Re: delayed rule evaluation order
- To: mathgroup at smc.vnet.net
- Subject: [mg68022] Re: [mg67967] delayed rule evaluation order
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 20 Jul 2006 06:05:02 -0400 (EDT)
- References: <11710934.1153306359682.JavaMail.root@eastrmwml07.mgt.cox.net> <acbec1a40607190514x62d0f07byeb91cf8b496bca33@mail.gmail.com> <3BA57237-C0B6-4C71-A8B0-3481DCDBC464@mimuw.edu.pl> <acbec1a40607190919p3efa8b30x4ae0cb6278444931@mail.gmail.com> <330E5DE6-73D2-4844-BACD-8D96B736EA76@mimuw.edu.pl> <F2BDC55B-557A-4968-B933-18548988AD0B@mimuw.edu.pl> <674A693A-FA92-4E9F-86A0-EA8214BD9FAC@mimuw.edu.pl>
- Sender: owner-wri-mathgroup at wolfram.com
I can see now what went wrong. The problem is with the use of
ExactNumberQ. Here is an approach that works:
f[1] = 1;
f[n_Integer] /; n > 1 = n f[n - 1];
InputForm[z = Trace[f[2]]];
v = z /. {blah_Integer :> SetPrecision[blah, 3]};
v/.p_SetPrecision:> With[{eval = p}, eval /; True]
{f(2.00),{2.00>1.00,True},2.00 f(-1.00+2.00),{{-1.00+2.00,1.00},f(
1.00),1.00},2.00 1.00,2.00}
Of course if you have Rationals in your expression and other non-
exact numbers you will have to deal with these too in a similar way.
Andrzej Kozlowski
On 19 Jul 2006, at 19:08, Andrzej Kozlowski wrote:
> O maybe that is not so ideal after all, since f got evaluated. You
> can of course combine it with the Block technique I used earlier.
>
> Andrzej
>
>
> On 19 Jul 2006, at 19:03, Andrzej Kozlowski wrote:
>
>> Here is another way, which you may like better. It uses the blah
>> approach and the Trott-Strzebonski partial evaluation technique.
>>
>> f[1] = 1;
>> f[n_Integer] /; n > 1 = n f[n - 1];
>> InputForm[z = Trace[f[2]]];
>>
>> v = z /. {blah_?ExactNumberQ :> SetPrecision[blah, 3]};
>>
>>
>>
>> v/.p_SetPrecision:> With[{eval = p}, eval /; True]
>>
>>
>> {2.00,{2.00>1.00,True},2.00,{{1.00,1.00},1.00,1.00},2.00,2.00}
>>
>> This must be finally what you wanted, isn't it?
>>
>> Andrzej Kozlowski
>>
>>
>>
>> On 19 Jul 2006, at 18:50, Andrzej Kozlowski wrote:
>>
>>> It's much easier to answer questions if the persons who pose them
>>> explain clearly what they mean.
>>>
>>> The most obvious way to modify my code seems to me to be:
>>>
>>>
>>> f[1] = 1;
>>> f[n_Integer] /; n > 1 = n f[n - 1];
>>> InputForm[z = Trace[f[2]]];
>>>
>>>
>>> Block[{f=g},z/.{HoldForm[a_]:>HoldForm@@{SetPrecision[a,3]}}]/.g->f
>>>
>>>
>>> {f(2.00),{True,True},2.00 f(1.00),{{1.00,1.00},f(1.00),1.00},
>>> 2.00,2.00}
>>>
>>> Now f is not evaluated. The only thing you might still complain
>>> about is that {2 > 1, True} evaluated to {True,True}. If you
>>> really care about this you, can prevent it in various ways, for
>>> example:
>>>
>>>
>>> Block[{f=g},
>>> z/.{HoldForm[a_]/;
>>> FreeQ[a,True]:>HoldForm@@{SetPrecision[a,3]}}]/.g->f
>>>
>>>
>>> {f(2.00),{2>1,True},2.00 f(1.00),{{1.00,1.00},f(1.00),1.00},
>>> 2.00,2.00}
>>>
>>> or
>>>
>>>
>>> Block[{f=g,Greater=greater},
>>> z/.{HoldForm[a_]/;
>>> FreeQ[a,True]:>HoldForm@@{SetPrecision[a,3]}}]/.{g-
>>> >f,greater->Greater}
>>>
>>>
>>> {f(2.00),{2.00>1.00,True},2.00 f(1.00),{{1.00,1.00},f(1.00),1.00},
>>> 2.00,2.00}
>>>
>>>
>>> There are many other possibilities.
>>> If there is still anything you do not like than it probably means
>>> you still have not explained completely what you want.
>>>
>>> Andrzej Kozlowski
>>>
>>> On 19 Jul 2006, at 18:19, Chris Chiasson wrote:
>>>
>>>>
>>>> What I want it to do is be able to replace numbers that aren't
>>>> direct
>>>> arguments of HoldForm (maybe they are nested a few levels deep,
>>>> etc).
>>>>
>>>> In the example you sent me, f is evaluated - which is
>>>> undesirable for me.
>>>>
>>>> On 7/19/06, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
>>>>> *This message was transferred with a trial version of
>>>>> It seems to me that a variant of my first suggestion works fine:
>>>>>
>>>>> In[1]:=
>>>>> f[1]=1;
>>>>> f[n_Integer]/;n>1=n f[n-1];
>>>>> InputForm[z=Trace[f[2]]];
>>>>> InputForm[z/.{HoldForm[a_]:>HoldForm@@{SetPrecision[a,3]}}]
>>>>>
>>>>> Out[4]//InputForm=
>>>>> {HoldForm[2.`2.9999999999999973],
>>>>> {HoldForm[True], HoldForm[True]},
>>>>> HoldForm[2.`2.9999999999999973],
>>>>> {{HoldForm[1.`2.9999999999999973],
>>>>> HoldForm[1.`2.9999999999999973]},
>>>>> HoldForm[1.`2.9999999999999973],
>>>>> HoldForm[1.`2.9999999999999973]},
>>>>> HoldForm[2.`2.9999999999999973],
>>>>> HoldForm[2.`2.9999999999999973]}
>>>>>
>>>>> Or is this not what you wanted?
>>>>>
>>>>> Andrzej Kozlowski
>>>>>
>>>>>
>>>>>
>>>>> On 19 Jul 2006, at 14:14, Chris Chiasson wrote:
>>>>>
>>>>> > Thanks to Kozlowski's, Hanlon's and Pein's solutions (haven't
>>>>> received
>>>>> > any others so far), I am now using this type of replacement:
>>>>> >
>>>>> > Hold[5.55555555]/.{blah_?InexactNumberQ:>
>>>>> > junk[SetPrecision[blah,3]]}/.junk->Evaluate
>>>>> >
>>>>> > Hold[5.56]
>>>>> >
>>>>> > However, this still does not totally work on Trace's output:
>>>>> >
>>>>> > In[1]:=
>>>>> > f[1]=1;
>>>>> > f[n_Integer]/;n>1=n f[n-1];
>>>>> > InputForm[z=Trace[f[2]]]
>>>>> >
>>>>> > Out[3]//InputForm=
>>>>> > {HoldForm[f[2]], {HoldForm[2 > 1], HoldForm[True]}, HoldForm
>>>>> [2*f[-1
>>>>> > + 2]],
>>>>> > {{HoldForm[-1 + 2], HoldForm[1]}, HoldForm[f[1]], HoldForm[1]},
>>>>> > HoldForm[2*1], HoldForm[2]}
>>>>> >
>>>>> > In[4]:=
>>>>> > InputForm[z/.{blah_?ExactNumberQ:>junk[SetPrecision[blah,
>>>>> 3]]}/.junk-
>>>>> > >Evaluate]
>>>>> >
>>>>> > Out[4]//InputForm=
>>>>> > {HoldForm[2.`2.9999999999999996], {HoldForm[Evaluate
>>>>> [SetPrecision[2,
>>>>> > 3]] > Evaluate[SetPrecision[1, 3]]],
>>>>> > HoldForm[True]}, HoldForm[2.`2.9999999999999996],
>>>>> > {{HoldForm[1.`2.9999999999999996], HoldForm
>>>>> [1.`2.9999999999999996]},
>>>>> > HoldForm[1.`2.9999999999999996],
>>>>> > HoldForm[1.`2.9999999999999996]}, HoldForm
>>>>> [2.`2.9999999999999996],
>>>>> > HoldForm[2.`2.9999999999999996]}
>>>>> >
>>>>> > Notice the leftover Evaluate and SetPrecision commands. Does
>>>>> anyone
>>>>> > have ideas on how to get this to work?
>>>>> >
>>>>> > On 7/19/06, Bob Hanlon <hanlonr at cox.net> wrote:
>>>>> >> Hold[{2, 3}] /.
>>>>> >> {Hold[{x_, y_}] :> Hold[Evaluate[x^y]]}
>>>>> >>
>>>>> >> Hold[8]
>>>>> >>
>>>>> >>
>>>>> >> Bob Hanlon
>>>>> >>
>>>>> >> ---- Chris Chiasson <chris at chiasson.name> wrote:
>>>>> >> > Hold[{2, 3}] /. {{x_, y_} :> x^y}
>>>>> >> >
>>>>> >> > the result is Hold[Power[2,3]]
>>>>> >> >
>>>>> >> > I would like the result to be Hold[8]
>>>>> >> >
>>>>> >> > The original context is post-processing of a large Trace
>>>>> output
>>>>> >> (via
>>>>> >> > SetPrecision to get rid of digits and improve readability).
>>>>> >> >
>>>>> >> > Any ideas?
>>>>> >> >
>>>>> >> > --
>>>>> >> > http://chris.chiasson.name/
>>>>> >> >
>>>>> >>
>>>>> >> --
>>>>> >>
>>>>> >> Bob Hanlon
>>>>> >> hanlonr at cox.net
>>>>> >>
>>>>> >>
>>>>> >>
>>>>> >
>>>>> >
>>>>> > --
>>>>> > http://chris.chiasson.name/
>>>>>
>>>>>
>>>>
>>>>
>>>> --
>>>> http://chris.chiasson.name/
>>>
>>
>