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From: yodaiken@chelm.cs.umass.edu (victor yodaiken)
Newsgroups: comp.lang.misc
Subject: Re: definitions
Message-ID: <30039@dime.cs.umass.edu>
Date: 3 May 91 10:44:15 GMT
References: <2494@optima.cs.arizona.edu>
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Reply-To: yodaiken@chelm.cs.umass.edu (victor yodaiken)
Organization: University of Massachusetts, Amherst
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In article <2494@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>I've decided to be a little more explicit about the fact that typing
>refers to machine representations, since that seems to be the major
>difference between the two extreme views.  In other words, if typing
>only refers to an arbitrary set of values, then most of the
>differences of opinion disappear.
>
>Typing: the machine representation of a value.  You must know the
>typing of a memory location to know how to interpret the bits as a
>value.
>

Oh, well, here's the problem. To me a "type" is not necessarily a
machine-related notion. The "type" of a mathematical object refers to the
operations which are meaningful on the object and the laws which govern
the behavior of the object. For example "1" can be an element of a boolean
algebra, the identity element of a group, an integer, or an abbreviation
for the textual symbol "successor(zero())".  Depending on the type which
we assign to "1" we will interpret "1+1" differently.  

>Static typing: the assignment of a typing to all the values that a
>given syntactic expression might produce.  This is generally
>implemented by having the programmer declare the typings of the
>variables, and then inferring the typing of compound expressions by the
>types of the operations.
>
>Dynamic typing: a programming language feature where the typing of a
>value can be determined from the value alone, without reference to the
>way in which the value is used.  This is generally implemented by
>adding a type tag to all values at runtime.  Note that since the sizes
>of values are not known statically, some form of automatic storage
>management is needed to implement dynamic typing.
>


>Strong typing: the feature that an operation cannot return an
>undefined result because it did not know the typing of one of its
>operands.  Strong static typing is implemented by only allowing
>operators to be applied to operands whose typing can be statically
>inferred to be correct for that operator.  Strong dynamic typing is
>implemented by having each operator dynamically check the type tags of
>its operands to make sure they are correct.
>

In fact, "dynamic typing" as you have defined it, forbids strong
typing unless we are willing to allow for "bad type" aborts and to 
consider these to be well defined results.