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MathGroup Archive 1998

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LocalRule & Local Set operators

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13908] LocalRule & Local Set operators
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Sun, 6 Sep 1998 02:55:44 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Recall the messages I sent on 28 Aug and 29 Aug. [mg13812] An operator
called-- LocalRule [mg13835] An operator called-- LocalSet

I have improved versions of these functions below (with usage messages).
The differences are:

(1)  The new versions will not look inside Verbatim[....] to find
patterns that should be evaluated inside a local environment.

(2)  The new versions use a new function PatternNames which may be
useful in it's own right.  The program for PatternNames is a bit
advanced, but it does with one application of Cases what took a few
lines in my previous version.

(3)  This version will not have trouble if the same pattern name appears
in (lhs) more than once.
(e.g.  f[x_, x_] )

Changes (1) and (2) are due to feedback I got from one of the gurus in
the group.  I understand there are still some subtle problems with
these programs, but they should be useful for many applications as they
are.

Cheers,
Ted Ersek


(*********************************)

Unprotect[LocalRule, RightArrow, LocalSet, DotEqual, PatternNames];

LocalRule::usage=
  "LocalRule[lhs,rhs] represents a rule where rhs is evaluated \
immediately using a local environment for any variable used as a \
pattern in lhs.  LocalRule[lhs,rhs] is equivalent to \
lhs\[RightArrow]rhs where \[RightArrow] is entered \ as
\\[RightArrow].";

 
RightArrow::usage=
  "lhs\[RightArrow]rhs represents a rule where rhs is evaluated \
immediately using a local environment for any variables used as a\
pattern in lhs.  Note: \[RightArrow] is entered as \\[RightArrow].\
  The expression lhs\[RightArrow]rhs is equivalent to \
LocalRule[lhs,rhs].";


LocalSet::usage=
  "LocalSet[lhs,rhs] evaluates rhs using a local environment for any \
variable used as a pattern in lhs.  From then on lhs is replaced by the
\ result of evaluating rhs whenever lhs appears.  LocalSet[lhs,rhs] is
\ equivalent to lhs\[DotEqual]rhs where \[DotEqual] is entered \ as
\\[DotEqual].";

 
DotEqual::usage=
  "lhs\[DotEqual]rhs evaluates rhs using a local environment for any \
variable used as a pattern in lhs.  From then on lhs is replaced by \
the result of evaluating rhs whenever lhs appears.  The expression \
lhs\[DotEqual]rhs, is equivalent to LocalSet[lhs,rhs].";


PatternNames::usage=
   "PatternNames[expr] returns a list of the names of patterns \
included in expr.  The list returned is wrapped in Hold. \ PatternNames
does not consider patterns that appear inside Verbatim. \ Example:\n 
PatternNames[foo[a_,b_:1,c_?NumericQ,d,e]] returns \n
 Hold[{a,b,c}].";


LocalSet=DotEqual;
LocalRule=RightArrow;
Attributes[DotEqual]={HoldAll,SequenceHold};
Attributes[RightArrow]={HoldRest,SequenceHold};
Attributes[PatternNames] = {HoldFirst};

  
PatternNames[lhs__] :=
Module[{lhsWithoutVerbatim, heldNames},
  lhsWithoutVerbatim = ReplaceAll[Hold[lhs], _Verbatim -> Null];
  heldNames = Cases[lhsWithoutVerbatim,
    Verbatim[Pattern][name_Symbol,_] :> Hold[name],
    {0,-2}, Heads -> True
  ];
  Thread[Union at heldNames, Hold]
]


RightArrow[lhs_,rhs_]:=Module[{q},
  q=PatternNames[lhs];
  If[q==={},(lhs:>Evaluate at rhs),
    Block@@Join[q,Hold[lhs:>Evaluate at rhs] ]
  ]]

 
DotEqual[lhs_,rhs_]:=Module[{b1,b2},(
  b1=PatternNames[lhs];
   If[b1==={},(Unevaluated at lhs:=Evaluate at rhs),
     b2=Hold[#:=Evaluate at rhs]& @@{Unevaluated at lhs};
     Block@@Join[b1,b2]
  ]
)]

Protect[LocalRule, RightArrow, LocalSet, DotEqual, PatternNames];


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