Re: Expanding a nested structure (pattern matching?)[Correction]

*To*: mathgroup at smc.vnet.net*Subject*: [mg24878] Re: [mg24835] Expanding a nested structure (pattern matching?)[Correction]*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Sat, 19 Aug 2000 04:45:51 -0400 (EDT)*References*: <8ndge7$ldi@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

[David Parks mailed me that the first posting had not come through correctly] David, Here are two more ways following on your mehod. I have abbreviated the name structureexpand to se (*David Park*) se[expr_] := FixedPoint[ Flatten[(# /. a_[b_List, c_List] :> Flatten[Outer[a, b, c]]) //. (a_ /; FreeQ[a, List])[b___, c_List, d___] :> ((a[b, #, d] &) /@ c)] &, expr] Two variants. se1[e_] := Flatten[e //. (f_ /; f =!= List)[a__] /; MemberQ[{a}, _List] :> ( Flatten[Outer[f, ##]] & @@ (Replace[{a}, x_ /; Head[x] =!= List -> {x}, {1}]))] se2[e_] := Flatten[e //. (f_ /; f =!= List)[a__] /; MemberQ[{f, a}, _List] :> ( Flatten[Outer[#[##2] &, ##]] & @@ (Replace[{f, a}, x_ /; Head[x] =!= List -> {x}, {1}]))] e1 = a[b, c, d[{f, g}, {h, j}]]; e2 = a[b, c, d[e, f[{f1, f2}, {f3, f4}]]]; e3 = a[b, c[{c1, c2}, {c3, c4}], d[e, f[{f1, f2}, {f3, f4}]]]; The outputs of se, se1,se2 agree on your sample inputs SameQ @@ Through[{se, se1, se2}[#]] & /@ {e1, e2, e3} {True, True, True} But se2 will also work over heads se2[{g, h}[{1, 2}, 3]] {g[1, 3], g[2, 3], h[1, 3], h[2, 3]} -- Allan --------------------- 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 "David Park" <djmp at earthlink.net> wrote in message news:8ndge7$ldi at smc.vnet.net... > Dear John, > > A wonderful question actually! I am looking forward to the answers you will > get. Here is one approach that seemed to work. (You don't want to use > capital D as a symbol because it has a predefined meaning. Best to stay with > small letters.) > > structureexpand[expr_] := > FixedPoint[ > Flatten[(# /. > a_[b_List, c_List] :> > Flatten[Outer[a, b, c]]) //. (a_ /; FreeQ[a, List])[b___, > c_List, d___] :> ((a[b, #, d] &) /@ c)] &, expr] > > I tried it on three expressions. > > e1 = a[b, c, d[{f, g}, {h, j}]] > e2 = a[b, c, d[e, f[{f1, f2}, {f3, f4}]]] > e3 = a[b, c[{c1, c2}, {c3, c4}], d[e, f[{f1, f2}, {f3, f4}]]] > > structureexpand[e1] > {a[b, c, d[f, h]], a[b, c, d[f, j]], a[b, c, d[g, h]], a[b, c, d[g, j]]} > > structureexpand[e2] > {a[b, c, d[e, f[f1, f3]]], a[b, c, d[e, f[f1, f4]]], a[b, c, d[e, f[f2, > f3]]], > a[b, c, d[e, f[f2, f4]]]} > > structureexpand[e3] > {a[b, c[c1, c3], d[e, f[f1, f3]]], a[b, c[c1, c3], d[e, f[f1, f4]]], > a[b, c[c1, c3], d[e, f[f2, f3]]], a[b, c[c1, c3], d[e, f[f2, f4]]], > a[b, c[c1, c4], d[e, f[f1, f3]]], a[b, c[c1, c4], d[e, f[f1, f4]]], > a[b, c[c1, c4], d[e, f[f2, f3]]], a[b, c[c1, c4], d[e, f[f2, f4]]], > a[b, c[c2, c3], d[e, f[f1, f3]]], a[b, c[c2, c3], d[e, f[f1, f4]]], > a[b, c[c2, c3], d[e, f[f2, f3]]], a[b, c[c2, c3], d[e, f[f2, f4]]], > a[b, c[c2, c4], d[e, f[f1, f3]]], a[b, c[c2, c4], d[e, f[f1, f4]]], > a[b, c[c2, c4], d[e, f[f2, f3]]], a[b, c[c2, c4], d[e, f[f2, f4]]]} > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > > -----Original Message----- > > From: John A. Gunnels [mailto:gunnels at cs.utexas.edu] To: mathgroup at smc.vnet.net > > Sent: Tuesday, August 15, 2000 3:04 AM > > To: mathgroup at smc.vnet.net > > Subject: [mg24878] [mg24835] Expanding a nested structure (pattern matching?) > > > > > > I hope that this is not a _really_ stupid question, but I have run > > into what appears to be a problem using rewrite rules to un-nest > > a structure. > > > > The crux of the problem (I have tried to make it as simple as possible > > without losing the essence of my difficulty) has to do with duplicating > > the structure surrounding the terms that I wish to rewrite. > > > > Any nested list is intended to represent a choice point and my rewrite > > rules are aimed at enumerating all of the possible sequences of choices. > > > > An example: > > Input: > > A[B, C, D[ {F, G}, {H, J}]] > > should become > > A[B, C, D[F, H]], > > A[B, C, D[F, J]], > > A[B, C, D[G, J]], > > A[B, C, D[G, J]] > > > > Obviously, the order isn't important, but the nesting isn't restricted > > to level 2 nor am I guaranteed that all heads or elements are unique. > > I realize that I may have to simply write the code that iterates through > > the different Depth[]s, but this seems like it might have a very clean > > answer that simply hasn't occurred to me. > > > > Thanks, > > John A. Gunnels > > gunnels at cs.utexas.edu > > > > > >