What is Expressiveness in a Computer Language

[Rob Thorpe]

Andreas Rossberg wrote:
> Rob Thorpe wrote:
> >>
> >>>No, that isn't what I said.  What I said was:
> >>>"A language is latently typed if a value has a property - called it's
> >>>type - attached to it, and given it's type it can only represent values
> >>>defined by a certain class."
> >>
> >>"it [= a value] [...] can [...] represent values"?
> >
> > ???
>
> I just quoted, in condensed form, what you said above: namely, that a
> value represents values - which I find a strange and circular definition.

Yes, but the point is, as the other poster mentioned: values defined by
a class.
For example, in lisp:
"xyz" is a string, #(1 2 3) is an array, '(1 2 3) is a list, 45 is a
fixed-point number.
Each item that can be stored has a type, no item can be stored without
one.  The types can be tested.  Most dynamic typed languages are like
that.

Compare this to an untyped language where types cannot generally be
tested.

> >>A (static) type system assigns types to (all) *expressions*.
> >
> > That's right most of the time yes, I probably should have said
> > expressions.  Though I can think of static typed languages where the
> > resulting type of an expression depends on the type of the variable it
> > is being assigned to.
>
> Yes, but that's no contradiction. A type system does not necessarily
> assign *unique* types to individual expressions (consider overloading,
> subtyping, polymorphism, etc).

That's a fair way of looking at it.

> > Well I haven't programmed in any statically typed language where values
> > have types themselves.
>
> They all have - the whole purpose of a type system is to ensure that any
> expression of type T always evaluates to a value of type T.

But it only gaurantees this because the variables themselves have a
type, the values themselves do not.  Most of the time the fact that the
variable they are held in has a type infers that the value does too.
But the value itself has no type, in a C program for example I can take
the value from some variable and recast it in any way I feel and the
language cannot correct any errors I make because their is no
information in the variable to indicate what type it is.

> So when you
> look at type systems formally then you certainly have to assign types to
> values, otherwise you couldn't prove any useful property about those
> systems (esp. soundness).

Yes, but indirectly.