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Types variables and values

From: David BL <davidbl_at_iinet.net.au>
Date: Sun, 21 Oct 2007 20:23:02 -0700
Message-ID: <1193023382.184353.189510@i38g2000prf.googlegroups.com>


In An Introduction to Database Systems, C.J. Date, characterises value, variable and type as follows:-

"value" : An "individual constant" - for example the individual
constant that is the integer 3. A value has no location in time or space.

"variable" : a holder for the appearance of a value. ... variables
unlike values can be updated.

"type" : a named set of values along with an associated set of
operators that can be applied to values and variables of the type in question.

According to Date, a type by definition is abstract, and should not be confused with a particular implementation of a type (which he calls a
"POSSREP").
It seems to me that these definitions are very important and useful but neverthess don't capture a general enough notion of "variable" and
"type".

That being said they're certainly appropriate for the topic of the book (Database Systems).

In the following it is convenient to use C++ code examples, while tending to use Date's terminology.

Firstly, let's agree that these definitions are perfectly adequate for the following types

    bool, int, float, string, Point, Circle, Ellipse

I would call these "value-types", to distinguish from the following Mutex class:-

    class Mutex
    {

        public:
            void Lock();
            void Unlock();
        private:
            < locking thread id, lock count, queue of waiting
threads ... >

    };

Consider the following declaration

    Mutex m;

Presumably we would say this declares a variable named 'm' of type Mutex. Is this compatible with Date's definition of "variable" and
"type"?

I would say it is inappropriate to regard a Mutex variable as holding a "value" that exists independently of the variable. That point of view raises more questions than answers...

  1. What does it mean to assign a value to a mutex variable? Assume that the mutex variable is currently counting the number of times a particular thread has locked it, and it has queued a number of threads blocking in an efficient wait state on the call to Lock().
  2. What operations exist on Mutex values?
  3. What does it mean to copy the value in a mutex variable?

I can think of lots of examples where I would say that a variable has state, but logically doesn't represent a "value".

a A node of a double linked list or red black tree b A thread pool
c A proxy for external hardware such as a printer or HDD

These types are characterised by not supporting copy and assignment operations.

Do Date's definitions apply reasonably to pointers? The answer would appear to be yes, because it is certainly useful (and common terminology) to distinguish between pointer types, pointer variables and pointer values. Pointer values can be assigned to pointer variables. Pointer values can be passed as arguments into functions, or returned from functions.

However, there is something strange going on. We would normally think of values as existing independently of variables (and in fact the abstract machine), and yet a (non-null) pointer value represents a reference to a particular variable that exists in a particular running process on a particular machine. Received on Sun Oct 21 2007 - 22:23:02 CDT

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