter too much if you use applicative over compositional. So really when I say you should do "point-free" to see the big picture I'm advocating that more for educational purposes rather than practical (though I'm not opposed to practical). That being said you and I are pretty much in agreement, I was just unaware of the whole academic thing.

throwaway17_17 7y ago
With regard to the prevalent academic opinions, I was really referring to the nature of programming language syntax and semantics. I would say that Category Theory is essentially about function composition, but that then gets filtered down into so-called applicative languages. This designation is based heavily on the lambda calculus, in which application of terms to other terms is the prime mover for computation. Backus certainly wasn't talking about lambda calculus based semantics for FP, he was focused on strict compositional semantics with only non-named pipelined data being fed to compositional units. Most language researchers and writers just assume that any programming language uses function application as the basic unit of computation and so the language is naturally built in layers on this basic unit. So, 'point-free' programming in a language like Haskell is typically just considered good programming style, it is still used in a primarily applicative way. I'm not quite a no-application purist, but I really do see the algebraic beauty in avoiding named variables and skipping application as anything other than a definable operator to work on other higher-order functions. Just for reference, if you want to see the divergence between applicative (which is basically every modern language in production or in research) and compositional look at some of Manfred von Thun's papers he wrote about the Joy Programming Language. Some people strongly disagree with his stance, but I find him easy to read in any event, see the link below. Also, in several places linked from [0], Thun discusses the Categorical Abstract Machine and has a few references which served as a nice jumping off point for more reading. [1] http://joy-lang.org/papers-on-joy/joy-compared-with-other-functional-languages http://joy-lang.org/papers-on-joy/joy-compared-with-other-fu...
- crimsonalucard 7y ago
  Thanks. Very informative. I actually didn't know about Backus. I just assumed because of CT all academics who study FP view FP this way. Do you have the source where Backus actually talks about the stuff you mentioned?
  - throwaway17_17 7y ago
    The canonical source for Backus is his Turing Award Lecture, which was turned into a paper, by which time he had renamed his system FFP (Formal Functional Programming). [0]. There was some longer term research into his FFP system, done by Williams and Wimmers (who gave a much loved talk titled ‘Sacrificing simplicity for convenience: Where do you draw the line?’ that I can not find a copy or transcript of to save my life in 1988) which evolved into The FL language also by Backus, with Williams and Wimmers[2]. There is a great succinct rundown of Backus’ work in this area and those who continued it in [3], it is a little lengthy so I didn’t want to just big block quote it. Also, with regard to the CT thing, I totally get that. The predominance of CT-based concepts (no matter how far they are actually removed from the mathematical background of actual CT) are one of the defining features of modern functional programming, to the point people make jokes about needing to know CT to write ‘Hello World’ in Haskell. However, and I admit to having an unhealthy obsession with following PLT academia, it really is a little bit of a smoke screen. Nearly all ‘functional’ languages are based on the lambda calculus and various augmentations thereto, and so most of the CT applied in the area tends to be refinements and imports of various constructs into some potentially BiCartesian Closed Category (which is what the lambda calculus with the common functional programming additions of product and sum types and 1st class functions is as a category). But as I said before, the fundamental construct in the computational model is application via substitution. All of the advanced categorical constructs and tools still hold for compositional languages, but, as the theory goes, you gain an algebraic theory of manipulation of the actual programming language by virtue of the categorical properties of composition (and the inferred lack of hand-wringing over the semantics of substitution. Sorry for the wall of text, this particular corner of CS and PLT is my favorite place, so any chance to talk about it I jump on. —————————————————————- 0 - https://www.thocp.net/biographies/papers/backus_turingaward_lecture.pdf https://www.thocp.net/biographies/papers/backus_turingaward_... 2 - http://citeseerx.ist.psu.edu/viewdoc/citations;jsessionid=B954240F0724D34E06A7F8334B11867E?doi=10.1.1.142.362 http://citeseerx.ist.psu.edu/viewdoc/citations;jsessionid=B9... 3 - http://joy-lang.org/papers-on-joy/joy-compared-with-other-functional-languages http://joy-lang.org/papers-on-joy/joy-compared-with-other-fu...

throwaway17_17 7y ago

With regard to the prevalent academic opinions, I was really referring to the nature of programming language syntax and semantics. I would say that Category Theory is essentially about function composition, but that then gets filtered down into so-called applicative languages. This designation is based heavily on the lambda calculus, in which application of terms to other terms is the prime mover for computation. Backus certainly wasn't talking about lambda calculus based semantics for FP, he was focused on strict compositional semantics with only non-named pipelined data being fed to compositional units. Most language researchers and writers just assume that any programming language uses function application as the basic unit of computation and so the language is naturally built in layers on this basic unit. So, 'point-free' programming in a language like Haskell is typically just considered good programming style, it is still used in a primarily applicative way. I'm not quite a no-application purist, but I really do see the algebraic beauty in avoiding named variables and skipping application as anything other than a definable operator to work on other higher-order functions. Just for reference, if you want to see the divergence between applicative (which is basically every modern language in production or in research) and compositional look at some of Manfred von Thun's papers he wrote about the Joy Programming Language. Some people strongly disagree with his stance, but I find him easy to read in any event, see the link below. Also, in several places linked from [0], Thun discusses the Categorical Abstract Machine and has a few references which served as a nice jumping off point for more reading. [1] http://joy-lang.org/papers-on-joy/joy-compared-with-other-functional-languages http://joy-lang.org/papers-on-joy/joy-compared-with-other-fu...

crimsonalucard 7y ago
Thanks. Very informative. I actually didn't know about Backus. I just assumed because of CT all academics who study FP view FP this way. Do you have the source where Backus actually talks about the stuff you mentioned?
- throwaway17_17 7y ago
  The canonical source for Backus is his Turing Award Lecture, which was turned into a paper, by which time he had renamed his system FFP (Formal Functional Programming). [0]. There was some longer term research into his FFP system, done by Williams and Wimmers (who gave a much loved talk titled ‘Sacrificing simplicity for convenience: Where do you draw the line?’ that I can not find a copy or transcript of to save my life in 1988) which evolved into The FL language also by Backus, with Williams and Wimmers[2]. There is a great succinct rundown of Backus’ work in this area and those who continued it in [3], it is a little lengthy so I didn’t want to just big block quote it. Also, with regard to the CT thing, I totally get that. The predominance of CT-based concepts (no matter how far they are actually removed from the mathematical background of actual CT) are one of the defining features of modern functional programming, to the point people make jokes about needing to know CT to write ‘Hello World’ in Haskell. However, and I admit to having an unhealthy obsession with following PLT academia, it really is a little bit of a smoke screen. Nearly all ‘functional’ languages are based on the lambda calculus and various augmentations thereto, and so most of the CT applied in the area tends to be refinements and imports of various constructs into some potentially BiCartesian Closed Category (which is what the lambda calculus with the common functional programming additions of product and sum types and 1st class functions is as a category). But as I said before, the fundamental construct in the computational model is application via substitution. All of the advanced categorical constructs and tools still hold for compositional languages, but, as the theory goes, you gain an algebraic theory of manipulation of the actual programming language by virtue of the categorical properties of composition (and the inferred lack of hand-wringing over the semantics of substitution. Sorry for the wall of text, this particular corner of CS and PLT is my favorite place, so any chance to talk about it I jump on. —————————————————————- 0 - https://www.thocp.net/biographies/papers/backus_turingaward_lecture.pdf https://www.thocp.net/biographies/papers/backus_turingaward_... 2 - http://citeseerx.ist.psu.edu/viewdoc/citations;jsessionid=B954240F0724D34E06A7F8334B11867E?doi=10.1.1.142.362 http://citeseerx.ist.psu.edu/viewdoc/citations;jsessionid=B9... 3 - http://joy-lang.org/papers-on-joy/joy-compared-with-other-functional-languages http://joy-lang.org/papers-on-joy/joy-compared-with-other-fu...