#

## Issue ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS Writeup

    Status:		Passed, Jan 89 X3J13

    Forum:         Cleanup

    Issue:         ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS

    References:    Data types and Type specifiers: CLtL p. 11; Sect. 4.5, p.45
                   Functions: TYPEP and SUBTYPEP; CLtL Sect. 6.2.1, p.72
                              ARRAY-ELEMENT-TYPE, CLtL p. 291
                   The type-specifiers:
                              ARRAY,  SIMPLE-ARRAY,  VECTOR,  SIMPLE-VECTOR
                              COMPLEX

    Related Issues: SUBTYPEP-TOO-VAGUE, LIST-TYPE-SPECIFIER

    Category:      CHANGE

    Edit history:  Version 1, 13-May-88, JonL
                   Version 2, 23-May-88, JonL
                    (typo fixes, comments from moon, rearrange some discussion)
                   Version 3, 02-Jun-88, JonL
                    (flush alternate proposal ["flush-upgrading"]; consequently,
                     move more of discussion back to discussion section.
                   Version 4, 01-Oct-88, Jan Pedersen & JonL
                    (reduce discussion, and "cleanup" wordings)
                   (Version 5 edit history missing)
                   Version 6, 6-Oct-88, Moon
                    (fix typos, cover subtypep explicitly, add complex,
                     change name of UPGRADE-ARRAY-ELEMENT-TYPE)
                   Version 7, 7-Oct-88, JonL (more name and wording changes)
                   Version 8,  8-Oct-88, Masinter (wording, discussion)
                   Version 9, 31-Oct-88, JonL (major re-wording to accommodate
    		 recent discussion; esp. re-introduce and clarify "upgrading")

    Problem description:

     CLtL occasionally draws a distinction between type-specifiers "for
     declaration" and "for discrimination";  see CLtL, section 4.5 "Type
     Specifiers That Specialize" (p.45 and following)  The phrase
     "for declaration"  encompasses type-specifiers passed in as the
     :element-type argument to  MAKE-ARRAY, passed in as the <result-type>
     argument to COERCE, and used in THE and DECLARE type declarations.  The
     phrase "for discrimination" refers to the type-specifiers passed in as
     the <type> argument(s) to TYPEP and SUBTYPEP.

     One consequence of this distinction is that a variable declared to be of
     type <certain-type>, and all of whose assigned objects are created in
     accordance with that type, may still have none of its values ever satisfy
     the TYPEP predicate with that type-specifier.   One type-specifier with
     this property is
             (ARRAY <element-type>)
     for various implementation dependent values of <element-type>.  For
     example, in most implementations of CL, an array X created with an
     element-type of (SIGNED-BYTE 5) will, depending on the vendor, either
     satisfy
            (TYPEP X '(ARRAY (SIGNED-BYTE 8))), or
            (TYPEP X '(ARRAY T))
     but (almost) never will it satisfy
            (TYPEP X '(ARRAY (SIGNED-BYTE 5))).

     This is entirely permissible within the scope of standardization on
     MAKE-ARRAY, where an implementation is required only to construct up the
     result out of "the most specialized [element] type that can nevertheless
     accommodate elements of the given type [the :element-type argument]"
     (see CLtL, p287).  That is, an implementation may in fact only provide a
     very small number of equivalence classes of element-types for storing
     arrays, corresponding to its repertoire of specialized storage techniques;
     and it is explicitly permitted to "upgrade" any element-type request into
     one of its built-in repertoire (see also  CLtL, p45, second and third
     paragraphs under Section 4.5.)

     As a practical matter, almost every existing implementation does some
     serious upgrading of the :element-type argument given to MAKE-ARRAY.
     Yet the difference between "for declaration" and "for discrimination"
     has been very confusing to many people.  Similarly, portability is
     hindered when users do not know just how a given implementation does
     upgrading.

     The type specifier (COMPLEX <part-type>) also falls in the  domain of CLtL
     Section 4.5.  Currently, only one implementation actually provides any kind
     of specialized storage for complex parts; and in this case, the practical
     matter is less urgent, since the kind of upgrading happening is so obvious
     as to cause little or no confusion.

    Proposal: (ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS:UNIFY-UPGRADING)

     Short Summary:

      ** Eliminate the distinction between type-specifiers "for declaration" and
         "for discrimination".  In short, change the meaning of array and
         complex type specifiers in favor of the "for declaration" meaning.

      ** Change the meaning of TYPEP to be in accord with "for declaration"
         meaning of type-specifiers.

      ** Add an implementation-dependent function that reveals how a given
         type-specifier for array element-types is upgraded.  Add another such
         function that reveals how a given type-specifier for complex parts is
         upgraded.

      ** Clarify that "upgrading" implies a movement upwards in the type-
         hierarchy lattice; i.e., if <type> upgrades to <Type>, then
         <Type> must be a super-type of <type>.

      ** Clarify that upgrading an array element-type is independent of any
         other property of arrays, such as rank, adjustability, fill-pointers,
         etc.

      ** Clarify how SUBTYPEP thus behaves on array type-specifiers.

      ** Define how SUBTYPEP behaves on complex type-specifiers.

     Note that despite this issue's name, the detailed specifications herein
     apply to the type system -- not to the behavior of MAKE-ARRAY, nor to how
     arrays are actually implemented.

     Details:

      First, some definitions: Two type-specifiers <type1> and <type2> are said
      to be "type-equivalent" if and only if each one specifies a subtype of the
      other one.  For example, (UNSIGNED-BYTE 5) and (MOD 32) are two different
      type- specifiers that always refer to the same sets of things; hence they
      are type-equivalent.  But (UNSIGNED-BYTE 5) and (SIGNED-BYTE 8) are not
      type- equivalent since the former refers to a proper subset of the latter.
      Two type-specifiers <type1> and <type2> are said to be "type-disjoint"
      if their specified intersection is null.  For example, INTEGER and FLOAT
      are type disjoint by definition (see CLtL p.33), and (INTEGER 3 5) and
      (INTEGER 7 10) are type-disjoint because the specified ranges have no
      elements in common.

     *. Eliminate the distinction between types "for declaration" and "for
        discrimination".  In particular, elminate any such reference in the
        discussion of array and complex type-specifiers; this would include
        documentation patterned after the discussion in section 4.5, pp. 45-7,
        especially the example on p.46 that says "See ARRAY-ELEMENT-TYPE".
        Change the meaning of (ARRAY <element-type>), as well as any of the
        subtypes of ARRAY (such as SIMPLE-ARRAY, VECTOR, etc.) in favor of the
        "for declaration" meaning.  Make the similar simplification for the
        <part-type> specifiers in the COMPLEX type-specifier.

     *. Change the meaning of (TYPEP <x> '(ARRAY <type>)), where <type> is not
        *, to be true if and only if <x> is an array that could be the result
        of giving <type> as the :element-type argument to MAKE-ARRAY.  While
        (ARRAY *) refers to all arrays regardless of element type, (ARRAY <type>)
        refers only to those arrays that can result from giving <type> as the
        :element-type argument to the function MAKE-ARRAY.  Change the meanings
        for (SIMPLE-ARRAY <type>) and (VECTOR <type>) in the same way.

        Change the meaning of (TYPEP <x> '(COMPLEX <type>)) similarly.  Thus,
        (COMPLEX <type>) refers to all complex numbers that can result from
        giving numbers of type <type> to the function COMPLEX, plus all other
        complex numbers of the same specialized representation.  Remember that
        both the real and the imaginary parts of any such complex number must
        satisfy:
                    (TYPEP <real-or-imag-part> '<type>).

     *. Add the function UPGRADED-ARRAY-ELEMENT-TYPE of one argument, which
        returns the element type of the most specialized array representation
        capable of holding items of the given argument type.   Note that except
        for storage allocation consequences, it could be defined as:

          (DEFUN UPGRADED-ARRAY-ELEMENT-TYPE (TYPE)
            (ARRAY-ELEMENT-TYPE (MAKE-ARRAY 0 :ELEMENT-TYPE TYPE)))

        Since element-type upgrading is a fundamental operation implicit in
        almost every existing implementation of MAKE-ARRAY, the purpose of this
        added function is primarily to reveal how an implementation does its
        upgrading.

        Add the function UPGRADED-COMPLEX-PART-TYPE of one argument that
        returns the part type of the most specialized complex number
        representation that can hold parts of the given argument type.

     *. Clarify that "upgrading" implies a movement upwards in the type-
        hierarchy lattice.  Specifically, the type-specifier <type> must be
        a subtype of (UPGRADED-ARRAY-ELEMENT-TYPE '<type>).  Furthermore, if
        <type1> is a subtype of <type2>, then:
                (UPGRADED-ARRAY-ELEMENT-TYPE '<type1>)
        must also be a subtype of:
                (UPGRADED-ARRAY-ELEMENT-TYPE '<type2>).
        Note however, that two type-disjoint types can in fact be upgraded into
        the same thing.

        Clarify that ARRAY-ELEMENT-TYPE returns the upgraded element type
        for the array; in particular, any documentation patterned after
        the sentence on p. 291 begining "This set may be larger than the
        set requested when the array was created; for example . . ." should
        be embellished with this clarification.

        Similarly, the type-specifier <type> must be a subtype of
        (UPGRADED-COMPLEX-PART-TYPE <type>).

     *. Clarify that upgrading an array element-type is independent of any
        other property of arrays, such as rank, adjustability, fill-pointers,
        displacement etc.  For all such properties other than rank this should
        be obvious (since they are not expressible in the language of
        type-specifiers); but note that unless it is also independent of rank,
        it would not be consistently possible to displace arrays to those of
        differing rank.

     *. Clarify that SUBTYPEP on ARRAY type-specifiers is as follows:

        For all type-specifiers <type1> and <type2> other than *, require
        (ARRAY <type1>) and (ARRAY <type2>) to be type-equivalent if and only
        if they refer to arrays of exactly the same specialized representation;
        and require them to be type-disjoint if and only if they refer to arrays
        of different, distinct specialized representations.  This definition
        follows that implicitly prescribed in CLtL.

        As a consequence of the preceding change to TYPEP and of the definition
        of UPGRADED-ARRAY-ELEMENT-TYPE, the two type specifiers
                    (ARRAY <type1>)  and
                    (ARRAY <type2>)
        are type-equivalent if and only if
                    (UPGRADED-ARRAY-ELEMENT-TYPE '<type1>)  and
                    (UPGRADED-ARRAY-ELEMENT-TYPE '<type2>)
        are type-equivalent.  This is another way of saying that `(ARRAY <type>)
        and `(ARRAY ,(UPGRADED-ARRAY-ELEMENT-TYPE '<type>)) refer to the same
        set of specialized array representations.

        This defines the behavior of SUBTYPEP on array type-specifiers; namely:
                    (SUBTYPEP '(ARRAY <type1>) '(ARRAY <type2>))
        is true if and only if
                    (UPGRADED-ARRAY-ELEMENT-TYPE '<type1>)  and
                    (UPGRADED-ARRAY-ELEMENT-TYPE '<type2>)
        are type-equivalent.

     *. Define SUBTYPEP on COMPLEX type-specifiers as follows:

        For all type-specifiers <type1> and <type2> other than *,
                (SUBTYPEP '(COMPLEX <type1>) '(COMPLEX <type2>))
        is  T T  if:
          1. <type1> is a subtype of <type2>, or
          2. (UPGRADED-COMPLEX-PART-TYPE '<type1>) is type-equivalent
             to (UPGRADED-COMPLEX-PART-TYPE '<type2>);  in this case,
             (COMPLEX <type1>) and (COMPLEX <type2>) both refer to the
             same specialized representation.
       The result is  NIL T  otherwise.

     The small differences between the SUBTYPEP specification for ARRAY and
     for COMPLEX are necessary because there is no creation function for
     complexes which allows one to specify the resultant part type independently
     of the actual types of the parts.  Thus in the case of COMPLEX, we must
     refer to the actual type of the parts, although a number can be a member
     of more than one type; e.g., 17 is of type (MOD 18) as well as of type
     (MOD 256); and 2.3f5 is of type SINGLE-FLOAT was well as FLOAT.
     The form:
         (SUBTYPEP '(COMPLEX SINGLE-FLOAT) '(COMPLEX FLOAT))
     must be true in all implementations; but:
         (SUBTYPEP '(ARRAY SINGLE-FLOAT) '(ARRAY FLOAT))
     is true only in implementations that do not have a specialized array
     representation for single-floats distinct from that for other floats.

    Examples:

     Let <aet-x> and <aet-y> be two distinct type specifiers that are
     definitely not type-equivalent in a given implementation, but for which
     make-array will return an object of the same array type.  This will be
     an implementation dependent search, but in every implementation that
     the proposer has tested, there will be some such types; often,
     (SIGNED-BYTE 5) and (SIGNED-BYTE 8) will work.

     Thus, in each case, both of the following forms return T T:

      (subtypep (array-element-type (make-array 0 :element-type '<aet-x>))
                (array-element-type (make-array 0 :element-type '<aet-y>)))

      (subtypep (array-element-type (make-array 0 :element-type '<aet-y>))
                (array-element-type (make-array 0 :element-type '<aet-x>)))

     To eliminate the distinction between "for declaration" and "for
     discrimination" both of the following should be true:

      [A]
       (typep (make-array 0 :element-type '<aet-x>)
              '(array <aet-x>))
       (typep (make-array 0 :element-type '<aet-y>)
              '(array <aet-y>))

     Since (array <aet-x>) and (array <aet-y>) are different names for
     exactly the same set of objects, these names should be type-equivalent.
     That implies that the following set of tests should also be true:

      [B]
       (subtypep '(array <aet-x>) '(array <aet-y>))
       (subtypep '(array <aet-y>) '(array <aet-x>))

     Additionally, to show that un-equivalent type-specifiers that use the
     same specialized array type should be equivalent as element-type
     specifiers, the following type tests should be true:

      [C]
       (typep (make-array 0 :element-type '<aet-y>)
              '(array <aet-x>))
       (typep (make-array 0 :element-type '<aet-x>)
              '(array <aet-y>))

    Rationale:

     This proposal legitimizes current practice, and removes the obscure and
     un-useful distinction between type-specifiers "for declaration" and
     "for discrimination".  The suggested changes to the interpretation of
     array and complex type-specifiers follow from defining type-specifiers
     as names for collections of objects, on TYPEP being a set membership
     test, and SUBTYPEP a subset test on collections of objects.

    Current Practice:

     Every vendor's implementation that the proposer has queried has a finite
     set of specialized array representations, such that two non-equivalent
     element types can be found that use the same specialized array
     representation; this includes Lucid, Vaxlisp, Symbolics, TI, Franz,
     and Xerox. Most implementations fail tests [A] and [C] part 1, but pass
     tests [A] and [C] part 2; this is a consequence of implementing the
     distinction between "for declaration" and "for discrimination".  Lucid
     and Xerox both pass test [B], and the other implementations fail it.
     The Explorer returns NIL for all six tests in [A], [B], and [C].

     Allegedly, the PCLS implementation does no "upgrading"; each array
     "remembers" exactly the type-specifier handed to the MAKE-ARRAY call
     that created it.  Thus the test cases are not applicable to PCLS,
     since the precondition cannot be met (i.e., find two non-type-equivalent
     type-specifiers that are non-trivially upgraded by make-array).

     The TI Explorer offers specialized representation for complexes;
     part types of SINGLE-FLOAT and DOUBLE-FLOAT are specialized.

    Cost to Implementors:

     This proposal is an incompatible change to the current language
     specification, but only a small amount of work should be required in
     each vendor's implementation of TYPEP and SUBTYPEP.

    Cost to Users:

     Because of the prevalence of confusion in this area, it seems unlikely
     that any user code will have to be changed.  In fact, it is more likely
     that some of the vendors will cease to get bug reports about MAKE-ARRAY
     returning a result that isn't of "the obvious type".  Since the change
     is incompatible, some user code might have to be changed.

    Cost of non-adoption:

     Continuing confusion in the user community.

    Benefits:

     It will greatly reduce confusion in the user community.  The fact that
     (MAKE-ARRAY <n> :ELEMENT-TYPE '<type>) frequently is not of type
     (ARRAY <type>) has been very confusing to almost everyone.

     Portability of applications will be increased slightly, since
     the behavior of
         (TYPEP (MAKE-ARRAY <n> :ELEMENT-TYPE <type>) '(ARRAY <type>))
      will no longer be implementation-dependent.

    Esthetics:

     Reducing the confusing distinction between type-specifiers "for
     declaration" and "for discrimination" is a simplifying step -- it is a
     much simpler rule to state that the type-specifiers actually describe
     the collections of data they purport to name.  Thus this is a step
     towards increased elegance.

    Discussion:

     This issue was prompted by a lengthy discussion on the Common Lisp
     mailing list.  See for example a series of exchanges started on Thu,
     17 Dec 87 10:48:05 PST by Jeff Barnett <jbarnett@nrtc.northrop.com>
     under the subject line of "Types in CL".  See also the exchange started
     Wed, 6 Jan 88 23:21:16 PST by Jon L White <edsel!jonl@labrea.stanford.edu>
     under the subject line of "TYPEP warp implications"

     Although the types STRING,  BIT-VECTOR,  SIMPLE-STRING, and
     SIMPLE-BIT-VECTOR are subtypes of the ARRAY type, they are not
     specifically discussed in this proposal.  The reason is that
     they are not type-specifiers "that specialize", but are merely
     abbreviations as follows:
       STRING             ==  (VECTOR STRING-CHAR)
       SIMPLE-STRING      ==  (SIMPLE-ARRAY STRING-CHAR (*))
       BIT-VECTOR         ==  (VECTOR BIT)
       SIMPLE-BIT-VECTOR  ==  (SIMPLE-ARRAY BIT (*))
     Thus their semantics could be affected only in an implementation that
     doesn't support a specific "specialized storage" type for arrays of
     bits and vectors of string-chars.  But in fact, every CL implementation
     must appear to support "specialized storage" for bit-arrays and strings,
     even if it means nothing more than remembering the fact that such an
     array was created with that element-type.  This is required in order
     for strings, bit-vectors,  and bit-arrays to be disjoint datatypes
     (see CLtL p.34; see also the definitions of BIT-ARRAY and STRING found
     in CLtL p.293, Section 17.4, and in CLtL p.299.)

     We considered the possibility of flushing the permission to "upgrade";
     for example, it could be made a requirement that:
         (ARRAY-ELEMENT-TYPE (MAKE-ARRAY <n> :ELEMENT-TYPE <type>))
     always be equal to <type> (or, at least type-equivalent to <type>)
     for all valid type specifiers <type>.  This has several problems: it
     increases the storage requirement for many kinds of arrays, and hides
     a relevant part of the underlying implementation for no apparently
     good reason.  However, it would increase portability, since it would be
     much more difficult, for example, to write a program that created an
     array with one element-type, say, (UNSIGNED-BYTE 5), but operated on it
     assuming a non-trivial upgraded element-type, say, (UNSIGNED-BYTE 8).
     Under this proposal, it is valid for an implementation of MAKE-ARRAY
     to have arrays "remember" the type-equivalence class of the original
     :element-type argument; such an implementation would satisfy all of
     the  constraints listed above.

     We considered a suggestion to restrict the set of "known" array element
     types; this would gain portability at the expense of limiting the
     language.

     We considered leaving out of the proposal the addition of the two
     functions UPGRADED-ARRAY-ELEMENT-TYPE and UPGRADED-COMPLEX-PART-TYPE.
     But it was noted that every implementation of CL supports exactly
     that functionality somewhere in its implementation of MAKE-ARRAY; and
     exposing this to the user would be a good thing.  Furthermore, the
     existence of at least UPGRADED-ARRAY-ELEMENT-TYPE makes the clarifications
     on "upgrading" and SUBTYPEP implications easier.  Finally, there would
     be no other way at all to pinpoint just how complex parts are upgraded,
     since there is no type information available except for the actual
     types of the parts.

     Since this proposal contains the implication:
         (ARRAY <type1>)  is-type-equivalent-to  (ARRAY <type2>)
         ==>
          <type1>  is-type-equivalent-to  <type2>
     then the question naturally arises "Does the reverse implication hold?"
     That is, should two non-EQ but type-equivalent type-specifiers <type1>
     and <type2> always give rise to the same array types?   For example,
     consider SHORT-FLOAT and SINGLE-FLOAT in an implementation where these
     are type-equivalent (see CLtL section 2.1.3).  One may desire to implement
     (ARRAY SHORT-FLOAT) and (ARRAY SINGLE-FLOAT) differently.  Say, for example
     that the former is packed into 16-bit half-words, whereas the latter is
     packed into 32-bit words; but for either kind of packing, the result of
     AREF is an ordinary "single-float".  The whole point of the type-specifier
     to make-array is merely to specify a packing technique for "packed float"
     arrays.  This "krinkle", however, will not be addressed by the proposal
     herein; it should simply be remembered that the implication above goes
     only one way, and is not an "if-and-only-if" link.

Copyright 1996-2005, LispWorks Ltd. All rights reserved.