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<H1> 4.5.1 Logical Operators and Short-circuit Control Forms</H1>
<H4 ALIGN=CENTER>Name Resolution Rules</H4>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2576"></A><A NAME="I2577"></A><A NAME="I2578"></A>An
<FONT FACE="Arial, Helvetica">expression</FONT> consisting of two <FONT FACE="Arial, Helvetica">relation</FONT>s
connected by <B>and then</B> or <B>or else</B> (a <I>short-circuit control
form</I>) shall resolve to be of some boolean type; <A NAME="I2579"></A>the
expected type for both <FONT FACE="Arial, Helvetica">relation</FONT>s
is that same boolean type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>1.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Reason: </B>This rule is written
this way so that overload resolution treats the two operands symmetrically;
the resolution of overloading present in either one can benefit from
the resolution of the other. Furthermore, the type expected by context
can help. </FONT></DIV>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <A NAME="I2580"></A><A NAME="I2581"></A><A NAME="I2582"></A><A NAME="I2583"></A><A NAME="I2584"></A><A NAME="I2585"></A><A NAME="I2586"></A><A NAME="I2587"></A>The
following logical operators are predefined for every boolean type <I>T</I>,
for every modular type <I>T</I>, and for every one-dimensional array
type <I>T</I> whose component type is a boolean type: <A NAME="I2588"></A></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="Examples"><TT><B>function</B> "<B>and</B>"(Left, Right : <I>T</I>) <B>return</B> <I>T</I><BR>
<B>function</B> "<B>or</B>" (Left, Right : <I>T</I>) <B>return</B> <I>T</I><BR>
<B>function</B> "<B>xor</B>"(Left, Right : <I>T</I>) <B>return</B> <I>T</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>To be honest: </B>For predefined
operators, the parameter and result subtypes shown as <I>T</I> are actually
the unconstrained subtype of the type. </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="Normal"> For boolean types, the predefined logical operators
<B>and</B>, <B>or</B>, and <B>xor</B> perform the conventional operations
of conjunction, inclusive disjunction, and exclusive disjunction, respectively.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="Normal"> For modular types, the predefined logical operators
are defined on a bit-by-bit basis, using the binary representation of
the value of the operands to yield a binary representation for the result,
where zero represents False and one represents True. If this result is
outside the base range of the type, a final subtraction by the modulus
is performed to bring the result into the base range of the type.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="Normal"> The logical operators on arrays are performed
on a component-by-component basis on matching components (as for equality
-- see <A HREF="AA-4-5-2.html">4.5.2</A>), using the predefined logical
operator for the component type. The bounds of the resulting array are
those of the left operand.</DIV>
<H4 ALIGN=CENTER>Dynamic Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2589"></A>The short-circuit control
forms <B>and then</B> and <B>or else</B> deliver the same result as the
corresponding predefined <B>and</B> and <B>or</B> operators for boolean
types, except that the left operand is always evaluated first, and the
right operand is not evaluated if the value of the left operand determines
the result.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2590"></A><A NAME="I2591"></A>For the
logical operators on arrays, a check is made that for each component
of the left operand there is a matching component of the right operand,
and vice versa. <A NAME="I2592"></A><A NAME="I2593"></A>Also, a check
is made that each component of the result belongs to the component subtype.
<A NAME="I2594"></A>The exception Constraint_Error is raised if either
of the above checks fails. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Discussion: </B>The check against
the component subtype is per AI83-00535. </FONT></DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Notes" Style="margin-bottom: 0.4em"><FONT SIZE=-1>12 The
conventional meaning of the logical operators is given by the following
truth table: </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1> A B (A <B>and</B> B) (A <B>or</B> B) (A <B>xor</B> B)<BR>
<BR>
True True True True False<BR>
True False False True True<BR>
False True False True True<BR>
False False False False False</FONT></DIV>
<H4 ALIGN=CENTER>Examples</H4>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <I>Examples of
logical operators:</I> </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Examples"><TT>Sunny <B>or</B> Warm<BR>
Filter(1 .. 10) <B>and</B> Filter(15 .. 24) <I>-- see <A HREF="AA-3-6-1.html">3.6.1</A> </I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Wide" Style="margin-bottom: 0.4em"> <I>Examples of short-circuit
control forms:</I> </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>14</FONT></DIV>
<DIV Class="Examples"><TT>Next_Car.Owner /= <B>null</B> <B>and</B> <B>then</B> Next_Car.Owner.Age > 25 <I>-- see <A HREF="AA-3-10-1.html">3.10.1</A></I><BR>
N = 0 <B>or</B> <B>else</B> A(N) = Hit_Value</TT></DIV>
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