Author: lwall
Date: 2010-02-20 03:49:29 +0100 (Sat, 20 Feb 2010)
New Revision: 29784
Modified:
docs/Perl6/Spec/S03-operators.pod
Log:
[S03] document how an "impossible" limit can terminate a series
Modified: docs/Perl6/Spec/S03-operators.pod
===================================================================
--- docs/Perl6/Spec/S03-operators.pod 2010-02-19 23:33:02 UTC (rev 29783)
+++ docs/Perl6/Spec/S03-operators.pod 2010-02-20 02:49:29 UTC (rev 29784)
@@ -1941,6 +1941,30 @@
If the list on the left is C<Nil>, we use the function C<{Nil}>.
+For intuited numeric generators that don't involve geometric sign changes, all
+values are assumed to be monotonically increasing or decreasing, as determined
+by the (up to) three values used above; if a supplied limt value is on the
+"wrong" side of the first of those values, Nil is returned, even though the
+limit value never matches, and never falls between two generated values.
+Examples:
+
+ my $n = 0;
+ 1,2,4 ... $n; # (), geometric increasing
+ -1,-2 ... $n; # (), arithmetic decreasing
+ 1 ... $n; # (), .succ increasing
+
+For a geometric series with sign changes, the same criterion is used, but
+applied only to the absolute value, and the impossibility of a limit is
+evaluated by whether it's inside or outside the possible range:
+
+ 1,-2,4 ... 0 # (), geometric alternating increasing abs
+ 1,-1/2,1/4 ... 2 # (), geometric alternating decreasing abs
+
+But note that both of these are infinite lists:
+
+ 1,1/2,1/4 ... 0 # 1,1/2,1/4 ... *
+ 1,-1/2,1/4 ... 0 # same as 1,-1/2,1/4 ... *
+
When an explicit limit function is used, it
may choose to terminate its list by returning any false value.
Since this operator is list associative, an inner function may be
