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Re: Evaluate/Module[Correction]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg16145] Re: Evaluate/Module[Correction]
*From*: "Allan Hayes" <hay at haystack.demon.co.uk>
*Date*: Sat, 27 Feb 1999 03:23:11 -0500
*Sender*: owner-wri-mathgroup at wolfram.com
Bernd Brandt has emailed me that he does not get the result that made me
think that I had got the evaluation of CompoundExpression wrong. On
re-evaluating the example I don't either -- there is a typo in my posting
which may be related.
I give variant of the example (In[1], below). This supports the original
account, which with apologies to all, I now revert to:
Normally, CompoundExpression evaluates its entries in order and then gives
the value of the last one. However, it has the attribute HoldAll, and if
some entries are wrapped in Evaluate[ ] they will be evaluated first, in
order, *and* the resulting expression will then be evaluated as usual.
So, writing ei* for the value of ei, we get the following steps
CompoundExpression[e1, Evaluate[e2], Evaluate[e3], e4]
CompoundExpression[e1, e2*, Evaluate[e3], e4]
CompoundExpression[e1, e2*, e3*, e4] (*restart!*)
CompoundExpression[e1*, e2*, e3*, e4]
CompoundExpression[e1*, e2**, e3*, e4]
CompoundExpression[e1*, e2**, e3**, e4]
CompoundExpression[e1*, e2**, e3**, e4*]
e4*
In[1]:=
pr=.;
In[2]:=
CompoundExpression[
{ Print[2], pr = Print }, Evaluate[ {Print[1], pr[3]} ], pr[4]
]
1
2
3
4
The 3 comes from the second evaluatio of the second entry
Bernd also asked in his email about the following result
In[3]:=
t=x^2+1;
Module[{x=4}, Evaluate[t=t-1;Print[t]; Evaluate[t]]]
\!\(x\^2\)
Out[3]=
17
The evaluation steps for this (with M for Module, Pr for Print) are:
The outer Evaluate cancels the HoldAll attribute of Module and the CompoundExpression
t=t-1;Print[t]; Evaluate[t]]
then evaluates , starting with the last entry:
M[{x=4}, t=t-1;Pr[t]; x^2+1]
M[{x=4}, t=x^2+1-1;Pr[t]; x^2+1]
M[{x=4}, t=x^2;Pr[t]; x^2+1 ]
M[{x=4}, x^2;Pr[t]; x^2+1 ] (t=x^2 stored)
M[{x=4}, x^2;Null; x^2+1 ], x^2 printed
M[{x=4}, x^2+1 ]
Compound Expression has now been evaluated
Module now evaluates
Module[{x$n=4}, x$n^2+1 ],
x$n^2+1 ,
(x$n=4 stored)
4^2 +1
17 (output)
This reversion to the orignal description of the evaluation of
CompoundExpression necessitates a change to my account in the previous
posting of the evaluation of one of Paul Abbot's examples:
In[1]:=
a = 1; a = a - 1; Evaluate[a]
Out[1]=
0
Evaluation steps (with CE for CompoundExpression)
CE[a = 1, a = a - 1, a]
CE[1, a = a - 1, a] (a =1 stored)
CE[1, a = 1- 1, a ] ,,
CE[1, a = 0, a ] ,,
CE[1, 0, a ] (a=0 stored)
CE[1, 0, 0 ] ,,
0
Previously the last two lines were
a ,,
0
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
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