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How to "soft-code" a Block?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113302] How to "soft-code" a Block?
  • From: dr DanW <dmaxwarren at gmail.com>
  • Date: Sat, 23 Oct 2010 07:03:48 -0400 (EDT)

Hard coding a Block is easy:
In[1]:= Block[{a = b, b = c, c = 3},
 {a, b, c}
 ]

Out[1]= {3, 3, 3}

But what if my variable list and expression are themselves values, as
in:
In[1]:= vals = {a = b, c = 3, b = c};
expr = {a, b, c};
Block[vals, expr]

During evaluation of In[1]:= Block::lvlist: Local variable
specification vals is not a List. >>

Out[3]= Block[vals, expr]

Which fails for many obvious reasons.  However, is there a way to do
this, as in:

In[1]:= vals = {a -> b, c -> 3, b -> c};
expr = {a, b, c};
RuleBlock[vals, expr]

Out[3]= {3, 3, 3}

How can I write RuleBlock[], which functions as a scoping construct
and Set's the left hand sides to the right hand sides of all the Rules
in the list?

Why do I need this?  I am writing a modeling program which builds up a
complicated compound expression in terms of some parameters.  The
expression can be evaluated quickly once numerical values of the
parameters are supplied.  I also want to be able to evaluate the
expression for different sets of parameters.

The obvious solution, using expr //. vals, does not always work for
several reasons:

* The expression contains several SparseArray's, and Replace does not
work within SparseArray's.
* The expression may contain other scoping structures or functions
which do not respond to Replace unless wrapped with Evaluate every
place it is used
* This is a complicated, programmatically generated expression, and
finding every instance where Replace would have to be Evaluate'd would
be tedious (meaning: error prone)

This would be so much easier with a scoping structure I could soft-
code.  I have attempted this with:

RuleBlock[r_?OptionQ, exp_] :=
   Block[
    Evaluate[r[[All, 1]]],
    Evaluate[r /. Rule -> Set];
    exp
    ]];

Which seems to work most of the time, but has failed me for reasons
that I cannot explain on some occasions.  I can't come up with a
simple example that demonstrates this failure.

Whenever I work this hard on something this low-level in Mathematica,
it usually means that there is an obvious solution I missed, or a
feature in Mathematica I am unaware of.  I have struggled with this
one for many years and have used various band-aids, but I am tired of
it and want to have a robust solution that works all the time.

Any suggestions?

Regards,
Daniel



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