Re: Re: RE: Behavior of ReplaceAll with Computed Results from a Conditional Test

*To*: mathgroup at smc.vnet.net*Subject*: [mg66825] Re: [mg66802] Re: [mg66770] RE: [mg66745] Behavior of ReplaceAll with Computed Results from a Conditional Test*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Wed, 31 May 2006 06:31:44 -0400 (EDT)*References*: <200605291006.GAA07644@smc.vnet.net> <200605300949.FAA14793@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The first sentence of my last email is backwards... Delayed evaluation of all rhs == Condition in head of lhs or rhs Immediate evaluation == Condition not in head of lhs or rhs On 5/30/06, Chris Chiasson <chris at chiasson.name> wrote: > The delayed evaluation of all right hand sides until after all testing > seems to happen when Condition is not the head of either the left or > right hand side of a rule. > > testQ[x_Symbol,y_Symbol,z_Symbol]:=(Print["testing tuple: ",{x,y,z}]; > If[x===z,seq=Unevaluated[Sequence[x^2,y]];True,False]) > > {{b,a,b},{a,b,c},{a,b,a}}/.{tuple___}/; > testQ[tuple]\[RuleDelayed](Print["acting on tuple: ",{tuple}, > " to write sequence: ",{seq}];{seq}) > > {{b,a,b},{a,b,c},{a,b, > a}}/.{tuple___}\[RuleDelayed](Print["acting on tuple: ",{tuple}, > " to write sequence: ",{seq}];{seq})/;testQ[tuple] > > {{b,a,b},{a,b,c},{a,b, > a}}/.{tuple___}\[RuleDelayed](Print["acting on tuple: ",{tuple}, > " to write sequence: ",{seq}];{seq}/;testQ[tuple]) > > Evaluate the above to see the results; then wrap the code in > FullForm[Hold[]] to see the structure. The only change from the 2nd > rule to the 3rd is the movement of "/;testQ[tuple]" inside the > parenthesis. This has the effect of bringing it inside > CompoundExpression, of which the infix form is usually a semicolon. > Perhaps the semicolon in the short form of Condition indicates > Condition is meant to become part of a preceeding (infix) > CompoundExpression. > > On 5/29/06, David Park <djmp at earthlink.net> wrote: > > I received several replies, and thanks for them, that suggested using two > > rules. In fact, that's what I did but I was still interested in the question > > because I think it is quite reasonable to calculate quantities as part of > > the test and have them available for the replacement code. It might not just > > be choosing between two alternatives, where we could substitute two rules, > > but might involve a complicated calculation as part of the test and we want > > the results of the computation in the replacement routine. > > > > With a little more investigation I have found that Mathematica does provide > > a method for doing this. The trick is to put the test after the body of the > > replacement Module. There is a note in the Module Help... > > > > "You can use Module[{vars}, body /; cond] as the right-hand side of a > > transformation rule with a condition attached." > > > > That forces the replacement to be done immediately and the test can return > > results that can be extracted. > > > > Clear[transformf] > > transformf[expr_] := > > Module[{testQ}, > > > > testQ[a_, b_, c_] := > > Module[{replacea = False, test}, > > test = > > Which[ > > c === a, replacea = True; True, > > c === b, replacea = False; True, > > True, False]; > > {test, replacea}]; > > > > expr /. (f[a_, b_]c_) :> > > Module[{replacea, work}, > > > > If[replacea, f[a^2, b], f[a, b^2]] /; (work = testQ[a, b, c]; > > replacea = Last[work]; First[work])] > > ] > > > > {f[a, b]a, f[a, b]b, f[a, b]c} // transformf > > {f[a^2, b], f[a, b^2], c*f[a, b]} > > > > David Park > > djmp at earthlink.net > > http://home.earthlink.net/~djmp/ > > > > > > > > From: David Park [mailto:djmp at earthlink.net] To: mathgroup at smc.vnet.net > > > > Dear MathGroup, > > > > Here is a routine that mimics a more complicated routine I was working on. I > > think it has strange behavior. The routine uses a conditional test on the > > pattern variables that as a side effect computes a parameter used in the > > replacement. When used on a list this doesn't work because Mathematica does > > all of the tests first, leaving only the parameter from the last test, and > > then does all of the replacements. Not what I want. > > > > The sample routine looks at expressions of the form f[a,b]c. If c ===a it > > returns f[a^2,b]. If c === b it returns f[a,b^2] and otherwise no > > replacement is done. I've added two Print statements to clarify what is > > happening. > > > > transformf[expr_] := > > Module[{testQ, replacea}, > > > > testQ[a_, b_, c_] := > > Module[{}, > > Print["Testing ", f[a, b]c]; > > Which[ > > c === a, replacea = True; True, > > c === b, replacea = False; True, > > True, False]]; > > > > expr /. (f[a_, b_]c_) /; testQ[a, b, c] :> > > Module[{}, > > Print["Processing " , f[a, b]c]; > > If[replacea, f[a^2, b], f[a, b^2]]] > > ] > > > > If I Map this onto the following list it works as expected. > > > > transformf /@ {f[a, b]a, f[a, b]b} > > Testing a f[a, b] > > Processing a f[a, b] > > Testing b f[a, b] > > Processing b f[a, b] > > {f[a^2, b], f[a, b^2]} > > > > However, if I use the routine on the entire list I obtain: > > > > {f[a, b]a, f[a, b]b} // transformf > > Testing a f[a, b] > > Testing b f[a, b] > > Processing a f[a, b] > > Processing b f[a, b] > > {f[a, b^2], f[a, b^2]} > > > > which I regard as incorrect. The Help for ReplaceAll says... > > > > "ReplaceAll looks at each part of expr, tries all the rules on it, and then > > goes on to the next part of expr." > > > > That seems to me to be a vague and inaccurate statement. One might think > > that if the rule matched then the replacement would be done - or at least > > calculated. Then ReplaceAll would go on to look at the next part of the > > expression. Instead all the tests are done first, and all the matching > > replacements are done afterwards. So in the above routine the replacea > > parameter is set to the last test result and then used in all of the > > replacements. > > > > That hardly seems fair. Is there a way around this behavior. > > > > David Park > > djmp at earthlink.net > > http://home.earthlink.net/~djmp/ > > > > Everyone should study mathematics - just so they will know what it is to be > > wrong. > > > > > > > > > > > > > > > > > > > > > > > -- > http://chris.chiasson.name/ > > -- http://chris.chiasson.name/

**References**:**RE: Behavior of ReplaceAll with Computed Results from a Conditional Test***From:*"David Park" <djmp@earthlink.net>

**Re: RE: Behavior of ReplaceAll with Computed Results from a Conditional Test***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: applied to numeric constants**

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**Re: RE: Behavior of ReplaceAll with Computed Results from a Conditional Test**

**Re: Behavior of ReplaceAll with Computed Results from a Conditional Test**