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A \spadtype{Stream} object is represented as a list whose last element contains the
wherewithal to create the next element, should it ever be required.
\xtc{
Let \spad{ints} be the infinite stream of non-negative integers.
}{
\spadpaste{ints := [i for i in 0..] \bound{ints}}
}
By default, ten stream elements are calculated.
This number may be changed to something else by the system command
\spadcmd{)set streams calculate}.
%-% \HDsyscmdindex{set streams calculate}{StreamXmpPage}{9.80}{Stream}
For the display purposes of this book, we have chosen a smaller value.
\xtc{
More generally, you can construct a stream by specifying its initial
value and a function which, when given an element, creates the next element.
}{
\spadpaste{f : List INT -> List INT \bound{fdec}}
}
\xtc{
}{
\spadpaste{f x == [x.1 + x.2, x.1] \bound{f}\free{fdec}}
}
\xtc{
}{
\spadpaste{fibs := [i.2 for i in [stream(f, [1, 1])]] \bound{fibs}\free{f}}
}
\xtc{
You can create the stream of odd non-negative integers by either filtering
them from the integers, or by evaluating an expression for each integer.
}{
\spadpaste{[i for i in ints | odd? i] \free{ints}}
}
\xtc{
}{
\spadpaste{odds := [2*i+1 for i in ints]\bound{odds}\free{ints}}
}
\xtc{
You can accumulate the initial segments of a stream using the
\spadfunFrom{scan}{StreamFunctions2} operation.
}{
\spadpaste{scan(0,+,odds) \free{odds}}
}
\xtc{
The corresponding elements of
two or more streams can be combined in this way.
}{
\spadpaste{[i*j for i in ints for j in odds]\free{ints} \free{odds}}
}
\xtc{
}{
\spadpaste{map(*,ints,odds)\free{ints odds}}
}
\xtc{
Many operations similar to those applicable to lists are available for
streams.
}{
\spadpaste{first ints \free{ints}}
}
\xtc{
}{
\spadpaste{rest ints \free{ints}}
}
\xtc{
}{
\spadpaste{fibs 20 \free{fibs}}
}
The packages \spadtype{StreamFunctions1},
%-% \HDexptypeindex{StreamFunctions1}{StreamXmpPage}{9.80}{Stream}
\spadtype{StreamFunctions2} and
%-% \HDexptypeindex{StreamFunctions2}{StreamXmpPage}{9.80}{Stream}
\spadtype{StreamFunctions3} export some useful stream manipulation
operations.
%-% \HDexptypeindex{StreamFunctions3}{StreamXmpPage}{9.80}{Stream}
For more information, see
\downlink{``\ugLangItsTitle''}{ugLangItsPage} in Section \ugLangItsNumber\ignore{ugLangIts},
\downlink{``\ugProblemSeriesTitle''}{ugProblemSeriesPage} in Section \ugProblemSeriesNumber\ignore{ugProblemSeries},
\downlink{`ContinuedFraction'}{ContinuedFractionXmpPage}\ignore{ContinuedFraction}, and
\downlink{`List'}{ListXmpPage}\ignore{List}.
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