What is orthogonality?

[Bruno Medeiros]

Bill Baxter wrote:
> The world orthogonality has been thrown around a bit here, me included.
> I just read this interesting interview with Matz, Ruby's creator where 
> he says he doesn't like orthogonality and gives an example of why it's bad:
> 
>  "An example of orthogonality is allowing any combination of small
>  features or syntax. For example, C++ supports both default parameter
>  values for functions and overloading of function names based on
>  parameters. Both are good features to have in a language, but because
>  they are orthogonal, you can apply both at the same time. The compiler
>  knows how to apply both at the same time. If it's ambiguous, the
>  compiler will flag an error. But if I look at the code, I need to apply
>  the rule with my brain too. I need to guess how the compiler works. If
>  I'm right, and I'm smart enough, it's no problem. But if I'm not smart
>  enough, and I'm really not, it causes confusion. The result will be
>  unexpected for an ordinary person. This is an example of how
>  orthogonality is bad."  -- Matz
> 
> First a definition. My concept of orthogonal comes mostly from linear 
> algebra.  If you have two vectors that are orthogonal there is no 
> component of one that can be represented using the other.  I.e. the 
> projection of one onto the other is zero.  They have zero overlap.
> 
> What Matz is talking about is more like "syntactic orthogonality".  The 
> syntax of those two features is orthogonal so they can coexist without 
> issues.  The syntax subspaces they cover have zero overlap.
> 
> That's important, but I think a low-level kind of orthogonality.  What 
> I'm talking about is more of a "semantic orthogonality".  What does the 
> feature let you express?  In the semantic sense his example of 
> overloading functions by number of paramters versus using default 
> parameters is exactly 100% UN-orthogonal.  They both achieve exactly the 
> same behavior.  They overlap 100% in terms of what you can express.
> 
> In the end he says he wants things to be "harmonious", which I think is 
> more or less equivalent to "semantically orthogonal".  Harmonious in the 
> sense that I do my job and you do yours, and we don't step on each 
> other's toes.  But that's precisely what orthogonality is -- not 
> overlapping.
> 
> The full interview is here:
> http://www.artima.com/intv/ruby.html
> 
> --bb

Hey, that's a pretty good comment. I subscribe exactly! When I think or 
speak of orthogonality it's usually not in the sense of merely allowing 
combinations of features(syntactic orthogonality, like you said), but 
instead, such additions and/or combination of features much result in a 
system/behavior which is as simple, or simpler, than the alternative. If 
  instead such modifications result in a system which is more 
complicated, harder to explain, has more special cases, etc., then it is 
not good "orthogonality" (i.e., it does not have semantic orthogonality).

Whenever power, expressiveness or elegance is not harmed, a language (or 
any system for that matter) should strive for more orthogonality. One 
reason is because it becomes simpler to explain and understand, but also 
because sometimes more orthogonality results in more of those 3 
aforementioned qualities.

On example of what I(and others) think is a severe breach of 
orthogonality in D are static arrays. Static arrays are a legacy C 
construct/design which should have no place in modern languages(in 
particular D) with their current behavior (broken value types).

-- 
Bruno Medeiros - MSc in CS/E student
http://www.prowiki.org/wiki4d/wiki.cgi?BrunoMedeiros#D