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Issue: ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS (Version 9)
- To: firstname.lastname@example.org
- Subject: Issue: ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS (Version 9)
- From: Jon L White <email@example.com>
- Date: Thu, 3 Nov 88 21:40:04 PST
This version is a substantial re-write, to address issues raised since
the X3J13 meeting in Fairfax, especially in the mail msgs:
10 Oct Jim McDonald <firstname.lastname@example.org>
13 Oct Kent M Pitman <KMP@STONY-BROOK.SCRC.Symbolics.COM>
13 Oct email@example.com (Sandra J Loosemore)
One major change is the re-introduction of "upgrading". Not only has
this word crept into most people's vocabulary, but Pedersen has provided
a sufficient rationale for using it -- it is a movement upward in the
type-hierarchy lattice. We have found one implementation that does no
upgrading; and we have had to clarify some things about upgrading, to
cover existing practice. This is reflected in two sub-items in the
Although the proposal is a CHANGE, is now consists of seven sub-items:
Two incompatible CHANGES
And "a partridge in a pear tree"
The seventh item is the definition for subtypep on complexes; I'm not
sure whether this is new (because CLtL forgot about it), or a change,
or simply a clarification. Let's hope it's at least right!
-- JonL --
P.S. I say "we" above, since many people helped in the production of
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
ARRAY, SIMPLE-ARRAY, VECTOR, SIMPLE-VECTOR
Related Issues: SUBTYPEP-TOO-VAGUE, LIST-TYPE-SPECIFIER
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")
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
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
(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
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.
** 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
** 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,
** 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.
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
(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
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:
must also be a subtype of:
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
*. 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
*. 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
are type-equivalent if and only if
(UPGRADED-ARRAY-ELEMENT-TYPE '<type1>) and
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
*. 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.
(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.
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:
(typep (make-array 0 :element-type '<aet-x>)
(typep (make-array 0 :element-type '<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:
(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:
(typep (make-array 0 :element-type '<aet-y>)
(typep (make-array 0 :element-type '<aet-x>)
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.
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).
Only the TI Explorer offers any 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.
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.
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.
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 <firstname.lastname@example.org>
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 <email@example.com>
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
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.