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The thing in this paper that I see missing from most discussions of Functional Programming is the use of an algebra to derive programs. I've worked a bit with

The thing in this paper that I see missing from most discussions of Functional Programming is the use of an algebra to derive programs. I've worked a bit with an FP concatenative language Joy and this sort of algebraic manipulation is easy and fun, and seems to permit (nearly) bug-free development. Here's a very simple example of deriving a function for the quadratic formula: https://joypy.osdn.io/notebooks/Quadratic.html https://joypy.osdn.io/notebooks/Quadratic.html A more complex example deriving a combinator "treestep" to process tree datastructures: https://joypy.osdn.io/notebooks/Treestep.html https://joypy.osdn.io/notebooks/Treestep.html

JoshuaAshton 5y ago
b sqr 4 a c * * - sqrt Yeah no. This being "bug free" seems like a joke.
- js8 5y ago
  This is just a "minor usability issue". Seriously. In Factor, you can solve this with references to local variables, which under the covers manipulate the stack as needed. It can also typecheck, so you wouldn't be able to write the expression in a way which unbalances the stack.
- morelisp 5y ago
  I don't see an objective reason this is more or less clear than sqrt(sqr(b) - 4 * a * c) or (sqrt (- (sqr b) (* 4 a c)) Honestly, by objective measures the traditional style is probably the worst. The Forth style makes it easy to see large stacks because you'll see long sequences of literals. The sexp style makes it easier to work with subexpressions. Both the Forth and sexp style don't require remembering PEMDAS. The sexp style is easier to parse, and the Forth style doesn't even need a parser. The only thing going for the traditional style is that it is an ugly approximation of mathematical notation - but that notation itself loses most of its value in the uglifying.
js8 5y ago
I came across this paper recently while looking at Kitten (it was actually mentioned in HN before): http://evincarofautumn.blogspot.com/2012/02/why-concatenative-programming-matters.html http://evincarofautumn.blogspot.com/2012/02/why-concatenativ... I think really explains the idea. I always liked combinatory logic more than lambda calculus, although it didn't click to me that the concatenative languages are essentially the formalism for it (as opposed to ML-style syntax). Although I would say functional programming is somewhat orthogonal concept, the concatenative languages can have functions with side effects, like Forth does.
deleted 5y ago
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ardit33 5y ago
Perhaps the universe is state based, and not function based... Programing language are away to represent reality, and manipulate it to your desire. Object Oriented, and Procedural programing both use functions to manipulate state, while in pure functional languages you use functions and unnamed variables to present state. The problem is when you communicate, you always do it with state and not functions. From API to storing data as it allows to very different systems to understand each other without to have the same internals. A java web based api/program and a swift/objective-c program running in a phone can easily communicate with each other via state (aka, rest of soap apis), and they don't have to know the internal state of each other. You can save functions, and pass them along, but the other part has to know how to run it, and have the same type of hardware in order to run it. I really think pure functional programming is a mathematicians pipe-dream, and theoretical CS nerds trying to shoehorn Math/Algebra equations into being the default type of programing paradigm, but for practical Computer Science problems the von Neumann style (statements and expressions) has won as it is the most practical The only true successful alternative to von neuman state type of languages, is really SQL and its derivatives, which is a declarative style of programing language. You can pass SQL queries around, and they will be understood by all kinds of systems. But, ultimately they all act on some kind of state/data in a table.
- deleted 5y ago
  [deleted]
- gmfawcett 5y ago
  > The problem is when you communicate, you always do it with state and not functions. I'm not sure that's true. A "callback" is way of communicating with a function as the message. Callbacks are a way for systems to communicate while hiding their implementation details. (One could argue that the callback itself is a first-order object -- a piece of state -- but nonetheless we are communicating with state and functions then.)
  - ardit33 5y ago
    Callbacks are a signal that your operation is done, and the data is ready... usually they have some kind of state (i.e. success, error, the data read from disk/api, etc). They are usually used within one program itself, and not across systems. Something like the Firebase real time database, or webhooks, are for callback achross systems, but they always are used to pass data/state, and not functions itself. Again, SQL and maybe Regex (which is not a full programming language anyway), as the most successful alternatives to normal Object Oriented/procedural programing. Most functional languages have not become successful. I learned Prolog in the 90s, and I could see how it might be useful in some situations, but it is hard to do anything practical with it. Some functional concepts, like map/reduce, have become popular in mainstream languages, as they are useful in certain scenarios, but pure functional languages have not.
vajrabum 5y ago
Richard Bird has pursued the algebraic approach in a lazy functional language context. He and Ooge de Moor presented their work on the algebraic approach to lazy functional languages in a textbook form in the book Algebra of Programming in late 90s. Not terribly update to date but still really great stuff and a place to start if you're wanting to understand the more up to date stuff. That book can be found on the web. Don't try to buy it on Amazon. They have a highway robbery price. If you need to buy it you might try Google Shopping. I saw several copies for under $10.
- carapace 5y ago
  Ah, that's a great book, thanks!

JoshuaAshton 5y ago

b sqr 4 a c * * - sqrt Yeah no. This being "bug free" seems like a joke.

js8 5y ago
This is just a "minor usability issue". Seriously. In Factor, you can solve this with references to local variables, which under the covers manipulate the stack as needed. It can also typecheck, so you wouldn't be able to write the expression in a way which unbalances the stack.
morelisp 5y ago
I don't see an objective reason this is more or less clear than sqrt(sqr(b) - 4 * a * c) or (sqrt (- (sqr b) (* 4 a c)) Honestly, by objective measures the traditional style is probably the worst. The Forth style makes it easy to see large stacks because you'll see long sequences of literals. The sexp style makes it easier to work with subexpressions. Both the Forth and sexp style don't require remembering PEMDAS. The sexp style is easier to parse, and the Forth style doesn't even need a parser. The only thing going for the traditional style is that it is an ugly approximation of mathematical notation - but that notation itself loses most of its value in the uglifying.

js8 5y ago

I came across this paper recently while looking at Kitten (it was actually mentioned in HN before): http://evincarofautumn.blogspot.com/2012/02/why-concatenative-programming-matters.html http://evincarofautumn.blogspot.com/2012/02/why-concatenativ... I think really explains the idea. I always liked combinatory logic more than lambda calculus, although it didn't click to me that the concatenative languages are essentially the formalism for it (as opposed to ML-style syntax). Although I would say functional programming is somewhat orthogonal concept, the concatenative languages can have functions with side effects, like Forth does.

deleted 5y ago

[deleted]

ardit33 5y ago

Perhaps the universe is state based, and not function based... Programing language are away to represent reality, and manipulate it to your desire. Object Oriented, and Procedural programing both use functions to manipulate state, while in pure functional languages you use functions and unnamed variables to present state. The problem is when you communicate, you always do it with state and not functions. From API to storing data as it allows to very different systems to understand each other without to have the same internals. A java web based api/program and a swift/objective-c program running in a phone can easily communicate with each other via state (aka, rest of soap apis), and they don't have to know the internal state of each other. You can save functions, and pass them along, but the other part has to know how to run it, and have the same type of hardware in order to run it. I really think pure functional programming is a mathematicians pipe-dream, and theoretical CS nerds trying to shoehorn Math/Algebra equations into being the default type of programing paradigm, but for practical Computer Science problems the von Neumann style (statements and expressions) has won as it is the most practical The only true successful alternative to von neuman state type of languages, is really SQL and its derivatives, which is a declarative style of programing language. You can pass SQL queries around, and they will be understood by all kinds of systems. But, ultimately they all act on some kind of state/data in a table.

deleted 5y ago
[deleted]
gmfawcett 5y ago
> The problem is when you communicate, you always do it with state and not functions. I'm not sure that's true. A "callback" is way of communicating with a function as the message. Callbacks are a way for systems to communicate while hiding their implementation details. (One could argue that the callback itself is a first-order object -- a piece of state -- but nonetheless we are communicating with state and functions then.)
- ardit33 5y ago
  Callbacks are a signal that your operation is done, and the data is ready... usually they have some kind of state (i.e. success, error, the data read from disk/api, etc). They are usually used within one program itself, and not across systems. Something like the Firebase real time database, or webhooks, are for callback achross systems, but they always are used to pass data/state, and not functions itself. Again, SQL and maybe Regex (which is not a full programming language anyway), as the most successful alternatives to normal Object Oriented/procedural programing. Most functional languages have not become successful. I learned Prolog in the 90s, and I could see how it might be useful in some situations, but it is hard to do anything practical with it. Some functional concepts, like map/reduce, have become popular in mainstream languages, as they are useful in certain scenarios, but pure functional languages have not.

vajrabum 5y ago

Richard Bird has pursued the algebraic approach in a lazy functional language context. He and Ooge de Moor presented their work on the algebraic approach to lazy functional languages in a textbook form in the book Algebra of Programming in late 90s. Not terribly update to date but still really great stuff and a place to start if you're wanting to understand the more up to date stuff. That book can be found on the web. Don't try to buy it on Amazon. They have a highway robbery price. If you need to buy it you might try Google Shopping. I saw several copies for under $10.

carapace 5y ago
Ah, that's a great book, thanks!