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MathGroup Archive 1990

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Re: replace by value in expr

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: Re: replace by value in expr
  • From: CAMERON at midd.cc.middlebury.edu
  • Date: Wed, 19 Dec 90 08:12:34 -0600

In a response to Charles Herrick about the workings of "/." (ReplaceAll)
and "->" (Rule), David Jacobson (jacobson at cello.hpl.hp.com) writes:

> ... If you want the x on the left of "->" to not be
> replaced by the value of x *before substition* use ":>" instead.

BUZZZ! Sorry, no, but thank you for playing... :-)

Using ":>" (RuleDelayed) instead of Rule defers evaluation of the
right-hand side of the rule only.  (This is because RuleDelayed has
the "HoldRest" attribute rather than the "HoldAll" attribute.)
If you want to defer evaluation on the left (with either Rule or
RuleDelayed), use Literal.  The following examples show the four
possibilities (hold neither, hold left, hold right, and hold both):

    In[6]:= x = 5

    Out[6]= 5

    In[7]:= x -> 1 + 1

    Out[7]= 5 -> 2

    In[8]:= x :> 1 + 1

    Out[8]= 5 :> 1 + 1

    In[9]:= Literal[x] -> 1 + 1

    Out[9]= Literal[x] -> 2

    In[10]:= Literal[x] :> 1 + 1

    Out[10]= Literal[x] :> 1 + 1

    In[11]:= Attributes[RuleDelayed]

    Out[11]= {HoldRest, Protected}

You could use Hold instead of Literal to defer evaluation in the
LHS of rules, but Literal is transparent to the pattern matcher
whereas Hold is not (i.e. "Literal[x]" will match in "x + 4"
but "Hold[x]" would not, because the matcher would look for
the symbol "Hold").

Perhaps WRI could have come up with a more symmetric way of holding
in rules (say, operators ->-, :>-, ->:, and :>: for holding nothing,
left, right, and both), but in practice it is FAR more common to want
to hold the right than the left side of a rule.

Hope this helps.
--Cameron Smith
  Mathematica Consultant
  CAMERON at MIDD.BITNET  --or--  cameron at midd.cc.middlebury.edu


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