[Haskell-cafe] category design approach for inconvenient concepts

Recently I read this article I happened across, about the categorical design pattern: http://www.haskellforall.com/2012/08/the-category-design-pattern.html Barely understood it, of course, but it was a rather intriguing concept. So now I'm looking at all my programming problems trying to make typ

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 18/12/2012, at 3:45 PM, Christopher Howard wrote: > Recently I read this article I happened across, about the categorical > design pattern: > > http://www.haskellforall.com/2012/08/the-category-design-pattern.html It's basically the very old idea that an Abstract Data Type should be a nice al

Re: [Haskell-cafe] category design approach for inconvenient concepts

Christopher Howard wrote: > Say you created a type called "Component" (C for short), the idea > being to compose Components out of other Components. Every C has zero > or more connectors on it. Two Cs can be connected to form a new C > using some kind of composition operator (say, <.>), provided

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/17/2012 06:30 PM, Richard O'Keefe wrote: > > On 18/12/2012, at 3:45 PM, Christopher Howard wrote: > > It's basically the very old idea that an Abstract Data Type > should be a nice algebra: things that look as though they > ought to fit together should just work, and rearrangements > of thi

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Tue, Dec 18, 2012 at 11:03 PM, Christopher Howard > > The original link I gave > purposely skipped > over any discussion of objects, morphisms, domains, and codomains. The > author stated, in his first example, that "Haskell functions" are a

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Tue, 18 Dec 2012, Christopher Howard wrote: On 12/17/2012 06:30 PM, Richard O'Keefe wrote: On 18/12/2012, at 3:45 PM, Christopher Howard wrote: It's basically the very old idea that an Abstract Data Type should be a nice algebra: things that look as though they ought to fit together shou

Re: [Haskell-cafe] category design approach for inconvenient concepts

Christopher Howard wrote: > Since I received the two responses to my question, I've been trying to > think deeply about this subject, and go back and understand the core > ideas. I think the problem is that I really don't have a clear > understanding of the basics of category theory, and even les

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 19/12/2012, at 11:03 AM, Christopher Howard wrote: > Since I received the two responses to my question, I've been trying to > think deeply about this subject, and go back and understand the core > ideas. I think the problem is that I really don't have a clear > understanding of the basics of ca

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Tue, Dec 18, 2012 at 4:49 PM, Ertugrul Söylemez wrote: > These laws make morphisms isolated and composition lightweight as well > as undisturbing. Now try to transfer these notions to a concrete > category, for example the category of web servers: The objects are sets > and a morphism f : A

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/17/12 9:45 PM, Christopher Howard wrote: However, what I'm wondering about is ideas that can be "composed" but that don't seem to fit the idea of "category", because they don't obey the associativity law. To give a specific example (pseudo code like, without any idea here of implementation

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/18/2012 08:02 PM, Gershom Bazerman wrote: > On 12/17/12 9:45 PM, Christopher Howard wrote: > > I don't think you're describing a "Category" in the sense of the Haskell > Category typeclass. But that's ok! Just because some things are > categories and are nice doesn't mean that we can't have

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Tue, Dec 18, 2012 at 11:53 PM, Christopher Howard < christopher.how...@frigidcode.com> wrote: > I really like the idea that all > parts of my program could be cleanly and systematically composed from > smaller pieces, in some beautiful design patter. Many of the problems in > my practical progr

Re: [Haskell-cafe] category design approach for inconvenient concepts

I have also become intrigued and confused by this "category theory" and how it relates to Haskell. It has been stated many times that you don't need to understand category theory to utilize the Haskell language but all the concepts, patterns and every paper describing them seems to be written by so

Re: [Haskell-cafe] category design approach for inconvenient concepts

Mark Flamer wrote: > I have also become intrigued and confused by this "category theory" > and how it relates to Haskell. It has been stated many times that you > don't need to understand category theory to utilize the Haskell > language but all the concepts, patterns and every paper describing >

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/17/12 9:45 PM, Christopher Howard wrote: So you could have... (coupler <.> thing) <.> gadget Because the coupler and the thing would combine to create a component with one spare connector. This would then combine with the gadget to make the final component. However, if you did... coupler

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/18/12 5:03 PM, Christopher Howard wrote: Since I received the two responses to my question, I've been trying to think deeply about this subject, and go back and understand the core ideas. I think the problem is that I really don't have a clear understanding of the basics of category theory,

Re: [Haskell-cafe] category design approach for inconvenient concepts

> the category of Haskell types and Haskell functions[1] > > [1] Note that this may not actually work out to be a category, but the basic > idea is sound. I would be curious to see this example carefully worked out. I often hear that Haskell types and Haskell functions constitute a category, but

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Thu, 20 Dec 2012, Oleksandr Manzyuk wrote: the category of Haskell types and Haskell functions[1] [1] Note that this may not actually work out to be a category, but the basic idea is sound. I would be curious to see this example carefully worked out. I often hear that Haskell types and

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Thu, Dec 20, 2012 at 12:53 PM, Oleksandr Manzyuk wrote: > I have no problems with the statement "Objects of the category Hask > are Haskell types." Types are well-defined syntactic entities. But > what is a morphism in the category Hask from a to b? Commonly, people > say "functions from a t

Re: [Haskell-cafe] category design approach for inconvenient concepts

On Fri, Dec 21, 2012 at 4:40 AM, Alexander Solla wrote: > > > On Thu, Dec 20, 2012 at 12:53 PM, Oleksandr Manzyuk > wrote: >> >> I have no problems with the statement "Objects of the category Hask >> are Haskell types." Types are well-defined syntactic entities. But >> what is a morphism in the

Re: [Haskell-cafe] category design approach for inconvenient concepts

On 12/21/12 3:27 AM, Oleksandr Manzyuk wrote: On Fri, Dec 21, 2012 at 4:40 AM, Alexander Solla wrote: I don't see how associativity fails, if we mod out alpha-equivalence. Can you give an example? (If it involves the value "undefined", I'll have something concrete to add vis a vis "moral" equ