What do you mean by the expressiveness of a programming language?

I like Matthias Felleisen's notion of expressive power, which is comparative:

• Language A is strictly more expressive than language B if both of the following are true:

  • Any program written in language B can be rewritten in language A while keeping the essential structure of the program intact.
  • Some programs written in language A have to be violently restructured in order to be written in language B.

Usually we want to make these comparisons by looking at some kind of "essential core" of a language—for example, maybe we want to consider a dialect of C with only while and not also for and do...while. Or maybe we want to consider a dialect of Perl with only a prefix if form and no unless form. But sometimes these superficial syntactic distinctions are exactly what we mean by "expressive power"; to some programmers it's important to say

die ("found no solutions") unless length(solutions) > 0;

instead of

if (length(solutions) == 0) { die("found no solutions"); }

So you have to establish whether you're asking about expressive power of surface syntax or deeper structure.

The other thing I like about Felleisen's idea is that it admits of the notion of two languages which are definitely different, but neither is more expressive than the other.

You can read a more detailed exposition in the first two pages of his paper On the Expressive Power of Programming Languages. After that comes a lot of pointy-headed theory :-)

"Expressiveness" means the ability to say only what you want done:

bad_event = events.find(&:bad)

rather than how you want it done:

i = 0
bad_event = nil
while i < events.size && bad_event.nil?
  event = events[i]
  if event.bad?
    bad_event = event
  end
  i += 1
end

Among the things that contribute to expressiveness are:

• A lack of required syntactic sugar
• First-class functions
• Garbage collection
• Either dynamic typing or type inference
• The language core not being slavishly minimalistic
• Good functionality in the standard library

To some degree, the expressiveness of any language can be increased by shoving as much "how to do it" off into subroutines/objects as possible so that most of the remaining code is "what to do." The amount of "how to do it" code needed in the most abstract code is one measure of a language's expressiveness: The more the code looks like pseudocode, the more expressive it is of the programmer's intent.

One can also think about the "meta-expressiveness" of a language: How expressive is the language at constructing Domain Specific Languages?

If you want an answer that's somewhat theoretical but more rigorous than most, you might want to look around for Matthias Felleisen's On the Expressive Power of Programming Languages. I'm pretty sure a bit of looking around the net will turn up at least a few copies.

If you want a more practical answer of what most people actually mean when they say it, that's, frankly, rather different. At least in my experience, an "expressive" language usually means: "I like the language, but can't cite much (if any) objective support for doing so." Conversely, things like "less expressive", or "not expressive" generally mean: "I don't like the language (or like it less), but can't cite much (if any) objective support for doing so."

"Not expressive" is often similar to a politician accusing another of being "fascist" -- clearly pejorative, but without any meaningful definition of what's supposedly wrong.

One of the big problems stems from a fundamental difference of opinion. There are at least two fundamentally different general ideas that people seem to have about expressiveness:

1. the ability to express a wide variety of ideas.
2. the ability to express some specific ideas clearly (and often succinctly).

To consider some extreme examples, assembly language would qualify as highly expressive by the first criteria--you can do essentially anything in assembly language that you can in a higher level language, and you can do some things in assembly language that you can't in essentially any higher level language.

Obviously, assembly language doesn't look nearly so good by the second measure--it typically requires quite a large amount of fairly opaque code to accomplish much. This measure would tend to favor a language like Haskell or APL, to give only a couple of examples.

These two notions of what "expressive" means are frequently close to diametrically opposed. The first tends to favor the "lowest" level languages, while the second tends to favor the "highest" level. At least from what I've seen, most people really start from the language they like, and their definition of "expressive" is basically whatever balance of the two criteria is required for their preferred language to be the "best".

Personally, I feel that the "expressiveness" of a language really comes down to how clearly the language constructs can "express" the developer's intentions.

For example, I feel that C# (especially LINQ via C# 3+) is becoming much more expressive. This LINQ statement is a great example:

var results = collection.Where(item => item > 5);

Without knowing the details of the language or the implementation being used, the developer intent is (in my opinion) very clear in the above statement.

I do not think that the verboseness of the language is equal to its expressiveness, however, there is some correlation in place. If a language requires a lot of code in order to express an abstraction, it is less expressive. These are two related, but different, concepts.

The same is true with power - although here a language's features (ie: power) must be complete enough to express the abstraction clearly. Without this, expressiveness will suffer. That being said, a language can be very "powerful" in terms of features, but not necessarily be expressive, if the feature set is difficult to understand.