Skip to main content

replacement - Safely nesting RuleDelayed


Say I have the following, straightforward-seeming functions:


makeARuleDelayed[a_, b_] :=
 With[{anotherRule = makeAnotherRuleDelayed[b]},
  v : a[b] :> ((v == 1 - v) /. anotherRule)];

makeAnotherRuleDelayed[x_] :=
  v : h_[x] :> foo[h, x];

If I use them to create a RuleDelayed, I get an error message:




a[b] /. makeARuleDelayed[a, b]

RuleDelayed::rhs: Pattern v$:h$_[b] appears on the right-hand side of rule v$:a[b]:>(v$==1-v$/. v$:h$_[b]:>foo[h$,b]) .



Examining the result indicates the problem:


v$ : a[b] :> (v$ == 1 - v$ /. v$ : h$_[b] :> foo[h$, b])

Using this rule fails in about the way you'd expect it to. The only workaround I could think of is adding a Module to the body of makeAnotherRule:


makeAnotherRuleDelayed[x_] :=

 Module[{v},
  v : h_[x] :> foo[h, x]]

This doesn't help at all; evidently there must be some sort of magical renaming going on somewhere inside of RuleDelayed that truncates the $nnn part of the name of the symbol generated by Module.


Without being able to nest rules without name clashes, I'm not sure how to go about creating nontrivial rules programmatically.



Answer



This is a renaming mechanism at work. I think, the "canonical" way to fool it is something like this:


makeARuleDelayed[a_, b_] :=
  With[{anotherRule = makeAnotherRuleDelayed[b]},
     v : a[b] :> ((v == 1 - v) /. anotherRule)];


makeAnotherRuleDelayed[x_] :=
  RuleDelayed @@ Hold[v : h_[x], foo[h, x]];

By using RuleDelayed@@Hold, we fool the renaming mechanism of With. Note that this whole issue is because With is a scoping construct which cares about inner scoping constructs and possible name collisions. You can use rules instead, which are much more intruding:


Clear[makeARuleDelayedAlt];
makeARuleDelayedAlt[a_, b_] :=
    v : a[b] :> ((v == 1 - v) /. makeAnotherRuleDelayed[b])

and then keep the original definition for makeAnotherRuleDelayed. I discussed these issues in more detail here.



Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more