What is Expressiveness in a Computer Language

[Rob Thorpe]

Rob Thorpe wrote:
> Chris Smith wrote:
> > Torben Ægidius Mogensen <torbenm at app-3.diku.dk> wrote:
> > > That's not really the difference between static and dynamic typing.
> > > Static typing means that there exist a typing at compile-time that
> > > guarantess against run-time type violations.  Dynamic typing means
> > > that such violations are detected at run-time.  This is orthogonal to
> > > strong versus weak typing, which is about whether such violations are
> > > detected at all.  The archetypal weakly typed language is machine code
> > > -- you can happily load a floating point value from memory, add it to
> > > a string pointer and jump to the resulting value.  ML and Scheme are
> > > both strongly typed, but one is statically typed and the other
> > > dynamically typed.
> >
> > Knowing that it'll cause a lot of strenuous objection, I'll nevertheless
> > interject my plea not to abuse the word "type" with a phrase like
> > "dynamically typed".  If anyone considers "untyped" to be perjorative,
> > as some people apparently do, then I'll note that another common term is
> > "type-free," which is marketing-approved but doesn't carry the
> > misleading connotations of "dynamically typed."  We are quickly losing
> > any rational meaning whatsoever to the word "type," and that's quite a
> > shame.
>
> I don't think dynamic typing is that nebulous.  I remember this being
> discussed elsewhere some time ago, I'll post the same reply I did then
> ..
> A language is statically typed if a variable 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.
>
> 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.
>
> Some people use dynamic typing as a word for latent typing, others use
> it to mean something slightly different.  But for most purposes the
> definition above works for dynamic typing also.
>
> Untyped and type-free mean something else: they mean no type checking
> is done.

Since people have found some holes in this definition I'll have another
go:-

Firstly, a definition, General expression (gexpr) are variables
(mutable or immutable), expressions and the entities functions return.

A statically typed language has a parameter associated with each gexpr
called it's type.  The code may test the type of a gexpr.  The language
will check if the gexprs of an operator/function have types that match
what is required, to some criteria of sufficiency. It will emit an
error/warning when they don't.  It will do so universally.

A latently typed language has a parameter associated with each value
called it's type.  The code may test the type of a value.  The language
may check if the gexprs of an operator/function have types that match
what is required, to some criteria of sufficiency.  It will not
necessarily do so universally.

An untyped language is one that does not possess either a static or
latent type system.  In an untyped language gexprs possess no type
information, and neither do values.

--

These definitions still have problems, they don't say anything about
languages that sit between the various categories for example.  I don't
know where HM type system would come in them.