4 ms·

> 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.

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.