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Cell["\<\
Author: 
\t\t\tLeonid B. Shifrin
\t\t\t
\t\t\tleonid@mathprogramming-intro.org, 
\t\t\tshifrinl@hotmail.com\
\>", "Subsection",
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\"manufacture\" from it another one, with a different set of attributes. This \
may be useful in various circumstances, for instance when a pure (unnamed) \
function is passed as an argument, and while we don' t have access to its \
name (it has no name), we want to ensure that its behavior is consistent with \
a given set of attributes (of which not all may be initially present in this \
pure function, and some that are present we may wish to disable). We can also \
convert the \"normal\" (DownValue-based) function into a pure function, but \
not all attributes acceptable for a symbol are legal in a pure function, so \
in general one can not assume that the \"converted\" pure function can be \
used everywhere where the original one is used, with the same effect.\n\nAn \
important thing to remember is that all functions of this package do not (and \
can not) change the \"initial\" pure function (since it is an expression, not \
an L-value), but rather produce a copy function with the desired set of \
attributes. This is consistent with the general trend of avoiding  \
side-effects in  idiomatic ",
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Let us remember that the original function did not change : all our \
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We can also work with functions defined with # - & notation :\
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Converting usual (DownValue-based) function to a pure function\
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Here we define some function of several variables. The first variable is \
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Since the first argument is passed unevaluated to the function, and then \
ignored (discarded) by the function itself, the stars are not printed :\
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We are wrong with the number of arguments here, but we can see that \
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Cell["\<\
This is how we could simulate the MapThread operation with our functions :\
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Cell["\<\
Our version is somewhat slower than built - in (which is expected of course) \
.\
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Cell["\<\
Note that a warning message has been generated. This is because not all \
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 Some attributes that are legitimate for symbols are not legitimate for pure \
functions :\
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Cell[TextData[{
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official ",
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Here is a higher - order function < processLists >, which takes another list \
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We now want to use our function to compare the sub - lists for equality \
element - by - element. We try :\
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The Equal function is not Listable, and so we just confirm  the fact that the \
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Suppose now that we require that the processing function is Listable. There \
are two possible types of behavior : either < processLists > complains upon \
receiving a non - Listable function : \
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Or, it makes it Listable by creating a Listable copy of the original function \
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Cell["\<\
In fact, in the latter case we may remove the restriction of the passed \
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The warning is to alert that not all attributes could be passed to a pure \
function wrapper. In this case, it does not matter.\
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Anyway, we got what we wanted. Even if this example is somewhat contrived, it \
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Cell[TextData[{
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pure function, use ",
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sense in the  pure function' s setting, will be set, and for the rest (if \
any), the warning message  is generated. \n  \n In all cases, the resulting \
pure function is a copy - no action is performed on the original pure \
function (this is not possible in general since a pure function is an \
expression and does not represent an L - value)"
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(* End of internal cache information *)