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> I’ll note that this says far more about category theory than it does about FP. In fact, I’d argue that it’s not particularly closely related to FP at all I'd

> I’ll note that this says far more about category theory than it does about FP. In fact, I’d argue that it’s not particularly closely related to FP at all I'd say CT is FP. FP is about doing algebra to derive programs and CT is the math that describes that. In Manfred von Thun’s article "Joy compared with other functional languages" ( https://www.kevinalbrecht.com/code/joy-mirror/j08cnt.html https://www.kevinalbrecht.com/code/joy-mirror/j08cnt.html ) he asks, > Could the language of categories be used for writing programs? Any lambda expression can be translated into a categorical expression, so the language of categories is expressively complete. But this does not make it a suitable language for writing programs. As it stands it is a very low-level language. I think this book could be seen as the (affirmative) answer to that question.

nlitened 4y ago
> FP is about doing algebra to derive programs I don’t think I can agree. Clojure is a functional programming language, but is far from doing any algebra.
- edgyquant 4y ago
  I don’t know about clojure but lisp definitely counts as an abstract algebra (and not in the same way most other languages are.) It’s also a weird derivation of set theory allowing it to be derived from first order logic.
  - throwawaymaths 4y ago
    Having studied abstract algebra, I disagree that the soul of lisp is abstract algebra. You're not really actively thinking algebraically when you're writing lisp, not in the same way that other languages have you "actively thinking about category theory". There are also other modern FP languages that are "basically lisps", like Julia or Elixir, that would be hard to call "algebraic".
- carapace 4y ago
  My opinion (and I don't insist that I'm right) is that you've got to go back to Backus' Turing award paper[1] to ground a definition of FP, and he was specifically talking about an algebraic approach. This is something that seems to get overlooked when people talk about FP, but I believe it's even more important than, say, referential transparency. [1] https://amturing.acm.org/award_winners/backus_0703524.cfm https://amturing.acm.org/award_winners/backus_0703524.cfm then click on "ACM Turing Award Lecture" or just -> https://dl.acm.org/ft_gateway.cfm?id=1283933&type=pdf https://dl.acm.org/ft_gateway.cfm?id=1283933&type=pdf
  - asdadssad 4y ago
    Functional programming is what people talk about when they "talk about FP". The historical story is that "functional programming" just meant purity, originally. Now it seems to mean purity + higher order functions + other strong, fancy types (which I'd claim include algebraic structures such as monads). This current meaning, exemplified by the ML/Haskell tradition, spiritually comes from Peter Landin's ideas in his paper "The mechanical evaluation of expressions" and its supporters don't revere Backus. Sure, algebraic laws characterise monads etc., and his work was foundational—but the Turing Award paper is not a script that everyone is following. On the specific topic of deriving programs with algebra, there is the book "Algebra of Programming" by Bird and de Moor from the 90s, (https://themattchan.com/docs/algprog.pdf https://themattchan.com/docs/algprog.pdf) but it is difficult to look at the functional programming scene now and conclude that deriving your program algebraically is a more essential aspect of the activity than using referentially transparent expressions. It may well be or become an important idea, but it's hardly the bread and butter of functional programming in practice (while maybe in your headcanon it is functional programming). I think part of the problem here is complexity/irregularity: it's simply not practical or helpful to describe typical desired systems algebraically and then derive code from that description.
    - carapace 4y ago
      > the Turing Award paper is not a script that everyone is following. Yah, that's my point. > it is difficult to look at the functional programming scene now and conclude that deriving your program algebraically is a more essential aspect of the activity than using referentially transparent expressions. Again, that's my point. It's not now but it should be. We are missing out. It's like we are still using Roman numerals even though the Indo-Arabic numeral system has been invented and is ever-so-slowly diffusing into common knowledge.
mbrodersen 4y ago
Not at all. Lambda Calculus is a much better mathematical foundational for functional programming that Category Theory is. I can teach a programmer Lambda Calculus in a few minutes and they will be able to use it for programming. Not so with CT. You need to add a lot of structure to get anything close to Lambda Calculus. Basically about 50% of a Typical CT book to get there.
- carapace 4y ago
  > I can teach a programmer Lambda Calculus in a few minutes and they will be able to use it for programming. Which programmer? Bare Lambda Calculus? Wouldn't that be pretty useless? > Not so with CT. You need to add a lot of structure to get anything close to Lambda Calculus. I'm not sure I follow, I've heard that "the simply typed lambda-calculus is modeled by any cartesian closed category (CCC)." http://conal.net/papers/compiling-to-categories/ http://conal.net/papers/compiling-to-categories/
  - mbrodersen 4y ago
    > Wouldn't that be pretty useless? Not at all. It is way more useful than learning CT. LC is the foundation used in almost all of computer science. You need to understand it to read any advanced Type Theory papers for example and you can directly use it as a starting point when designing a functional programming language. > “the simply typed lambda-calculus is modeled by any cartesian closed category (CCC) That is correct. You can model pretty much anything in Category Theory. The same way you can model pretty much anything in Type Theory or Set Theory. However IMHO it takes a lot more structure to build up to CCC than it does to simply use LC. The paper you are referencing is great. However the author might as well have used LC to achieve the same goal.
    - carapace 4y ago
      I dunno, I've been messing around with Joy recently and it's put me off LC. https://en.wikipedia.org/wiki/Joy_(programming_language) https://en.wikipedia.org/wiki/Joy_(programming_language)

nlitened 4y ago

> FP is about doing algebra to derive programs I don’t think I can agree. Clojure is a functional programming language, but is far from doing any algebra.

edgyquant 4y ago
I don’t know about clojure but lisp definitely counts as an abstract algebra (and not in the same way most other languages are.) It’s also a weird derivation of set theory allowing it to be derived from first order logic.
- throwawaymaths 4y ago
  Having studied abstract algebra, I disagree that the soul of lisp is abstract algebra. You're not really actively thinking algebraically when you're writing lisp, not in the same way that other languages have you "actively thinking about category theory". There are also other modern FP languages that are "basically lisps", like Julia or Elixir, that would be hard to call "algebraic".
carapace 4y ago
My opinion (and I don't insist that I'm right) is that you've got to go back to Backus' Turing award paper[1] to ground a definition of FP, and he was specifically talking about an algebraic approach. This is something that seems to get overlooked when people talk about FP, but I believe it's even more important than, say, referential transparency. [1] https://amturing.acm.org/award_winners/backus_0703524.cfm https://amturing.acm.org/award_winners/backus_0703524.cfm then click on "ACM Turing Award Lecture" or just -> https://dl.acm.org/ft_gateway.cfm?id=1283933&type=pdf https://dl.acm.org/ft_gateway.cfm?id=1283933&type=pdf
- asdadssad 4y ago
  Functional programming is what people talk about when they "talk about FP". The historical story is that "functional programming" just meant purity, originally. Now it seems to mean purity + higher order functions + other strong, fancy types (which I'd claim include algebraic structures such as monads). This current meaning, exemplified by the ML/Haskell tradition, spiritually comes from Peter Landin's ideas in his paper "The mechanical evaluation of expressions" and its supporters don't revere Backus. Sure, algebraic laws characterise monads etc., and his work was foundational—but the Turing Award paper is not a script that everyone is following. On the specific topic of deriving programs with algebra, there is the book "Algebra of Programming" by Bird and de Moor from the 90s, (https://themattchan.com/docs/algprog.pdf https://themattchan.com/docs/algprog.pdf) but it is difficult to look at the functional programming scene now and conclude that deriving your program algebraically is a more essential aspect of the activity than using referentially transparent expressions. It may well be or become an important idea, but it's hardly the bread and butter of functional programming in practice (while maybe in your headcanon it is functional programming). I think part of the problem here is complexity/irregularity: it's simply not practical or helpful to describe typical desired systems algebraically and then derive code from that description.
  - carapace 4y ago
    > the Turing Award paper is not a script that everyone is following. Yah, that's my point. > it is difficult to look at the functional programming scene now and conclude that deriving your program algebraically is a more essential aspect of the activity than using referentially transparent expressions. Again, that's my point. It's not now but it should be. We are missing out. It's like we are still using Roman numerals even though the Indo-Arabic numeral system has been invented and is ever-so-slowly diffusing into common knowledge.

mbrodersen 4y ago

Not at all. Lambda Calculus is a much better mathematical foundational for functional programming that Category Theory is. I can teach a programmer Lambda Calculus in a few minutes and they will be able to use it for programming. Not so with CT. You need to add a lot of structure to get anything close to Lambda Calculus. Basically about 50% of a Typical CT book to get there.

carapace 4y ago
> I can teach a programmer Lambda Calculus in a few minutes and they will be able to use it for programming. Which programmer? Bare Lambda Calculus? Wouldn't that be pretty useless? > Not so with CT. You need to add a lot of structure to get anything close to Lambda Calculus. I'm not sure I follow, I've heard that "the simply typed lambda-calculus is modeled by any cartesian closed category (CCC)." http://conal.net/papers/compiling-to-categories/ http://conal.net/papers/compiling-to-categories/
- mbrodersen 4y ago
  > Wouldn't that be pretty useless? Not at all. It is way more useful than learning CT. LC is the foundation used in almost all of computer science. You need to understand it to read any advanced Type Theory papers for example and you can directly use it as a starting point when designing a functional programming language. > “the simply typed lambda-calculus is modeled by any cartesian closed category (CCC) That is correct. You can model pretty much anything in Category Theory. The same way you can model pretty much anything in Type Theory or Set Theory. However IMHO it takes a lot more structure to build up to CCC than it does to simply use LC. The paper you are referencing is great. However the author might as well have used LC to achieve the same goal.
  - carapace 4y ago
    I dunno, I've been messing around with Joy recently and it's put me off LC. https://en.wikipedia.org/wiki/Joy_(programming_language) https://en.wikipedia.org/wiki/Joy_(programming_language)