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<!-- Common Lisp HyperSpec (TM), version 7.0 generated by Kent M. Pitman on Mon, 11-Apr-2005 2:31am EDT -->
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<TITLE>CLHS: Issue ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS Writeup</TITLE>
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<H1><A REV=MADE HREF="http://www.lispworks.com/"><IMG WIDTH=80 HEIGHT=65 ALT="[LISPWORKS]" SRC="../Graphics/LWSmall.gif" ALIGN=Bottom></A><A REL=TOP HREF="../Front/index.htm"><IMG WIDTH=237 HEIGHT=65 ALT="[Common Lisp HyperSpec (TM)]" SRC="../Graphics/CLHS_Sm.gif" ALIGN=Bottom></A> <A REL=PREV HREF="../Issues/iss014_w.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="../Issues/iss015.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="../Issues/iss016_w.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Next]" SRC="../Graphics/Next.gif" ALIGN=Bottom></A></H1>
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<H2>Issue ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS Writeup</H2>
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<PRE><B>Status:</B> Passed, Jan 89 X3J13<P>
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<P>
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<B>Forum:</B> Cleanup<P>
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<P>
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<B>Issue:</B> <A HREF="iss015.htm">ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS</A><P>
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<P>
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<B>References:</B> Data types and Type specifiers: CLtL p. 11; Sect. 4.5, p.45<P>
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Functions: <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> and SUBTYPEP; CLtL Sect. 6.2.1, p.72<P>
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<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>ARRAY-ELEMENT-TYPE</B></A>, CLtL p. 291<P>
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The type-specifiers:<P>
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<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A>, <A REL=DEFINITION HREF="../Body/t_smp_ar.htm#simple-array"><B>SIMPLE-ARRAY</B></A>, <A REL=DEFINITION HREF="../Body/a_vector.htm#vector"><B>VECTOR</B></A>, <A REL=DEFINITION HREF="../Body/t_smp_ve.htm#simple-vector"><B>SIMPLE-VECTOR</B></A><P>
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<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A><P>
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<P>
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Related Issues: <A HREF="iss335.htm">SUBTYPEP-TOO-VAGUE</A>, LIST-TYPE-SPECIFIER<P>
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<P>
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<B>Category:</B> CHANGE<P>
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<P>
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<B>Edit history:</B> Version 1, 13-May-88, JonL<P>
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Version 2, 23-May-88, JonL <P>
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(typo fixes, comments from moon, rearrange <A REL=DEFINITION HREF="../Body/f_everyc.htm#some"><B>some</B></A> discussion)<P>
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Version 3, 02-Jun-88, JonL <P>
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(flush alternate proposal ["flush-upgrading"]; consequently,<P>
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move more of discussion back to discussion section.<P>
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Version 4, 01-Oct-88, Jan Pedersen & JonL<P>
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(<A REL=DEFINITION HREF="../Body/f_reduce.htm#reduce"><B>reduce</B></A> discussion, <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> "cleanup" wordings)<P>
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(Version 5 edit history missing)<P>
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Version 6, 6-Oct-88, Moon<P>
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(fix typos, cover <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>subtypep</B></A> explicitly, add <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>complex</B></A>,<P>
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change name of UPGRADE-ARRAY-ELEMENT-TYPE)<P>
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Version 7, 7-Oct-88, JonL (more name <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> wording changes)<P>
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Version 8, 8-Oct-88, Masinter (wording, discussion)<P>
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Version 9, 31-Oct-88, JonL (major re-wording to accommodate<P>
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recent discussion; esp. re-introduce <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> clarify "upgrading")<P>
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<P>
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<P>
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<B>Problem description:<P>
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</B><P>
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CLtL occasionally draws a distinction between type-specifiers "for<P>
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declaration" and "for discrimination"; see CLtL, section 4.5 "Type <P>
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Specifiers That Specialize" (p.45 and following) The phrase <P>
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"for declaration" encompasses type-specifiers passed in as the <P>
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:element-type argument to <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>, passed in as the <result-type> <P>
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argument to <A REL=DEFINITION HREF="../Body/f_coerce.htm#coerce"><B>COERCE</B></A>, and used in <A REL=DEFINITION HREF="../Body/s_the.htm#the"><B>THE</B></A> and <A REL=DEFINITION HREF="../Body/s_declar.htm#declare"><B>DECLARE</B></A> type declarations. The <P>
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phrase "for discrimination" refers to the type-specifiers passed in as <P>
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the <type> argument(s) to <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> and <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A>.<P>
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<P>
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One consequence of this distinction is that a variable declared to be of <P>
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type <certain-type>, and all of whose assigned objects are created in <P>
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accordance with that type, may still have none of its values ever satisfy <P>
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the <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> predicate with that type-specifier. One type-specifier with <P>
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this property is <P>
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(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <element-type>) <P>
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for various implementation dependent values of <element-type>. For<P>
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example, in most implementations of CL, an array X created with an<P>
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element-type of (<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 5) will, depending on the vendor, either<P>
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satisfy<P>
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(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> X '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> (<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 8))), or<P>
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(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> X '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> T)) <P>
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but (almost) never will it satisfy <P>
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(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> X '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> (<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 5))).<P>
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<P>
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This is entirely permissible within the scope of standardization on<P>
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<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>, where an implementation is required only to construct up the<P>
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result out of "the most specialized [element] type that can nevertheless<P>
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accommodate elements of the given type [the :element-type argument]"<P>
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(see CLtL, p287). That is, an implementation may in fact only <A REL=DEFINITION HREF="../Body/f_provid.htm#provide"><B>provide</B></A> a <P>
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very small number of equivalence classes of element-types for storing <P>
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arrays, corresponding to its repertoire of specialized storage techniques;<P>
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and it is explicitly permitted to "upgrade" any element-type request into <P>
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one of its built-in repertoire (see also CLtL, p45, second and third<P>
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paragraphs under Section 4.5.)<P>
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<P>
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As a practical matter, almost every existing implementation does some <P>
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serious upgrading of the :element-type argument given to <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>. <P>
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Yet the difference between "for declaration" and "for discrimination" <P>
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has been very confusing to many people. Similarly, portability is<P>
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hindered when users do not know just how a given implementation does <P>
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upgrading.<P>
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<P>
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The type specifier (<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <part-type>) also falls in the domain of CLtL<P>
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Section 4.5. Currently, only one implementation actually provides any kind <P>
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of specialized storage for complex parts; and in this case, the practical<P>
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matter is less urgent, since the kind of upgrading happening is so obvious <P>
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as to cause little or no confusion.<P>
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<P>
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<P>
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Proposal: (<A HREF="iss015.htm">ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS:UNIFY-UPGRADING</A>)<P>
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<P>
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Short Summary:<P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Eliminate the distinction between type-specifiers "for declaration" and<P>
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"for discrimination". In short, change the meaning of array and<P>
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complex type specifiers in favor of the "for declaration" meaning.<P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Change the meaning of <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> to be in accord with "for declaration"<P>
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meaning of type-specifiers.<P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Add an implementation-dependent function that reveals how a given <P>
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type-specifier for array element-types is upgraded. Add another such <P>
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function that reveals how a given type-specifier for complex parts is<P>
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upgraded.<P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Clarify that "upgrading" implies a movement upwards in the type-<P>
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hierarchy lattice; i.e., if <type> upgrades to <Type>, then<P>
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<Type> must be a super-type of <type>.<P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Clarify that upgrading an array element-type is independent of any <P>
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other property of arrays, such as rank, adjustability, fill-pointers, <P>
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etc. <P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Clarify how <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> thus behaves on array type-specifiers. <P>
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<P>
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<A REL=DEFINITION HREF="../Body/v__stst_.htm#STST"><B>**</B></A> Define how <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> behaves on complex type-specifiers. <P>
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<P>
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Note that despite this issue's name, the detailed specifications herein <P>
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apply to the type system -- not to the behavior of <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>, nor to how<P>
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arrays are actually implemented.<P>
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<P>
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Details:<P>
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<P>
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First, some definitions: Two type-specifiers <type1> and <type2> are said <P>
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to be "type-equivalent" if and only if each one specifies a subtype of the<P>
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other one. For example, (<A REL=DEFINITION HREF="../Body/t_unsgn_.htm#unsigned-byte"><B>UNSIGNED-BYTE</B></A> 5) and (<A REL=DEFINITION HREF="../Body/a_mod.htm#mod"><B>MOD</B></A> 32) are two different <P>
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type- specifiers that always refer to the same sets of things; hence they <P>
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are type-equivalent. But (<A REL=DEFINITION HREF="../Body/t_unsgn_.htm#unsigned-byte"><B>UNSIGNED-BYTE</B></A> 5) and (<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 8) are not <P>
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type- equivalent since the former refers to a proper subset of the latter.<P>
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Two type-specifiers <type1> and <type2> are said to be "type-disjoint"<P>
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if their specified intersection is null. For example, <A REL=DEFINITION HREF="../Body/t_intege.htm#integer"><B>INTEGER</B></A> and <A REL=DEFINITION HREF="../Body/a_float.htm#float"><B>FLOAT</B></A> <P>
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are type disjoint by definition (see CLtL p.33), and (<A REL=DEFINITION HREF="../Body/t_intege.htm#integer"><B>INTEGER</B></A> 3 5) and <P>
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(<A REL=DEFINITION HREF="../Body/t_intege.htm#integer"><B>INTEGER</B></A> 7 10) are type-disjoint because the specified ranges have no<P>
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elements in common.<P>
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<P>
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*. Eliminate the distinction between types "for declaration" and "for <P>
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discrimination". In particular, elminate any such reference in the <P>
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discussion of array and complex type-specifiers; this would include <P>
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documentation patterned after the discussion in section 4.5, pp. 45-7, <P>
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especially the example on p.46 that says "See ARRAY-ELEMENT-TYPE".<P>
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Change the meaning of (<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <element-type>), as well as any of the<P>
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subtypes of <A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> (such as <A REL=DEFINITION HREF="../Body/t_smp_ar.htm#simple-array"><B>SIMPLE-ARRAY</B></A>, <A REL=DEFINITION HREF="../Body/a_vector.htm#vector"><B>VECTOR</B></A>, etc.) in favor of the <P>
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"for declaration" meaning. Make the similar simplification for the <P>
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<part-type> specifiers in the <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> type-specifier.<P>
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<P>
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*. Change the meaning of (<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> <x> '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type>)), where <type> is not <P>
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*, to be true if and only if <x> is an array that could be the result <P>
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of giving <type> as the :element-type argument to <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>. While<P>
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(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> *) refers to all arrays regardless of element type, (<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type>)<P>
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refers only to those arrays that can result from giving <type> as the<P>
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:element-type argument to the function <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>. Change the meanings<P>
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for (<A REL=DEFINITION HREF="../Body/t_smp_ar.htm#simple-array"><B>SIMPLE-ARRAY</B></A> <type>) and (<A REL=DEFINITION HREF="../Body/a_vector.htm#vector"><B>VECTOR</B></A> <type>) in the same way.<P>
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<P>
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Change the meaning of (<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> <x> '(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type>)) similarly. Thus,<P>
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(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type>) refers to all complex numbers that can result from <P>
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giving numbers of type <type> to the function <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A>, plus all other <P>
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complex numbers of the same specialized representation. Remember that<P>
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both the real and the imaginary parts of any such complex number must <P>
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satisfy:<P>
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(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> <real-or-imag-part> '<type>). <P>
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<P>
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*. Add the function <A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> of one argument, which<P>
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returns the element type of the most specialized array representation<P>
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capable of holding items of the given argument type. Note that except<P>
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for storage allocation consequences, it could be defined as:<P>
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<P>
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(<A REL=DEFINITION HREF="../Body/m_defun.htm#defun"><B>DEFUN</B></A> <A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> (<A REL=DEFINITION HREF="../Body/a_type.htm#type"><B>TYPE</B></A>)<P>
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(<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>ARRAY-ELEMENT-TYPE</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> 0 :ELEMENT-TYPE <A REL=DEFINITION HREF="../Body/a_type.htm#type"><B>TYPE</B></A>)))<P>
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<P>
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Since element-type upgrading is a fundamental operation implicit in <P>
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almost every existing implementation of <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A>, the purpose of this <P>
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added function is primarily to reveal how an implementation does its<P>
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upgrading.<P>
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<P>
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Add the function <A REL=DEFINITION HREF="../Body/f_upgrad.htm#upgraded-complex-part-type"><B>UPGRADED-COMPLEX-PART-TYPE</B></A> of one argument that<P>
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returns the part type of the most specialized complex number<P>
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representation that can hold parts of the given argument type.<P>
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<P>
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*. Clarify that "upgrading" implies a movement upwards in the type-<P>
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hierarchy lattice. Specifically, the type-specifier <type> must be<P>
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a subtype of (<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type>). Furthermore, if <P>
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<type1> is a subtype of <type2>, then:<P>
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(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type1>)<P>
|
||
|
|
must also be a subtype of:<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type2>). <P>
|
||
|
|
Note however, that two type-disjoint types can in fact be upgraded into <P>
|
||
|
|
the same thing.<P>
|
||
|
|
<P>
|
||
|
|
Clarify that <A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>ARRAY-ELEMENT-TYPE</B></A> returns the upgraded element type<P>
|
||
|
|
for the array; in particular, any documentation patterned after <P>
|
||
|
|
the sentence on p. 291 begining "This set may be larger than the <P>
|
||
|
|
set requested when the array was created; for example . . ." should<P>
|
||
|
|
be embellished with this clarification.<P>
|
||
|
|
<P>
|
||
|
|
Similarly, the type-specifier <type> must be a subtype of <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgrad.htm#upgraded-complex-part-type"><B>UPGRADED-COMPLEX-PART-TYPE</B></A> <type>).<P>
|
||
|
|
<P>
|
||
|
|
*. Clarify that upgrading an array element-type is independent of any <P>
|
||
|
|
other property of arrays, such as rank, adjustability, fill-pointers, <P>
|
||
|
|
displacement etc. For all such properties other than rank this should <P>
|
||
|
|
be obvious (since they are not expressible in the language of <P>
|
||
|
|
type-specifiers); but note that unless it is also independent of rank, <P>
|
||
|
|
it would not be consistently possible to displace arrays to those of <P>
|
||
|
|
differing rank.<P>
|
||
|
|
<P>
|
||
|
|
*. Clarify that <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> on <A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> type-specifiers is as follows: <P>
|
||
|
|
<P>
|
||
|
|
For all type-specifiers <type1> and <type2> other than *, <A REL=DEFINITION HREF="../Body/f_provid.htm#require"><B>require</B></A> <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type1>) and (<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type2>) to be type-equivalent if and only <P>
|
||
|
|
if they refer to arrays of exactly the same specialized representation; <P>
|
||
|
|
and <A REL=DEFINITION HREF="../Body/f_provid.htm#require"><B>require</B></A> them to be type-disjoint if and only if they refer to arrays <P>
|
||
|
|
of different, distinct specialized representations. This definition<P>
|
||
|
|
follows that implicitly prescribed in CLtL.<P>
|
||
|
|
<P>
|
||
|
|
As a consequence of the preceding change to <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> and of the definition <P>
|
||
|
|
of <A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A>, the two type specifiers <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type1>) and <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type2>)<P>
|
||
|
|
are type-equivalent if and only if<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type1>) and<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type2>) <P>
|
||
|
|
are type-equivalent. This is another way of saying that `(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type>)<P>
|
||
|
|
and `(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> ,(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type>)) refer to the same<P>
|
||
|
|
set of specialized array representations.<P>
|
||
|
|
<P>
|
||
|
|
This defines the behavior of <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> on array type-specifiers; namely:<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type1>) '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type2>))<P>
|
||
|
|
is true if and only if<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type1>) and<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> '<type2>)<P>
|
||
|
|
are type-equivalent.<P>
|
||
|
|
<P>
|
||
|
|
*. Define <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> on <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> type-specifiers as follows: <P>
|
||
|
|
<P>
|
||
|
|
For all type-specifiers <type1> and <type2> other than *, <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> '(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type1>) '(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type2>))<P>
|
||
|
|
is T T if:<P>
|
||
|
|
1. <type1> is a subtype of <type2>, or<P>
|
||
|
|
2. (<A REL=DEFINITION HREF="../Body/f_upgrad.htm#upgraded-complex-part-type"><B>UPGRADED-COMPLEX-PART-TYPE</B></A> '<type1>) is type-equivalent<P>
|
||
|
|
to (<A REL=DEFINITION HREF="../Body/f_upgrad.htm#upgraded-complex-part-type"><B>UPGRADED-COMPLEX-PART-TYPE</B></A> '<type2>); in this case,<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type1>) and (<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <type2>) both refer to the <P>
|
||
|
|
same specialized representation.<P>
|
||
|
|
The result is <A REL=DEFINITION HREF="../Body/a_nil.htm#nil"><B>NIL</B></A> T otherwise.<P>
|
||
|
|
<P>
|
||
|
|
The small differences between the <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> specification for <A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> and <P>
|
||
|
|
for <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> are necessary because there is no creation function for <P>
|
||
|
|
complexes which allows one to specify the resultant part type independently<P>
|
||
|
|
of the actual types of the parts. Thus in the case of <A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A>, we must <P>
|
||
|
|
refer to the actual type of the parts, although a number can be a member <P>
|
||
|
|
of more than one type; e.g., 17 is of type (<A REL=DEFINITION HREF="../Body/a_mod.htm#mod"><B>MOD</B></A> 18) as well as of type<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/a_mod.htm#mod"><B>MOD</B></A> 256); <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> 2.3f5 is of <A REL=DEFINITION HREF="../Body/a_type.htm#type"><B>type</B></A> <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A> was well as <A REL=DEFINITION HREF="../Body/a_float.htm#float"><B>FLOAT</B></A>.<P>
|
||
|
|
The form:<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> '(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A>) '(<A REL=DEFINITION HREF="../Body/a_comple.htm#complex"><B>COMPLEX</B></A> <A REL=DEFINITION HREF="../Body/a_float.htm#float"><B>FLOAT</B></A>))<P>
|
||
|
|
must be true in all implementations; but:<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A>) '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <A REL=DEFINITION HREF="../Body/a_float.htm#float"><B>FLOAT</B></A>))<P>
|
||
|
|
is true only in implementations that do not have a specialized array<P>
|
||
|
|
representation for single-floats distinct from that for other floats.<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Examples:<P>
|
||
|
|
</B><P>
|
||
|
|
Let <aet-x> and <aet-y> be two distinct type specifiers that are<P>
|
||
|
|
definitely not type-equivalent in a given implementation, but for which<P>
|
||
|
|
<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> will return an object of the same array type. This will be<P>
|
||
|
|
an implementation dependent search, but in every implementation that<P>
|
||
|
|
the proposer has tested, there will be some such types; often,<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 5) and (<A REL=DEFINITION HREF="../Body/t_sgn_by.htm#signed-byte"><B>SIGNED-BYTE</B></A> 8) will work.<P>
|
||
|
|
<P>
|
||
|
|
Thus, in each case, both of the following forms return T T:<P>
|
||
|
|
<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>subtypep</B></A> (<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>array-element-type</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-x>))<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>array-element-type</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-y>)))<P>
|
||
|
|
<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>subtypep</B></A> (<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>array-element-type</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-y>))<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>array-element-type</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-x>)))<P>
|
||
|
|
<P>
|
||
|
|
To eliminate the distinction between "for declaration" and "for<P>
|
||
|
|
discrimination" both of the following should be true:<P>
|
||
|
|
<P>
|
||
|
|
[A]<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>typep</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-x>)<P>
|
||
|
|
'(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-x>))<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>typep</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-y>)<P>
|
||
|
|
'(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-y>))<P>
|
||
|
|
<P>
|
||
|
|
Since (array <aet-x>) and (array <aet-y>) are different names for<P>
|
||
|
|
exactly the same set of objects, these names should be type-equivalent.<P>
|
||
|
|
That implies that the following set of tests should also be true:<P>
|
||
|
|
<P>
|
||
|
|
[B]<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>subtypep</B></A> '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-x>) '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-y>))<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>subtypep</B></A> '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-y>) '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-x>))<P>
|
||
|
|
<P>
|
||
|
|
Additionally, to show that un-equivalent type-specifiers that use the<P>
|
||
|
|
same specialized array type should be equivalent as element-type<P>
|
||
|
|
specifiers, the following type tests should be true:<P>
|
||
|
|
<P>
|
||
|
|
[C]<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>typep</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-y>)<P>
|
||
|
|
'(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-x>))<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>typep</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> 0 :element-type '<aet-x>)<P>
|
||
|
|
'(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>array</B></A> <aet-y>))<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Rationale:<P>
|
||
|
|
</B><P>
|
||
|
|
This proposal legitimizes current practice, and removes the obscure and<P>
|
||
|
|
un-useful distinction between type-specifiers "for declaration" and<P>
|
||
|
|
"for discrimination". The suggested changes to the interpretation of<P>
|
||
|
|
array and complex type-specifiers follow from defining type-specifiers<P>
|
||
|
|
as names for collections of objects, on <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> being a set membership<P>
|
||
|
|
test, and <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> a subset test on collections of objects.<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Current Practice:<P>
|
||
|
|
</B><P>
|
||
|
|
Every vendor's implementation that the proposer has queried has a finite <P>
|
||
|
|
set of specialized array representations, such that two non-equivalent <P>
|
||
|
|
element types can be found that use the same specialized array <P>
|
||
|
|
representation; this includes Lucid, Vaxlisp, Symbolics, TI, Franz,<P>
|
||
|
|
and Xerox. Most implementations fail tests [A] and [C] part 1, but pass<P>
|
||
|
|
tests [A] and [C] part 2; this is a consequence of implementing the<P>
|
||
|
|
distinction between "for declaration" and "for discrimination". Lucid<P>
|
||
|
|
and Xerox both pass test [B], and the other implementations fail it.<P>
|
||
|
|
The Explorer returns <A REL=DEFINITION HREF="../Body/a_nil.htm#nil"><B>NIL</B></A> for all six tests in [A], [B], and [C].<P>
|
||
|
|
<P>
|
||
|
|
Allegedly, the PCLS implementation does no "upgrading"; each array<P>
|
||
|
|
"remembers" exactly the type-specifier handed to the <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> call<P>
|
||
|
|
that created it. Thus the test cases are not applicable to PCLS,<P>
|
||
|
|
since the precondition cannot be met (i.e., find two non-type-equivalent<P>
|
||
|
|
type-specifiers that are non-trivially upgraded by <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A>).<P>
|
||
|
|
<P>
|
||
|
|
The TI Explorer offers specialized representation for complexes;<P>
|
||
|
|
part types of <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A> and <A REL=DEFINITION HREF="../Body/t_short_.htm#double-float"><B>DOUBLE-FLOAT</B></A> are specialized.<P>
|
||
|
|
<P>
|
||
|
|
<B>Cost to Implementors:<P>
|
||
|
|
</B><P>
|
||
|
|
This proposal is an incompatible change to the current language<P>
|
||
|
|
specification, but only a small amount of work should be required in<P>
|
||
|
|
each vendor's implementation of <A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> and <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A>.<P>
|
||
|
|
<P>
|
||
|
|
<B>Cost to Users:<P>
|
||
|
|
</B><P>
|
||
|
|
Because of the prevalence of confusion in this area, it seems unlikely<P>
|
||
|
|
that any user code will have to be changed. In fact, it is more likely<P>
|
||
|
|
that some of the vendors will cease to get bug reports about <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A><P>
|
||
|
|
returning a result that isn't of "the obvious type". Since the change<P>
|
||
|
|
is incompatible, some user code might have to be changed.<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Cost of non-adoption:<P>
|
||
|
|
</B><P>
|
||
|
|
Continuing confusion in the user community.<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Benefits:<P>
|
||
|
|
</B><P>
|
||
|
|
It will greatly reduce confusion in the user community. The fact that<P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> <n> :ELEMENT-TYPE '<type>) frequently is not of type <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type>) has been very confusing to almost everyone. <P>
|
||
|
|
<P>
|
||
|
|
Portability of applications will be increased slightly, since<P>
|
||
|
|
the behavior of <P>
|
||
|
|
(<A REL=DEFINITION HREF="../Body/f_typep.htm#typep"><B>TYPEP</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> <n> :ELEMENT-TYPE <type>) '(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type>))<P>
|
||
|
|
will no longer be implementation-dependent. <P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Esthetics:<P>
|
||
|
|
</B><P>
|
||
|
|
Reducing the confusing distinction between type-specifiers "for<P>
|
||
|
|
declaration" and "for discrimination" is a simplifying step -- it is a<P>
|
||
|
|
much simpler rule to state that the type-specifiers actually describe<P>
|
||
|
|
the collections of data they purport to name. Thus this is a step<P>
|
||
|
|
towards increased elegance.<P>
|
||
|
|
<P>
|
||
|
|
<P>
|
||
|
|
<B>Discussion:<P>
|
||
|
|
</B><P>
|
||
|
|
This issue was prompted by a lengthy discussion on the Common Lisp<P>
|
||
|
|
mailing list. See for example a series of exchanges started on Thu, <P>
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17 Dec 87 10:48:05 PST by Jeff Barnett <jbarnett@nrtc.northrop.com><P>
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under the subject line of "Types in CL". See also the exchange started <P>
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Wed, 6 Jan 88 23:21:16 PST by Jon L White <edsel!jonl@labrea.stanford.edu><P>
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under the subject line of "TYPEP warp implications"<P>
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<P>
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Although the types <A REL=DEFINITION HREF="../Body/a_string.htm#string"><B>STRING</B></A>, <A REL=DEFINITION HREF="../Body/t_bt_vec.htm#bit-vector"><B>BIT-VECTOR</B></A>, <A REL=DEFINITION HREF="../Body/t_smp_st.htm#simple-string"><B>SIMPLE-STRING</B></A>, and <P>
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<A REL=DEFINITION HREF="../Body/t_smp_bt.htm#simple-bit-vector"><B>SIMPLE-BIT-VECTOR</B></A> are subtypes of the <A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> type, they are not<P>
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specifically discussed in this proposal. The reason is that <P>
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they are not type-specifiers "that specialize", but are merely <P>
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abbreviations as follows:<P>
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<A REL=DEFINITION HREF="../Body/a_string.htm#string"><B>STRING</B></A> == (<A REL=DEFINITION HREF="../Body/a_vector.htm#vector"><B>VECTOR</B></A> STRING-CHAR)<P>
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<A REL=DEFINITION HREF="../Body/t_smp_st.htm#simple-string"><B>SIMPLE-STRING</B></A> == (<A REL=DEFINITION HREF="../Body/t_smp_ar.htm#simple-array"><B>SIMPLE-ARRAY</B></A> STRING-CHAR (*))<P>
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<A REL=DEFINITION HREF="../Body/t_bt_vec.htm#bit-vector"><B>BIT-VECTOR</B></A> == (<A REL=DEFINITION HREF="../Body/a_vector.htm#vector"><B>VECTOR</B></A> <A REL=DEFINITION HREF="../Body/a_bit.htm#bit"><B>BIT</B></A>)<P>
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<A REL=DEFINITION HREF="../Body/t_smp_bt.htm#simple-bit-vector"><B>SIMPLE-BIT-VECTOR</B></A> == (<A REL=DEFINITION HREF="../Body/t_smp_ar.htm#simple-array"><B>SIMPLE-ARRAY</B></A> <A REL=DEFINITION HREF="../Body/a_bit.htm#bit"><B>BIT</B></A> (*))<P>
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Thus their semantics could be affected only in an implementation that<P>
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doesn't support a specific "specialized storage" type for arrays of<P>
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bits and vectors of string-chars. But in fact, every CL implementation <P>
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must appear to support "specialized storage" for bit-arrays and strings,<P>
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even if it means nothing more than remembering the fact that such an<P>
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array was created with that element-type. This is required in order<P>
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for strings, bit-vectors, and bit-arrays to be disjoint datatypes <P>
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(see CLtL p.34; see also <A REL=DEFINITION HREF="../Body/s_the.htm#the"><B>the</B></A> definitions of BIT-ARRAY <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> <A REL=DEFINITION HREF="../Body/a_string.htm#string"><B>STRING</B></A> found <P>
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in CLtL p.293, Section 17.4, <A REL=DEFINITION HREF="../Body/a_and.htm#and"><B>and</B></A> in CLtL p.299.)<P>
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<P>
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We considered the possibility of flushing the permission to "upgrade";<P>
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for example, it could be made a requirement that:<P>
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(<A REL=DEFINITION HREF="../Body/f_ar_ele.htm#array-element-type"><B>ARRAY-ELEMENT-TYPE</B></A> (<A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> <n> :ELEMENT-TYPE <type>))<P>
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always be equal to <type> (or, at least type-equivalent to <type>)<P>
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for all valid type specifiers <type>. This has several problems: it<P>
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increases the storage requirement for many kinds of arrays, and hides<P>
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a relevant part of the underlying implementation for no apparently <P>
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good reason. However, it would increase portability, since it would be <P>
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much more difficult, for example, to write a program that created an<P>
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array with one element-type, say, (<A REL=DEFINITION HREF="../Body/t_unsgn_.htm#unsigned-byte"><B>UNSIGNED-BYTE</B></A> 5), but operated on it <P>
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assuming a non-trivial upgraded element-type, say, (<A REL=DEFINITION HREF="../Body/t_unsgn_.htm#unsigned-byte"><B>UNSIGNED-BYTE</B></A> 8).<P>
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Under this proposal, it is valid for an implementation of <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>MAKE-ARRAY</B></A> <P>
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to have arrays "remember" the type-equivalence <A REL=DEFINITION HREF="../Body/t_class.htm#class"><B>class</B></A> of the original <P>
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:element-type argument; such an implementation would satisfy all of <P>
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the constraints listed above.<P>
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<P>
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We considered a suggestion to restrict the set of "known" array element <P>
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types; this would gain portability at the expense of limiting the <P>
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language.<P>
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<P>
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We considered leaving out of the proposal the addition of the two<P>
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functions <A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> and <A REL=DEFINITION HREF="../Body/f_upgrad.htm#upgraded-complex-part-type"><B>UPGRADED-COMPLEX-PART-TYPE</B></A>.<P>
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But it was noted that every implementation of CL supports exactly<P>
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that functionality somewhere in its implementation of MAKE-ARRAY; and<P>
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exposing this to the user would be a good thing. Furthermore, the<P>
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existence of at least <A REL=DEFINITION HREF="../Body/f_upgr_1.htm#upgraded-array-element-type"><B>UPGRADED-ARRAY-ELEMENT-TYPE</B></A> makes the clarifications<P>
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on "upgrading" and <A REL=DEFINITION HREF="../Body/f_subtpp.htm#subtypep"><B>SUBTYPEP</B></A> implications easier. Finally, there would<P>
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be no other way at all to pinpoint just how complex parts are upgraded,<P>
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since there is no type information available except for the actual<P>
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types of the parts.<P>
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<P>
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Since this proposal contains the implication:<P>
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(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type1>) is-type-equivalent-to (<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <type2>)<P>
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==> <P>
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<type1> is-type-equivalent-to <type2><P>
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then the question naturally arises "Does the reverse implication hold?" <P>
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That is, should two non-EQ but type-equivalent type-specifiers <type1><P>
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and <type2> always give rise to the same array types? For example, <P>
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consider <A REL=DEFINITION HREF="../Body/t_short_.htm#short-float"><B>SHORT-FLOAT</B></A> and <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A> in an implementation where these <P>
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are type-equivalent (see CLtL section 2.1.3). One may desire to implement <P>
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(<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <A REL=DEFINITION HREF="../Body/t_short_.htm#short-float"><B>SHORT-FLOAT</B></A>) and (<A REL=DEFINITION HREF="../Body/t_array.htm#array"><B>ARRAY</B></A> <A REL=DEFINITION HREF="../Body/t_short_.htm#single-float"><B>SINGLE-FLOAT</B></A>) differently. Say, for example <P>
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that the former is packed into 16-bit half-words, whereas the latter is <P>
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packed into 32-bit words; but for either kind of packing, the result of <P>
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<A REL=DEFINITION HREF="../Body/f_aref.htm#aref"><B>AREF</B></A> is an ordinary "single-float". The whole point of the type-specifier<P>
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to <A REL=DEFINITION HREF="../Body/f_mk_ar.htm#make-array"><B>make-array</B></A> is merely to specify a packing technique for "packed float" <P>
|
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arrays. This "krinkle", however, will not be addressed by the proposal <P>
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herein; it should simply be remembered that the implication above goes <P>
|
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only one way, and is not an "if-and-only-if" link.<P>
|
||
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</PRE>
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