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<h1 class="chapter"> 8. Control Structures </h1>
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<tr><td align="left" valign="top"><a href="#SEC321">8.1 Control</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC353">8.2 Template-based Iteration</a></td><td> </td><td align="left" valign="top">
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<h2 class="section"> 8.1 Control </h2>
<p>Note: in the following descriptions, an <em>instructionlist</em> can be a list or
a word. In the latter case, the word is parsed into list form before it is
run. Thus, <tt>RUN READWORD</tt> or <tt>RUN READLIST</tt> will work. The
former is slightly preferable because it allows for a continued line (with <code>~</code>)
that includes a comment (with <code>;</code>) on the first line.
</p>
<p>A <var>tf</var> input must be the word <code>TRUE</code>, the word <code>FALSE</code>, or a list. If it's a
list, then it must be a Logo expression, which will be evaluated to produce
a value that must be <code>TRUE</code> or <code>FALSE</code>. The comparisons with <code>TRUE</code> and <code>FALSE</code>
are always case-insensitive.
</p>
<p>A runlist can consist of either a single expression (that produces a value)
or zero or more instructions (that do something, rather than output a value),
depending on the context:
</p>
<table><tr><td> </td><td><pre class="example">PRINT IFELSE :X<0 ["NEGATIVE] ["POSITIVE] ; one value in each case
REPEAT 4 [PRINT "A PRINT "B] ; two instructions
</pre></td></tr></table>
<table class="menu" border="0" cellspacing="0">
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</td></tr>
<tr><td align="left" valign="top"><a href="#SEC323">runresult</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#SEC324">repeat</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#SEC325">forever</a></td><td> </td><td align="left" valign="top">
</td></tr>
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<tr><td align="left" valign="top"><a href="#SEC341">.maybeoutput</a></td><td> </td><td align="left" valign="top"> MAYBEOUTPUT
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</td></tr>
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</td></tr>
<tr><td align="left" valign="top"><a href="#SEC344">ignore</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC345">`</a></td><td> </td><td align="left" valign="top"></td></tr>
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</td></tr>
<tr><td align="left" valign="top"><a href="#SEC347">do.while</a></td><td> </td><td align="left" valign="top"> DO.WHILE
</td></tr>
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</td></tr>
<tr><td align="left" valign="top"><a href="#SEC349">do.until</a></td><td> </td><td align="left" valign="top"> DO.UNTIL
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</td></tr>
<tr><td align="left" valign="top"><a href="#SEC351">case</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC352">cond</a></td><td> </td><td align="left" valign="top">
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<h3 class="unnumberedsubsec"> run </h3>
<table><tr><td> </td><td><pre class="example">RUN instructionlist
</pre></td></tr></table>
<p>command or operation. Runs the Logo instructions in the input list;
outputs if the list contains an expression that outputs.
</p>
<p>See section <a href="usermanual_3.html#SEC74">readword</a> ,
<a href="usermanual_3.html#SEC73">readlist</a> .
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<h3 class="unnumberedsubsec"> runresult </h3>
<table><tr><td> </td><td><pre class="example">RUNRESULT instructionlist
</pre></td></tr></table>
<p>runs the instructions in the input; outputs an empty list if those
instructions produce no output, or a list whose only member is the
output from running the input instructionlist. Useful for inventing
command-or-operation control structures:
</p>
<table><tr><td> </td><td><pre class="example">local "result
make "result runresult [something]
if emptyp :result [stop]
output first :result
</pre></td></tr></table>
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<h3 class="unnumberedsubsec"> repeat </h3>
<table><tr><td> </td><td><pre class="example">REPEAT num instructionlist
</pre></td></tr></table>
<p>command. Runs the <var>instructionlist</var> repeatedly, <var>num</var> times.
</p>
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<h3 class="unnumberedsubsec"> forever </h3>
<table><tr><td> </td><td><pre class="example">FOREVER instructionlist
</pre></td></tr></table>
<p>command. Runs the "instructionlist" repeatedly, until something inside
the instructionlist (such as <code>STOP</code> or <code>THROW</code>) makes it stop.
</p>
<p>See section <a href="#SEC332">stop</a> ,
See section <a href="#SEC335">throw</a> .
</p>
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<h3 class="unnumberedsubsec"> repcount </h3>
<table><tr><td> </td><td><pre class="example">REPCOUNT
</pre></td></tr></table>
<p>outputs the repetition count of the innermost current <code>REPEAT</code> or
<code>FOREVER</code>, starting from 1. If no <code>REPEAT</code> or <code>FOREVER</code>
is active, outputs –1.
</p>
<p>The abbreviation <code>#</code> can be used for <code>REPCOUNT</code> unless the
<code>REPEAT</code> is inside the template input to a higher order procedure
such as <code>FOREACH</code>, in which case <code>#</code> has a different meaning.
</p>
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<h3 class="unnumberedsubsec"> if </h3>
<table><tr><td> </td><td><pre class="example">IF tf instructionlist
(IF tf instructionlist1 instructionlist2)
</pre></td></tr></table>
<p>command. If the first input has the value <code>TRUE</code>, then <code>IF</code> runs the second
input. If the first input has the value <code>FALSE</code>, then <code>IF</code> does nothing.
(If given a third input, IF acts like <code>IFELSE</code>, as described below.) It
is an error if the first input is not either <code>TRUE</code> or <code>FALSE</code>.
</p>
<p>For compatibility with earlier versions of Logo, if an <code>IF</code> instruction is
not enclosed in parentheses, but the first thing on the instruction line
after the second input expression is a literal list (i.e., a list in
square brackets), the <code>IF</code> is treated as if it were <code>IFELSE</code>, but a warning
message is given. If this aberrant <code>IF</code> appears in a procedure body, the
warning is given only the first time the procedure is invoked in each
Logo session.
</p>
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<h3 class="unnumberedsubsec"> ifelse </h3>
<table><tr><td> </td><td><pre class="example">IFELSE tf instructionlist1 instructionlist2
</pre></td></tr></table>
<p>command or operation. If the first input has the value <code>TRUE</code>, then
<code>IFELSE</code> runs the second input. If the first input has the value <code>FALSE</code>,
then <code>IFELSE</code> runs the third input. <code>IFELSE</code> outputs a value if the
<var>instructionlist</var> contains an expression that outputs a value.
</p>
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<h3 class="unnumberedsubsec"> test </h3>
<table><tr><td> </td><td><pre class="example">TEST tf
</pre></td></tr></table>
<p>command. Remembers its input, which must be <code>TRUE</code> or <code>FALSE</code>, for
use by later <code>IFTRUE</code> or <code>IFFALSE</code> instructions. The effect of
<code>TEST</code> is local to the procedure in which it is used; any corresponding
<code>IFTRUE</code> or <code>IFFALSE</code> must be in the same procedure or a subprocedure.
</p>
<p>See section <a href="#SEC331">iffalse</a> .
</p>
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<h3 class="unnumberedsubsec"> iftrue </h3>
<table><tr><td> </td><td><pre class="example">IFTRUE instructionlist
IFT instructionlist
</pre></td></tr></table>
<p>command. Runs its input if the most recent <code>TEST</code> instruction had a <code>TRUE</code>
input. The <code>TEST</code> must have been in the same procedure or a
superprocedure.
</p>
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<h3 class="unnumberedsubsec"> iffalse </h3>
<table><tr><td> </td><td><pre class="example">IFFALSE instructionlist
IFF instructionlist
</pre></td></tr></table>
<p>command. Runs its input if the most recent <code>TEST</code> instruction had a <code>FALSE</code>
input. The <code>TEST</code> must have been in the same procedure or a
superprocedure.
</p>
<p>See section <a href="#SEC329">test</a> .
</p>
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<h3 class="unnumberedsubsec"> stop </h3>
<table><tr><td> </td><td><pre class="example">STOP
</pre></td></tr></table>
<p>command. Ends the running of the procedure in which it appears.
Control is returned to the context in which that procedure was invoked.
The stopped procedure does not output a value.
</p>
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<h3 class="unnumberedsubsec"> output </h3>
<table><tr><td> </td><td><pre class="example">OUTPUT value
OP value
</pre></td></tr></table>
<p>command. Ends the running of the procedure in which it appears. That
procedure outputs the value <var>value</var> to the context in which it was
invoked. Don't be confused: <code>OUTPUT</code> itself is a command, but the
procedure that invokes <code>OUTPUT</code> is an operation.
</p>
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<h3 class="unnumberedsubsec"> catch </h3>
<table><tr><td> </td><td><pre class="example">CATCH tag instructionlist
</pre></td></tr></table>
<p>command or operation. Runs its second input. Outputs if that
<var>instructionlist</var> outputs. If, while running the instructionlist, a
<code>THROW</code> instruction is executed with a tag equal to the first input
(case-insensitive comparison), then the running of the <var>instructionlist</var> is
terminated immediately. In this case the <code>CATCH</code> outputs if a value input is
given to <code>THROW</code>. The <var>tag</var> must be a word.
</p>
<p>If the tag is the word <code>ERROR</code>, then any error condition that arises
during the running of the instructionlist has the effect of <tt>THROW "ERROR</tt>
instead of printing an error message and returning to toplevel. The
<code>CATCH</code> does not output if an error is caught. Also, during the running
of the instructionlist, the variable <code>ERRACT</code> is temporarily unbound. (If
there is an error while <code>ERRACT</code> has a value, that value is taken as an
instructionlist to be run after printing the error message. Typically
the value of <code>ERRACT</code>, if any, is the list <code>[PAUSE]</code>.)
</p>
<p>See section <a href="#SEC336">error</a> ,
<a href="usermanual_11.html#SEC378">erract</a> ,
<a href="#SEC337">pause</a> .
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<h3 class="unnumberedsubsec"> throw </h3>
<table><tr><td> </td><td><pre class="example">THROW tag
(THROW tag value)
</pre></td></tr></table>
<p>command. Must be used within the scope of a <code>CATCH</code> with an equal tag.
Ends the running of the instructionlist of the <code>CATCH</code>. If <code>THROW</code> is used
with only one input, the corresponding <code>CATCH</code> does not output a value.
If <code>THROW</code> is used with two inputs, the second provides an output for the
<code>CATCH</code>.
</p>
<p><tt>THROW "TOPLEVEL</tt> can be used to terminate all running procedures and
interactive pauses, and return to the toplevel instruction prompt. Typing the
system interrupt character (<alt-S> for wxWidgets; otherwise normally
<control-C> for Unix, <control-Q> for DOS, or <command-period> for
Mac) has the same effect.
</p>
<p><tt>THROW "ERROR</tt> can be used to generate an error condition. If the error
is not caught, it prints a message (<code>THROW "ERROR</code>) with the usual
indication of where the error (in this case the <code>THROW</code>) occurred. If a
second input is used along with a tag of <code>ERROR</code>, that second input is
used as the text of the error message instead of the standard message.
Also, in this case, the location indicated for the error will be, not
the location of the <code>THROW</code>, but the location where the procedure
containing the <code>THROW</code> was invoked. This allows user-defined procedures
to generate error messages as if they were primitives. Note: in this
case the corresponding <tt>CATCH "ERROR</tt>, if any, does not output, since the
second input to <code>THROW</code> is not considered a return value.
</p>
<p><tt>THROW "SYSTEM</tt> immediately leaves Logo, returning to the operating
system, without printing the usual parting message and without deleting
any editor temporary file written by EDIT.
</p>
<p>See section <a href="usermanual_7.html#SEC300">edit</a> .
</p>
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<h3 class="unnumberedsubsec"> error </h3>
<table><tr><td> </td><td><pre class="example">ERROR
</pre></td></tr></table>
<p>outputs a list describing the error just caught, if any. If there was not an
error caught since the last use of <code>ERROR</code>, the empty list will be
output. The error list contains four members: an integer code corresponding
to the type of error, the text of the error message (as a single word
including spaces), the name of the procedure in which the error occurred, and
the instruction line on which the error occurred.
</p>
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<h3 class="unnumberedsubsec"> pause </h3>
<table><tr><td> </td><td><pre class="example">PAUSE
</pre></td></tr></table>
<p>command or operation. Enters an interactive pause. The user is
prompted for instructions, as at toplevel, but with a prompt that
includes the name of the procedure in which <code>PAUSE</code> was invoked. Local
variables of that procedure are available during the pause. <code>PAUSE</code>
outputs if the pause is ended by a <code>CONTINUE</code> with an input.
</p>
<p>If the variable <code>ERRACT</code> exists, and an error condition occurs, the
contents of that variable are run as an instructionlist. Typically
<code>ERRACT</code> is given the value <code>[PAUSE]</code> so that an interactive pause will be
entered in the event of an error. This allows the user to check values
of local variables at the time of the error.
</p>
<p>Typing the system quit character (<alt-S> for wxWidgets; otherwise
normally <control-\> for Unix, <control-W> for DOS, or
<command-comma> for Mac) will also enter a pause.
</p>
<p>See section <a href="usermanual_11.html#SEC378">erract</a> .
</p>
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<h3 class="unnumberedsubsec"> continue </h3>
<table><tr><td> </td><td><pre class="example">CONTINUE value
CO value
(CONTINUE)
(CO)
</pre></td></tr></table>
<p>command. Ends the current interactive pause, returning to the context
of the <code>PAUSE</code> invocation that began it. If <code>CONTINUE</code> is given an input,
that value is used as the output from the <code>PAUSE</code>. If not, the <code>PAUSE</code> does
not output.
</p>
<p>Exceptionally, the <code>CONTINUE</code> command can be used without its default
input and without parentheses provided that nothing follows it on the
instruction line.
</p>
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<h3 class="unnumberedsubsec"> wait </h3>
<table><tr><td> </td><td><pre class="example">WAIT time
</pre></td></tr></table>
<p>command. Delays further execution for <var>time</var> 60ths of a second. Also
causes any buffered characters destined for the terminal to be printed
immediately. <tt>WAIT 0</tt> can be used to achieve this buffer flushing without actually waiting.
</p>
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<h3 class="unnumberedsubsec"> bye </h3>
<table><tr><td> </td><td><pre class="example">BYE
</pre></td></tr></table>
<p>command. Exits from Logo; returns to the operating system.
</p>
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<h3 class="unnumberedsubsec"> .maybeoutput </h3>
<table><tr><td> </td><td><pre class="example">.MAYBEOUTPUT value (special form)
</pre></td></tr></table>
<p>works like <code>OUTPUT</code> except that the expression that provides the input
value might not, in fact, output a value, in which case the effect is
like <code>STOP</code>. This is intended for use in control structure definitions,
for cases in which you don't know whether or not some expression
produces a value. Example:
</p>
<table><tr><td> </td><td><pre class="example">to invoke :function [:inputs] 2
.maybeoutput apply :function :inputs
end
? (invoke "print "a "b "c)
a b c
? print (invoke "word "a "b "c)
abc
</pre></td></tr></table>
<p>This is an alternative to <code>RUNRESULT</code>. It's fast and easy to use, at the
cost of being an exception to Logo's evaluation rules. (Ordinarily, it
should be an error if the expression that's supposed to provide an input
to something doesn't have a value.)
</p>
<p>See section <a href="#SEC333">output</a> ,
<a href="#SEC332">stop</a> ,
<a href="#SEC323">runresult</a> .
</p>
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<h3 class="unnumberedsubsec"> goto </h3>
<table><tr><td> </td><td><pre class="example">GOTO word
</pre></td></tr></table>
<p>command. Looks for a <code>TAG</code> command with the same input in the same
procedure, and continues running the procedure from the location of that
<code>TAG</code>. It is meaningless to use <code>GOTO</code> outside of a procedure.
</p>
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<h3 class="unnumberedsubsec"> tag </h3>
<table><tr><td> </td><td><pre class="example">TAG quoted.word
</pre></td></tr></table>
<p>command. Does nothing. The input must be a literal word following a
quotation mark (<code>"</code>), not the result of a computation. Tags are used by
the <code>GOTO</code> command.
</p>
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<h3 class="unnumberedsubsec"> ignore </h3>
<table><tr><td> </td><td><pre class="example">IGNORE value (library procedure)
</pre></td></tr></table>
<p>command. Does nothing. Used when an expression is evaluated for a side
effect and its actual value is unimportant.
</p>
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<h3 class="unnumberedsubsec"> ` </h3>
<table><tr><td> </td><td><pre class="example">` list (library procedure)
</pre></td></tr></table>
<p>outputs a list equal to its input but with certain substitutions. If a
member of the input list is the word ‘<samp>,</samp>’ (comma) then the following
member should be an instructionlist that produces an output when run.
That output value replaces the comma and the instructionlist. If a
member of the input list is the word ‘<samp>,@</samp>’ (comma atsign) then the
following member should be an instructionlist that outputs a list when
run. The members of that list replace the ‘<samp>,@</samp>’ and the instructionlist.
Example:
</p>
<table><tr><td> </td><td><pre class="example">show `[foo baz ,[bf [a b c]] garply ,@[bf [a b c]]]
</pre></td></tr></table>
<p>will print
</p>
<table><tr><td> </td><td><pre class="example">[foo baz [b c] garply b c]
</pre></td></tr></table>
<p>A word starting with ‘<samp>,</samp>’ or ‘<samp>,@</samp>’ is treated as if the rest of the
word were a one-word list, e.g., ‘<samp>,:foo</samp>’ is equivalent to ‘<samp>,[:Foo]</samp>’.
</p>
<p>A word starting with ‘<samp>",</samp>’ (quote comma) or ‘<samp>:,</samp>’ (colon comma)
becomes a word starting with ‘<samp>"</samp>’ or ‘<samp>:</samp>’ but with the result of
running the substitution (or its first word, if the result is a list)
replacing what comes after the comma.
</p>
<p>Backquotes can be nested. Substitution is done only for commas at
the same depth as the backquote in which they are found:
</p>
<table><tr><td> </td><td><pre class="example">? show `[a `[b ,[1+2] ,[foo ,[1+3] d] e] f]
[a ` [b , [1+2] , [foo 4 d] e] f]
?make "name1 "x
?make "name2 "y
? show `[a `[b ,:,:name1 ,",:name2 d] e]
[a ` [b , [:x] , ["y] d] e]
</pre></td></tr></table>
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<h3 class="unnumberedsubsec"> for </h3>
<table><tr><td> </td><td><pre class="example">FOR forcontrol instructionlist (library procedure)
</pre></td></tr></table>
<p>command. The first input must be a list containing three or four
members: (1) a word, which will be used as the name of a local variable;
(2) a word or list that will be evaluated as by <code>RUN</code> to determine a
number, the starting value of the variable; (3) a word or list that will
be evaluated to determine a number, the limit value of the variable; (4)
an optional word or list that will be evaluated to determine the step
size. If the fourth member is missing, the step size will be 1 or –1
depending on whether the limit value is greater than or less than the
starting value, respectively.
</p>
<p>The second input is an instructionlist. The effect of <code>FOR</code> is to run
that instructionlist repeatedly, assigning a new value to the control
variable (the one named by the first member of the <var>forcontrol</var> list) each
time. First the starting value is assigned to the control variable.
Then the value is compared to the limit value. <code>FOR</code> is complete when the
sign of <code>(current - limit)</code> is the same as the sign of the step size. (If
no explicit step size is provided, the instructionlist is always run at
least once. An explicit step size can lead to a zero-trip <code>FOR</code>, e.g.,
<tt>FOR [I 1 0 1] ...</tt>). Otherwise, the instructionlist is run, then the step is added to the current value of the control variable and FOR returns to
the comparison step.
</p>
<table><tr><td> </td><td><pre class="example">? for [i 2 7 1.5] [print :i]
2
3.5
5
6.5
?
</pre></td></tr></table>
<p>See section <a href="#SEC322">run</a> .
</p>
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<h3 class="unnumberedsubsec"> do.while </h3>
<table><tr><td> </td><td><pre class="example">DO.WHILE instructionlist tfexpression (library procedure)
</pre></td></tr></table>
<p>command. Repeatedly evaluates the <var>instructionlist</var> as long as the
evaluated
remains <code>TRUE</code>. Evaluates the first input first,
so the <var>instructionlist</var> is always run at least once. The
<var>tfexpression</var> must be an expressionlist whose value when evaluated is
<code>TRUE</code> or <code>FALSE</code>.
</p>
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<h3 class="unnumberedsubsec"> while </h3>
<table><tr><td> </td><td><pre class="example">WHILE tfexpression instructionlist (library procedure)
</pre></td></tr></table>
<p>command. Repeatedly evaluates the <var>instructionlist</var> as long as the
evaluated
remains <code>TRUE</code>. Evaluates the first input first,
so the <var>instructionlist</var> may never be run at all. The <var>tfexpression</var>
must be an expressionlist whose value when evaluated is <code>TRUE</code> or <code>FALSE</code>.
</p>
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<h3 class="unnumberedsubsec"> do.until </h3>
<table><tr><td> </td><td><pre class="example">DO.UNTIL instructionlist tfexpression (library procedure)
</pre></td></tr></table>
<p>command. Repeatedly evaluates the <var>instructionlist</var> as long as the
evaluated
remains <code>FALSE</code>. Evaluates the first input
first, so the <var>instructionlist</var> is always run at least once. The
<var>tfexpression</var> must be an expressionlist whose value when evaluated is
<code>TRUE</code> or <code>FALSE</code>.
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<h3 class="unnumberedsubsec"> until </h3>
<table><tr><td> </td><td><pre class="example">UNTIL tfexpression instructionlist (library procedure)
</pre></td></tr></table>
<p>command. Repeatedly evaluates the <var>instructionlist</var> as long as the
evaluated
remains <code>FALSE</code>. Evaluates the first input
first, so the <var>instructionlist</var> may never be run at all. The
<var>tfexpression</var> must be an expressionlist whose value when evaluated is
<code>TRUE</code> or <code>FALSE</code>.
</p>
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<h3 class="unnumberedsubsec"> case </h3>
<table><tr><td> </td><td><pre class="example">CASE value clauses (library procedure)
</pre></td></tr></table>
<p>command or operation. The second input is a list of lists (clauses);
each clause is a list whose first element is either a list of values
or the word <code>ELSE</code> and whose butfirst is a Logo expression or
instruction. <code>CASE</code> examines the clauses in order. If a clause begins
with the word <code>ELSE</code> (upper or lower case), then the butfirst of that
clause is evaluated and <code>CASE</code> outputs its value, if any. If the first
input to CASE is a member of the first element of a clause, then the
butfirst of that clause is evaluated and <code>CASE</code> outputs its value, if
any. If neither of these conditions is met, then <code>CASE</code> goes on to the
next clause. If no clause is satisfied, <code>CASE</code> does nothing.
Example:
</p>
<table><tr><td> </td><td><pre class="example">to vowelp :letter
output case :letter [ [[a e i o u] "true] [else "false] ]
end
</pre></td></tr></table>
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<h3 class="unnumberedsubsec"> cond </h3>
<table><tr><td> </td><td><pre class="example">COND clauses (library procedure)
</pre></td></tr></table>
<p>command or operation. The input is a list of lists (clauses); each
clause is a list whose first element is either an expression whose
value is <code>TRUE</code> or <code>FALSE</code>, or the word <code>ELSE</code>, and whose butfirst is a Logo
expression or instruction. <code>COND</code> examines the clauses in order. If a
clause begins with the word <code>ELSE</code> (upper or lower case), then the
butfirst of that clause is evaluated and <code>CASE</code> outputs its value, if
any. Otherwise, the first element of the clause is evaluated; the
resulting value must be <code>TRUE</code> or <code>FALSE</code>. If it's <code>TRUE</code>, then the
butfirst of that clause is evaluated and <code>COND</code> outputs its value, if
any. If the value is <code>FALSE</code>, then <code>COND</code> goes on to the next clause. If
no clause is satisfied, <code>COND</code> does nothing. Example:
</p>
<table><tr><td> </td><td><pre class="example">to evens :numbers ; select even numbers from a list
op cond [ [[emptyp :numbers] []]
[[evenp first :numbers] ; assuming EVENP is defined
fput first :numbers evens butfirst :numbers]
[else evens butfirst :numbers] ]
end
</pre></td></tr></table>
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<h2 class="section"> 8.2 Template-based Iteration </h2>
<p>The procedures in this section are iteration tools based on the idea of a
<em>template.</em> This is a generalization of an instruction list or an
expression list in which <em>slots</em> are provided for the tool to insert varying
data. Four different forms of template can be used.
</p>
<p>The most commonly used form for a template is ‘<samp>explicit-slot</samp>’ form, or
‘<samp>question mark</samp>’ form. Example:
</p>
<table><tr><td> </td><td><pre class="example">? show map [? * ?] [2 3 4 5]
[4 9 16 25]
?
</pre></td></tr></table>
<p>In this example, the <code>MAP</code> tool evaluated the template <code>[? * ?]</code>
repeatedly, with each of the members of the data list <code>[2 3 4 5]</code>
substituted in turn for the question marks. The same value was used for every
question mark in a given evaluation. Some tools allow for more than one datum
to be substituted in parallel; in these cases the slots are indicated by
<code>?1</code> for the first datum, <code>?2</code> for the second, and so on:
</p>
<table><tr><td> </td><td><pre class="example">? show (map [(word ?1 ?2 ?1)] [a b c] [d e f])
[ada beb cfc]
?
</pre></td></tr></table>
<p>If the template wishes to compute the datum number, the form <code>(? 1)</code> is
equivalent to <code>?1</code>, so <code>(? ?1)</code> means the datum whose number is given in
datum number 1. Some tools allow additional slot designations, as shown
in the individual descriptions.
</p>
<p>The second form of template is the ‘<samp>named-procedure</samp>’ form. If the
template is a word rather than a list, it is taken as the name of a procedure.
That procedure must accept a number of inputs equal to the number of parallel
data slots provided by the tool; the procedure is applied to all of the
available data in order. That is, if data <code>?1</code> through <code>?3</code> are
available, the template <code>"PROC</code> is equivalent to <tt>[PROC ?1 ?2 ?3]</tt>.
</p>
<table><tr><td> </td><td><pre class="example">? show (map "word [a b c] [d e f])
[ad be cf]
?
to dotprod :a :b ; vector dot product
op apply "sum (map "product :a :b)
end
</pre></td></tr></table>
<p>The third form of template is ‘<samp>named-slot</samp>’ or ‘<samp>lambda</samp>’ form. This
form is indicated by a template list containing more than one member, whose
first member is itself a list. The first member is taken as a list of names;
local variables are created with those names and given the available data in
order as their values. The number of names must equal the number of available
data. This form is needed primarily when one iteration tool must be used
within the template list of another, and the <code>?</code> notation would be ambiguous in
the inner template. Example:
</p>
<table><tr><td> </td><td><pre class="example">to matmul :m1 :m2 [:tm2 transpose :m2] ; multiply two matrices
output map [[row] map [[col] dotprod :row :col] :tm2] :m1
end
</pre></td></tr></table>
<p>The fourth form is ‘<samp>procedure text</samp>’ form, a variant of lambda form. In
this form, the template list contains at least two members, all of which are
lists. This is the form used by the <code>DEFINE</code> and <code>TEXT</code> primitives,
and <code>APPLY</code> accepts it so that the text of a defined procedure can be
used as a template.
</p>
<p>Note: The fourth form of template is interpreted differently from the others,
in that Logo considers it to be an independent defined procedure for the
purposes of <code>OUTPUT</code> and <code>STOP</code>. For example, the following two
instructions are identical:
</p>
<table><tr><td> </td><td><pre class="example">? print apply [[x] :x+3] [5]
8
? print apply [[x] [output :x+3]] [5]
8
</pre></td></tr></table>
<p>although the first instruction is in named-slot form and the second is in
procedure-text form. The named-slot form can be understood as telling Logo to
evaluate the expression <tt>:x+3</tt> in place of the entire invocation of
apply, with the variable <code>x</code> temporarily given the value <code>5</code>. The
procedure-text form can be understood as invoking the procedure
</p>
<table><tr><td> </td><td><pre class="example">to foo :x
output :x+3
end
</pre></td></tr></table>
<p>with input <code>5</code>, but without actually giving the procedure a name. If
the use of <code>OUTPUT</code> were interchanged in these two examples, we'd get errors:
</p>
<table><tr><td> </td><td><pre class="example">? print apply [[x] output :x+3] [5]
Can only use output inside a procedure
? print apply [[x] [:x+3]] [5]
You don't say what to do with 8
</pre></td></tr></table>
<p>The named-slot form can be used with <code>STOP</code> or <code>OUTPUT</code> inside a procedure,
to stop the enclosing procedure.
</p>
<p>The following iteration tools are extended versions of the ones in Appendix
B of the book <cite>Computer Science Logo Style, Volume 3: Advanced Topics</cite> by
Brian Harvey [MIT Press, 1987]. The extensions are primarily to allow for
variable numbers of inputs.
</p>
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<h3 class="unnumberedsubsec"> apply </h3>
<table><tr><td> </td><td><pre class="example">APPLY template inputlist
</pre></td></tr></table>
<p>command or operation. Runs the <var>template</var>, filling its slots with the
members of <var>inputlist.</var> The number of members in <var>inputlist</var> must be an
acceptable number of slots for <var>template</var>. It is illegal to apply the
primitive <code>TO</code> as a template, but anything else is okay. <code>APPLY</code> outputs
what <var>template</var> outputs, if anything.
</p>
<p>See section <a href="usermanual_7.html#SEC233">to</a> .
</p>
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<h3 class="unnumberedsubsec"> invoke </h3>
<table><tr><td> </td><td><pre class="example">INVOKE template input (library procedure)
(INVOKE template input1 input2 ...)
</pre></td></tr></table>
<p>command or operation. Exactly like <code>APPLY</code> except that the inputs are
provided as separate expressions rather than in a list.
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<h3 class="unnumberedsubsec"> foreach </h3>
<table><tr><td> </td><td><pre class="example">FOREACH data template (library procedure)
(FOREACH data1 data2 ... template)
</pre></td></tr></table>
<p>command. Evaluates the <var>template</var> list repeatedly, once for each member
of the <var>data</var> list. If more than one <var>data</var> list are given, each of them
must be the same length. (The <var>data</var> inputs can be words, in which case
the template is evaluated once for each character.)
</p>
<p>In a template, the symbol <code>?REST</code> represents the portion of the
<var>data</var> input to the right of the member currently being used as the
<code>?</code> slot-filler. That is, if the <var>data</var> input is
<code>[A B C D E]</code> and the template is being evaluated with <code>?</code>
replaced by <code>B</code>, then <code>?REST</code> would be replaced by
<code>[C D E]</code>. If multiple parallel slots are used, then
<tt>(?REST 1)</tt> goes with ?1, etc.
</p>
<p>In a template, the symbol <code>#</code> represents the position in the <var>data</var>
input of the member currently being used as the <code>?</code> slot-filler. That is, if
the data input is <code>[A B C D E]</code> and the template is being evaluated with
<code>?</code> replaced by <code>B</code>, then <code>#</code> would be replaced by <code>2</code>.
</p>
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<h3 class="unnumberedsubsec"> map </h3>
<table><tr><td> </td><td><pre class="example">MAP template data (library procedure)
(MAP template data1 data2 ...)
</pre></td></tr></table>
<p>outputs a word or list, depending on the type of the <var>data</var> input, of the
same length as that <var>data</var> input. (If more than one <var>data</var> input are
given, the output is of the same type as <var>data1</var>.) Each member of the
output is the result of evaluating the <var>template</var> list, filling the slots
with the corresponding member(s) of the <var>data</var> input(s). (All <var>data</var>
inputs must be the same length.) In the case of a word output, the results of
the template evaluation must be words, and they are concatenated with
<code>WORD</code>.
</p>
<p>In a template, the symbol <code>?REST</code> represents the portion of the data
input to the right of the member currently being used as the <code>?</code>
slot-filler. That is, if the <var>data</var> input is <code>[A B C D E]</code> and
the <var>template</var> is being evaluated with <code>?</code> replaced by <code>B</code>, then
<code>?REST</code> would be replaced by <code>[C D E]</code>. If multiple parallel
slots are used, then <tt>(?REST 1)</tt> goes with <code>?1</code>, etc.
</p>
<p>In a template, the symbol <code>#</code> represents the position in the <var>data</var>
input of the member currently being used as the <code>?</code> slot-filler. That
is, if the data input is <code>[A B C D E]</code> and the template is being
evaluated with <code>?</code> replaced by <code>B</code>, then <code>#</code> would be replaced
by <code>2</code>.
</p>
<p>See section <a href="usermanual_2.html#SEC8">word</a> .
</p>
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<h3 class="unnumberedsubsec"> map.se </h3>
<table><tr><td> </td><td><pre class="example">MAP.SE template data (library procedure)
(MAP.SE template data1 data2 ...)
</pre></td></tr></table>
<p>outputs a list formed by evaluating the <var>template</var> list repeatedly and
concatenating the results using <code>SENTENCE</code>. That is, the members of the
output are the members of the results of the evaluations. The output
list might, therefore, be of a different length from that of the <var>data</var>
input(s). (If the result of an evaluation is the empty list, it
contributes nothing to the final output.) The <var>data</var> inputs may be words
or lists.
</p>
<p>In a template, the symbol <code>?REST</code> represents the portion of the data
input to the right of the member currently being used as the <code>?</code>
slot-filler. That is, if the data input is <code>[A B C D E]</code> and the
template is being evaluated with <code>?</code> replaced by <code>B</code>, then
<code>?REST</code> would be replaced by <code>[C D E]</code>. If multiple parallel
slots are used, then <tt>(?REST 1)</tt> goes with <code>?1</code>, etc.
</p>
<p>In a template, the symbol <code>#</code> represents the position in the <var>data</var>
input of the member currently being used as the <code>?</code> slot-filler. That
is, if the data input is <code>[A B C D E]</code> and the template is being
evaluated with <code>?</code> replaced by <code>B</code>, then <code>#</code> would be replaced
by <code>2</code>.
</p>
<p>See section <a href="usermanual_2.html#SEC10">sentence</a> .
</p>
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<h3 class="unnumberedsubsec"> filter </h3>
<table><tr><td> </td><td><pre class="example">FILTER tftemplate data (library procedure)
</pre></td></tr></table>
<p>outputs a word or list, depending on the type of the <var>data</var> input,
containing a subset of the members (for a list) or characters (for a
word) of the input. The template is evaluated once for each member or
character of the data, and it must produce a <code>TRUE</code> or <code>FALSE</code> value. If
the value is <code>TRUE</code>, then the corresponding input constituent is included
in the output.
</p>
<table><tr><td> </td><td><pre class="example">? print filter "vowelp "elephant
eea
?
</pre></td></tr></table>
<p>In a template, the symbol <code>?REST</code> represents the portion of the
<var>data</var> input to the right of the member currently being used as the
<code>?</code> slot-filler. That is, if the data input is <code>[A B C D E]</code>
and the template is being evaluated with <code>?</code> replaced by <code>B</code>, then
<code>?REST</code> would be replaced by <code>[C D E]</code>.
</p>
<p>In a template, the symbol <code>#</code> represents the position in the <var>data</var>
input of the member currently being used as the <code>?</code> slot-filler. That
is, if the data input is <code>[A B C D E]</code> and the template is being
evaluated with <code>?</code> replaced by <code>B</code>, then <code>#</code> would be replaced
by <code>2</code>.
</p>
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<h3 class="unnumberedsubsec"> find </h3>
<table><tr><td> </td><td><pre class="example">FIND tftemplate data (library procedure)
</pre></td></tr></table>
<p>outputs the first constituent of the <var>data</var> input (the first member of a
list, or the first character of a word) for which the value produced by
evaluating the <var>template</var> with that consituent in its slot is <code>TRUE</code>.
If there is no such constituent, the empty list is output.
</p>
<p>In a template, the symbol <code>?REST</code> represents the portion of the
<var>data</var> input to the right of the member currently being used as the
<code>?</code> slot-filler. That is, if the data input is <code>[A B C D E]</code>
and the template is being evaluated with <code>?</code> replaced by <code>B</code>, then
<code>?REST</code> would be replaced by <code>[C D E]</code>.
</p>
<p>In a template, the symbol <code>#</code> represents the position in the <var>data</var>
input of the member currently being used as the <code>?</code> slot-filler. That
is, if the data input is <code>[A B C D E]</code> and the template is being
evaluated with <code>?</code> replaced by <code>B</code>, then <code>#</code> would be replaced
by <code>2</code>.
</p>
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<h3 class="unnumberedsubsec"> reduce </h3>
<table><tr><td> </td><td><pre class="example">REDUCE template data (library procedure)
</pre></td></tr></table>
<p>outputs the result of applying the <var>template</var> to accumulate the members of
the <var>data</var> input. The template must be a two-slot function. Typically it
is an associative function name like <code>SUM</code>. If the <var>data</var> input has
only one constituent (member in a list or character in a word), the output is
that consituent. Otherwise, the template is first applied with <code>?1</code>
filled with the next-to-last consitient and <code>?2</code> with the last
constituent. Then, if there are more constituents, the template is applied
with <code>?1</code> filled with the next constituent to the left and <code>?2</code> with
the result from the previous evaluation. This process continues until all
constituents have been used. The data input may not be empty.
</p>
<p>Note: If the template is, like <code>SUM</code>, the name of a procedure that is
capable of accepting arbitrarily many inputs, it is more efficient to
use <code>APPLY</code> instead of <code>REDUCE</code>. The latter is good for associative
procedures that have been written to accept exactly two inputs:
</p>
<table><tr><td> </td><td><pre class="example">to max :a :b
output ifelse :a > :b [:a] [:b]
end
print reduce "max [...]
</pre></td></tr></table>
<p>Alternatively, <code>REDUCE</code> can be used to write <code>MAX</code> as a procedure
that accepts any number of inputs, as <code>SUM</code> does:
</p>
<table><tr><td> </td><td><pre class="example">to max [:inputs] 2
if emptyp :inputs ~
[(throw "error [not enough inputs to max])]
output reduce [ifelse ?1 > ?2 [?1] [?2]] :inputs
end
</pre></td></tr></table>
<p>See section <a href="usermanual_4.html#SEC116">sum</a> ,
<a href="#SEC354">apply</a> .
</p>
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<h3 class="unnumberedsubsec"> crossmap </h3>
<table><tr><td> </td><td><pre class="example">CROSSMAP template listlist (library procedure)
(CROSSMAP template data1 data2 ...)
</pre></td></tr></table>
<p>outputs a list containing the results of template evaluations. Each
<var>data</var> list contributes to a slot in the template; the number of slots is
equal to the number of <var>data</var> list inputs. As a special case, if only one
<var>data</var> list input is given, that list is taken as a list of data lists,
and each of its members contributes values to a slot. <code>CROSSMAP</code> differs
from <code>MAP</code> in that instead of taking members from the data inputs in
parallel, it takes all possible combinations of members of data inputs,
which need not be the same length.
</p>
<table><tr><td> </td><td><pre class="example">? show (crossmap [word ?1 ?2] [a b c] [1 2 3 4])
[a1 a2 a3 a4 b1 b2 b3 b4 c1 c2 c3 c4]
?
</pre></td></tr></table>
<p>For compatibility with the version in the first edition of CSLS
<a name="DOCF1" href="usermanual_fot.html#FOOT1">(1)</a>, <code>CROSSMAP</code> templates may
use the notation <code>:1</code> instead of <code>?1</code> to indicate slots.
</p>
<p>See section <a href="#SEC357">map</a> .
</p>
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<h3 class="unnumberedsubsec"> cascade </h3>
<table><tr><td> </td><td><pre class="example">CASCADE endtest template startvalue (library procedure)
(CASCADE endtest tmp1 sv1 tmp2 sv2 ...)
(CASCADE endtest tmp1 sv1 tmp2 sv2 ... finaltemplate)
</pre></td></tr></table>
<p>outputs the result of applying a template (or several templates, as
explained below) repeatedly, with a given value filling the slot the
first time, and the result of each application filling the slot for the
following application.
</p>
<p>In the simplest case, <code>CASCADE</code> has three inputs. The second input is a
one-slot expression template. That template is evaluated some number of
times (perhaps zero). On the first evaluation, the slot is filled with
the third input; on subsequent evaluations, the slot is filled with the
result of the previous evaluation. The number of evaluations is
determined by the first input. This can be either a nonnegative
integer, in which case the template is evaluated that many times, or a
predicate expression template, in which case it is evaluated (with the
same slot filler that will be used for the evaluation of the second
input) repeatedly, and the <code>CASCADE</code> evaluation continues as long as the
predicate value is <code>FALSE</code>. (In other words, the predicate template
indicates the condition for stopping.)
</p>
<p>If the template is evaluated zero times, the output from <code>CASCADE</code> is the
third (<var>startvalue</var>) input. Otherwise, the output is the value produced
by the last template evaluation.
</p>
<p><code>CASCADE</code> templates may include the symbol <code>#</code> to represent the
number of times the template has been evaluated. This slot is filled with 1
for the first evaluation, 2 for the second, and so on.
</p>
<table><tr><td> </td><td><pre class="example">? show cascade 5 [lput # ?] []
[1 2 3 4 5]
? show cascade [vowelp first ?] [bf ?] "spring
ing
? show cascade 5 [# * ?] 1
120
?
</pre></td></tr></table>
<p>Several cascaded results can be computed in parallel by providing additional
template-startvalue pairs as inputs to <code>CASCADE</code>. In this case, all
templates (including the endtest template, if used) are multi-slot, with the
number of slots equal to the number of pairs of inputs. In each round of
evaluations, <code>?2</code>, for example, represents the result of evaluating the
second template in the previous round. If the total number of inputs
(including the first endtest input) is odd, then the output from CASCADE is
the final value of the first template. If the total number of inputs is even,
then the last input is a template that is evaluated once, after the end test
is satisfied, to determine the output from <code>CASCADE</code>.
</p>
<table><tr><td> </td><td><pre class="example">to fibonacci :n
output (cascade :n [?1 + ?2] 1 [?1] 0)
end
to piglatin :word
output (cascade [vowelp first ?] ~
[word bf ? first ?] ~
:word ~
[word ? "ay])
end
</pre></td></tr></table>
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<h3 class="unnumberedsubsec"> cascade.2 </h3>
<table><tr><td> </td><td><pre class="example">CASCADE.2 endtest temp1 startval1 temp2 startval2 (library procedure)
</pre></td></tr></table>
<p>outputs the result of invoking <code>CASCADE</code> with the same inputs. The only
difference is that the default number of inputs is five instead of three.
</p>
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<h3 class="unnumberedsubsec"> transfer </h3>
<table><tr><td> </td><td><pre class="example">TRANSFER endtest template inbasket (library procedure)
</pre></td></tr></table>
<p>outputs the result of repeated evaluation of the <var>template</var>. The template
is evaluated once for each member of the list <var>inbasket</var>. <code>TRANSFER</code>
maintains an <em>outbasket</em> that is initially the empty list. After each
evaluation of the template, the resulting value becomes the new
outbasket.
</p>
<p>In the template, the symbol <code>?IN</code> represents the current member from the
inbasket; the symbol <code>?OUT</code> represents the entire current outbasket.
Other slot symbols should not be used.
</p>
<p>If the first (<var>endtest</var>) input is an empty list, evaluation continues
until all inbasket members have been used. If not, the first input must
be a predicate expression template, and evaluation continues until
either that template's value is <code>TRUE</code> or the inbasket is used up.
</p>
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