Iterative constants and variables definitions

[rych]

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

[dimm...@yahoo.com]

Ο/Η rych έγραψε:

[dimm...@yahoo.com]

Very good your attempt.
I do not have anything to suggest/comment apart from
that you could do all these using Block.

Block[{a = 1, c = 2, b = 7*a}, a*b*c]
14

Module cannot be applied here

Module[{a = 1, c = 2, b = 7*a}, a*b*c]
14*a

Use Trace to see why

Trace[With[{a=1,c=2,b=7 a},a b c]]
{With[{a=1,c=2,b=7 a},a b c],(7 a) 2,2 (7 a),2 7 a,14 a}

Trace[Block[{a=1,c=2,b=7 a},a b c]]
{Block[{a=1,c=2,b=7 a},a b c],{a=1,1},{c=2,2},{b=7 a,7 a,{a,1},7 1,7},
{{a,1},{b,7 a,{a,1},7 1,7},{c,2},7 2,14},14}

Trace[Module[{a=1,c=2,b=7 a},a b c]]
{Module[{a=1,c=2,b=7 a},a b c],{a$17=1,1},{c$17=2,2},{b$17=7 a,7 a},
{{a$17,1},{b$17,7 a},{c$17,2},(7 a) 2,2 (7 a),2 7 a,14 a},14 a}

Regards
Dimitris