Iterative constants and variables definitions

• To: mathgroup at smc.vnet.net
• Subject: [mg69662] Iterative constants and variables definitions
• From: "rych" <rychphd at gmail.com>
• Date: Wed, 20 Sep 2006 02:44:09 -0400 (EDT)

```Thanks to everyone who commented on my previous topic "function's local
constants interdependence". I'd like to introduce 2 new functions, that
automate the nesting of several With[ and one Module[. I'd be thankful
for further suggestions.

(*Problem*)
In:=
With[{a=1,c=2,b=7a},a*b*c]
Out=
14 a
(*we wanted "14" *)

(*Solution*)

In[1483]:=
(*Hold'ed definitions*)
ClearAll[WithWith,WithModule]
SetAttributes[{WithWith,WithModule},HoldAll]

WithWith[x__,expr_]:=Fold[With[#2,#1]&,Hold[expr],
Reverse@Map[Hold,Unevaluated@{x}]/.Hold[h_[y__]]\[RuleDelayed]Hold[{h[y]}]/;h=!=
List]

WithModule[x__,expr_]:=With[{xh=Reverse@Map[Hold,Unevaluated@{x}]/.Hold[h_[y__]]\[RuleDelayed]Hold[{h[y]}]/;h=!=
List},With[{xh1=First@xh},Fold[With[#2,#1]&,Module[xh1,Hold[expr]],Rest@xh]]]

(*usage*)
Off[With::"lvlist"]
Off[Module::"lvlist"]
Clear[a,b,c]
b=100; c=200;

WithWith[{a=1, c=2},b=7a, a*b*c]
WithModule[{a=1, c=2},b=7a, a*b*c]

Out[1491]=
With[Hold[{a=1,c=2}],With[Hold[{b=7 a}],Hold[a b c]]]
Out[1492]=
With[Hold[{a=1,c=2}],Module[Hold[{b=7 a}],Hold[a b c]]]

(*final definitions*)
In[1494]:=
ClearAll[WithWith,WithModule]
SetAttributes[{WithWith,WithModule},HoldAll]
WithWith[x__,expr_]:=ReleaseHold@Fold[With[#2,#1]&,Hold[expr],Reverse@Map[Hold,Unevaluated@{x}]/.Hold[h_[y__]]\[RuleDelayed]Hold[{h[y]}]/;h=!=List]

WithModule[x__,expr_]:=With[{xh=Reverse@Map[Hold,Unevaluated@{x}]/.Hold[h_[y__]]\[RuleDelayed]Hold[{h[y]}]/;h=!=List},With[{xh1=First@xh},ReleaseHold@Fold[With[#2,#1]&,Module[xh1,Hold[expr]],Rest@xh]]]

(*usage*)
Off[With::"lvlist"]
Off[Module::"lvlist"]
Clear[a,b,c]
b=100;c=200;
WithWith[{a=1,c=2},b=7a,a*b*c]
WithModule[{a=1,c=2},b=7a,a*b*c]

Out[1502]=
14
Out[1503]=
14

```

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