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133 lines
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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: Function SUBTYPEP</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="m_deftp.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="c_types_.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="f_tp_of.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Next]" SRC="../Graphics/Next.gif" ALIGN=Bottom></A></H1>
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<A NAME="subtypep"><I>Function</I> <B>SUBTYPEP</B></A> <P>
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<P>
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<P><B>Syntax:</B><P>
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<P>
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<B>subtypep</B> <I>type-1 type-2 <TT>&optional</TT> environment</I> => <I>subtype-p, valid-p</I><P>
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<P>
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<P><B>Arguments and Values:</B><P>
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<P>
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<I>type-1</I>---a <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifier</I></A>. <P>
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<I>type-2</I>---a <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifier</I></A>. <P>
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<I>environment</I>---an <A REL=DEFINITION HREF="26_glo_e.htm#environment"><I>environment</I></A> <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>object</I></A>. The default is <A REL=DEFINITION HREF="a_nil.htm#nil"><B>nil</B></A>, denoting the <A REL=DEFINITION HREF="26_glo_n.htm#null_lexical_environment"><I>null lexical environment</I></A> and the current <A REL=DEFINITION HREF="26_glo_g.htm#global_environment"><I>global environment</I></A>. <P>
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<I>subtype-p</I>---a <A REL=DEFINITION HREF="26_glo_g.htm#generalized_boolean"><I>generalized boolean</I></A>. <P>
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<I>valid-p</I>---a <A REL=DEFINITION HREF="26_glo_g.htm#generalized_boolean"><I>generalized boolean</I></A>. <P>
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<P><B>Description:</B><P>
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<P>
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If <I>type-1</I> is a <A REL=DEFINITION HREF="26_glo_r.htm#recognizable_subtype"><I>recognizable subtype</I></A> of <I>type-2</I>, the first <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A> is <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A>. Otherwise, the first <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A> is <A REL=DEFINITION HREF="26_glo_f.htm#false"><I>false</I></A>, indicating that either <I>type-1</I> is not a <A REL=DEFINITION HREF="26_glo_s.htm#subtype"><I>subtype</I></A> of <I>type-2</I>, or else <I>type-1</I> is a <A REL=DEFINITION HREF="26_glo_s.htm#subtype"><I>subtype</I></A> of <I>type-2</I> but is not a <A REL=DEFINITION HREF="26_glo_r.htm#recognizable_subtype"><I>recognizable subtype</I></A>. <P>
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A second <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A> is also returned indicating the `certainty' of the first <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A>. If this value is <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A>, then the first value is an accurate indication of the <A REL=DEFINITION HREF="26_glo_s.htm#subtype"><I>subtype</I></A> relationship. (The second <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A> is always <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> when the first <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>value</I></A> is <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A>.) <P>
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The next figure summarizes the possible combinations of <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> that might result. <P>
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<PRE>
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Value 1 Value 2 Meaning
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<A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> type-1 is definitely a <A REL=DEFINITION HREF="26_glo_s.htm#subtype">subtype</A> of type-2.
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<A REL=DEFINITION HREF="26_glo_f.htm#false">false</A> <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> type-1 is definitely not a <A REL=DEFINITION HREF="26_glo_s.htm#subtype">subtype</A> of type-2.
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<A REL=DEFINITION HREF="26_glo_f.htm#false">false</A> <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A> <A REL=DEFINITION HREF="#subtypep">subtypep</A> could not determine the relationship,
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so type-1 might or might not be a <A REL=DEFINITION HREF="26_glo_s.htm#subtype">subtype</A> of type-2.
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</PRE>
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<P><B>Figure 4-9. Result possibilities for subtypep</B> <P>
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<P>
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<A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> is permitted to return the <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> <A REL=DEFINITION HREF="26_glo_f.htm#false"><I>false</I></A> and <A REL=DEFINITION HREF="26_glo_f.htm#false"><I>false</I></A> only when at least one argument involves one of these <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A>: <B>and</B>, <B>eql</B>, the list form of <B>function</B>, <B>member</B>, <B>not</B>, <B>or</B>, <B>satisfies</B>, or <B>values</B>. (A <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifier</I></A> `involves' such a <A REL=DEFINITION HREF="26_glo_s.htm#symbol"><I>symbol</I></A> if, after being <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <I>expanded</I>, it contains that <A REL=DEFINITION HREF="26_glo_s.htm#symbol"><I>symbol</I></A> in a position that would call for its meaning as a <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifier</I></A> to be used.) One consequence of this is that if neither <I>type-1</I> nor <I>type-2</I> involves any of these <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A>, then <A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> is obliged to determine the relationship accurately. In particular, <A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> returns the <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> and <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> if the arguments are <A REL=DEFINITION HREF="f_equal.htm#equal"><B>equal</B></A> and do not involve any of these <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A>. <P>
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<A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> never returns a second value of <A REL=DEFINITION HREF="a_nil.htm#nil"><B>nil</B></A> when both <I>type-1</I> and <I>type-2</I> involve only the names in <A REL=DEFINITION HREF="04_bc.htm#standardizedatomictypespecs">Figure 4-2</A>, or names of <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>types</I></A> defined by <A REL=DEFINITION HREF="m_defstr.htm#defstruct"><B>defstruct</B></A>, <A REL=DEFINITION HREF="m_defi_5.htm#define-condition"><B>define-condition</B></A>, or <A REL=DEFINITION HREF="m_defcla.htm#defclass"><B>defclass</B></A>, or <A REL=DEFINITION HREF="26_glo_d.htm#derived_type"><I>derived types</I></A> that expand into only those names. While <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> listed in <A REL=DEFINITION HREF="04_bc.htm#standardizedatomictypespecs">Figure 4-2</A> and names of <A REL=DEFINITION HREF="m_defcla.htm#defclass"><B>defclass</B></A> and <A REL=DEFINITION HREF="m_defstr.htm#defstruct"><B>defstruct</B></A> can in some cases be implemented as <A REL=DEFINITION HREF="26_glo_d.htm#derived_type"><I>derived types</I></A>, <A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> regards them as primitive. <P>
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The relationships between <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>types</I></A> reflected by <A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> are those specific to the particular implementation. For example, if an implementation supports only a single type of floating-point numbers, in that implementation <TT>(subtypep 'float 'long-float)</TT> returns the <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> and <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> (since the two <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>types</I></A> are identical). <P>
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For all <I>T1</I> and <I>T2</I> other than <TT>*</TT>, <TT>(array </TT><I>T1</I><TT>)</TT> and <TT>(array </TT><I>T2</I><TT>)</TT> are two different <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> that always refer to the same sets of things if and only if they refer to <A REL=DEFINITION HREF="26_glo_a.htm#array"><I>arrays</I></A> of exactly the same specialized representation, i.e., if <TT>(upgraded-array-element-type '</TT><I>T1</I><TT>)</TT> and <TT>(upgraded-array-element-type '</TT><I>T2</I><TT>)</TT> return two different <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> that always refer to the same sets of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A>. This is another way of saying that <TT>`(array </TT><I>type-specifier</I><TT>)</TT> and <TT>`(array ,(upgraded-array-element-type '</TT><I>type-specifier</I><TT>))</TT> refer to the same set of specialized <A REL=DEFINITION HREF="26_glo_a.htm#array"><I>array</I></A> representations. For all <I>T1</I> and <I>T2</I> other than <TT>*</TT>, the intersection of <TT>(array </TT><I>T1</I><TT>)</TT> and <TT>(array </TT><I>T2</I><TT>)</TT> is the empty set if and only if they refer to <A REL=DEFINITION HREF="26_glo_a.htm#array"><I>arrays</I></A> of different, distinct specialized representations. <P>
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Therefore, <P>
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<PRE>
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(subtypep '(array T1) '(array T2)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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</PRE>
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</TT> if and only if <P>
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<PRE>
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(upgraded-array-element-type 'T1) and
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(upgraded-array-element-type 'T2)
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</PRE>
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</TT> <P>
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return two different <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> that always refer to the same sets of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A>. <P>
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For all type-specifiers <I>T1</I> and <I>T2</I> other than <TT>*</TT>, <P>
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<PRE>
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(subtypep '(complex T1) '(complex T2)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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</PRE>
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</TT> <P>
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if: <P><DL><DT>1. <TT>T1</TT> is a <A REL=DEFINITION HREF="26_glo_s.htm#subtype"><I>subtype</I></A> of <TT>T2</TT>, or <DD><DT>2. <TT>(upgraded-complex-part-type '</TT><I>T1</I><TT>)</TT> and <TT>(upgraded-complex-part-type '</TT><I>T2</I><TT>)</TT> return two different <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> that always refer to the same sets of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A>; in this case, <TT>(complex </TT><I>T1</I><TT>)</TT> and <TT>(complex </TT><I>T2</I><TT>)</TT> both refer to the same specialized representation. <P><DD></DL>The <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> are <A REL=DEFINITION HREF="26_glo_f.htm#false"><I>false</I></A> and <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> otherwise. <P>
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The form <P>
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<PRE>
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(subtypep '(complex single-float) '(complex float))
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</PRE>
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</TT> must return <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> in all implementations, but <P>
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<PRE>
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(subtypep '(array single-float) '(array float))
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</PRE>
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</TT> <P>
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returns <A REL=DEFINITION HREF="26_glo_t.htm#true"><I>true</I></A> only in implementations that do not have a specialized <A REL=DEFINITION HREF="26_glo_a.htm#array"><I>array</I></A> representation for <A REL=DEFINITION HREF="26_glo_s.htm#single_float"><I>single floats</I></A> distinct from that for other <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>floats</I></A>. <P>
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<P>
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<P><B>Examples:</B><P>
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<P>
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<PRE>
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(subtypep 'compiled-function 'function) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep 'null 'list) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep 'null 'symbol) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep 'integer 'string) => <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep '(satisfies dummy) nil) => <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>, <A REL=DEFINITION HREF="26_glo_i.htm#implementation-dependent">implementation-dependent</A>
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(subtypep '(integer 1 3) '(integer 1 4)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep '(integer (0) (0)) 'nil) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep 'nil '(integer (0) (0))) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep '(integer (0) (0)) '(member)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> ;or <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>, <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>
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(subtypep '(member) 'nil) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> ;or <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>, <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>
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(subtypep 'nil '(member)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A> ;or <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>, <A REL=DEFINITION HREF="26_glo_f.htm#false">false</A>
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</PRE>
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</TT> <P>
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Let <TT><aet-x></TT> and <TT><aet-y></TT> be two distinct <A REL=DEFINITION HREF="26_glo_t.htm#type_specifier"><I>type specifiers</I></A> that do not always refer to the same sets of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A> in a given implementation, but for which <A REL=DEFINITION HREF="f_mk_ar.htm#make-array"><B>make-array</B></A>, will return an <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>object</I></A> of the same <A REL=DEFINITION HREF="26_glo_a.htm#array"><I>array</I></A> <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A>. <P>
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Thus, in each case, <P>
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<PRE>
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(subtypep (array-element-type (make-array 0 :element-type '<aet-x>))
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(array-element-type (make-array 0 :element-type '<aet-y>)))
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=> <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep (array-element-type (make-array 0 :element-type '<aet-y>))
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(array-element-type (make-array 0 :element-type '<aet-x>)))
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=> <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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</PRE>
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</TT> <P>
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If <TT>(array <aet-x>)</TT> and <TT>(array <aet-y>)</TT> are different names for exactly the same set of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A>, these names should always refer to the same sets of <A REL=DEFINITION HREF="26_glo_o.htm#object"><I>objects</I></A>. That implies that the following set of tests are also true: <P>
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<PRE>
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(subtypep '(array <aet-x>) '(array <aet-y>)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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(subtypep '(array <aet-y>) '(array <aet-x>)) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>, <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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</PRE>
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</TT> <P>
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<P><B>Side Effects:</B> None.
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<P>
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<P><B>Affected By:</B> None.
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<P>
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<P><B>Exceptional Situations:</B> None.
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<P>
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<P><B>See Also:</B><P>
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<P>
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<A REL=CHILD HREF="04_b.htm">Section 4.2 (Types)</A> <P>
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<P><B>Notes:</B><P>
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<P>
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The small differences between the <A REL=DEFINITION HREF="#subtypep"><B>subtypep</B></A> specification for the <A REL=DEFINITION HREF="t_array.htm#array"><B>array</B></A> and <A REL=DEFINITION HREF="t_comple.htm#complex"><B>complex</B></A> types are necessary because there is no creation function for <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complexes</I></A> which allows the specification of the resultant part type independently of the actual types of the parts. Thus in the case of the <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <A REL=DEFINITION HREF="t_comple.htm#complex"><B>complex</B></A>, the actual type of the parts is referred to, although a <A REL=DEFINITION HREF="26_glo_n.htm#number"><I>number</I></A> can be a member of more than one <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A>. For example, <TT>17</TT> is of <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <TT>(mod 18)</TT> as well as <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <TT>(mod 256)</TT> and <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <A REL=DEFINITION HREF="t_intege.htm#integer"><B>integer</B></A>; and <TT>2.3f5</TT> is of <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <A REL=DEFINITION HREF="t_short_.htm#single-float"><B>single-float</B></A> as well as <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> <A REL=DEFINITION HREF="t_float.htm#float"><B>float</B></A>. <P>
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<P>
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<P><HR>The following <A REL=META HREF="../Front/X3J13Iss.htm">X3J13 cleanup issues</A>, <I>not part of the specification</I>, apply to this section:<P><UL><LI> <A REL=CHILD HREF="../Issues/iss015.htm">ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS:UNIFY-UPGRADING</A><LI> <A REL=CHILD HREF="../Issues/iss335.htm">SUBTYPEP-TOO-VAGUE:CLARIFY-MORE</A><LI> <A REL=CHILD HREF="../Issues/iss334.htm">SUBTYPEP-ENVIRONMENT:ADD-ARG</A><P></UL><HR>
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