Sorting the words of a phrase by defined variables/associations

Question

Is it possible to change the word order of a phrase by creating a list of possible values/variables and using the Sort function?

I want a specific word order always. $(a>b>c>d)$ But the values represented will change example to example. Associations may be what I'm actually trying to create, I'm not sure of the correct term.

Some examples of variables/associations:

a={"Left" or "Right" or "Top" or "Bottom"}
b={"Red" or "Blue" or "Green" or "Yellow"}
c={"Closing" or "Rolling" or "Running" or "Cleaning"}
d={"Paper" or "Note" or "Cat" or "Dog"}

Then I want to create a function:

neworder=Sort[a,b,c,d]

Then apply the function to a phrase (that has already been StringSplit):

neworder["Running","Dog","Blue"]

out = {"Blue","Running","Dog"}

Another example:

neworder["Red","Paper","Cleaning","Top"]

out = {"Top","Red","Cleaning","Paper"}

Is it possible to us Sort/SortBy in this manner? I know there are a few options in the way Sort works, but hadn't seen this method before. (Sorting a phrase by WordData, "PartsOfSpeech" is also on my radar, because that is essentially how I'm defining my variables/associations.)

Answer 1

Straightforward way:

a = {"Left", "Right", "Top", "Bottom"};
b = {"Red", "Blue", "Green", "Yellow"};
c = {"Closing", "Rolling", "Running", "Cleaning"};
d = {"Paper", "Note", "Cat", "Dog"};
weights = 
  Transpose@
     Flatten[#, 
      1] &@(Transpose@{#1, ConstantArray[#2, Length@#1]} & @@@ {{a, 
       1}, {b, 2}, {c, 3}, {d, 4}});


sort[phrase_, weights_] := 
  SortBy[phrase, First@Pick[weights[[2]], weights[[1]], #] &];
sort[{"Red", "Paper", "Cleaning", "Top"}, weights]

{"Top", "Red", "Cleaning", "Paper"}

Or if you want to deal with "unknown" words by placing them in the end.

sort[phrase_, weights_] := 
  SortBy[phrase, 
   If[# == {}, Infinity, First[#]] &@
     Pick[weights[[2]], weights[[1]], #] &];
sort[{"Red", "blah", "Paper", "Cleaning", "Top", "babah"}, weights]

{"Top", "Red", "Cleaning", "Paper", "babah", "blah"}

You can of course define weights any way you want. I just followed your data.

Update If your phrase consists of words from list a only, the order will be changed, which I think is bad. So I modified the sorting function:

sort3[phrase_, weights_] := Module[{phind},
   phind = MapIndexed[{#1, First@#2} &, phrase];
   First@Transpose@
     SortBy[phind, 
      Function[x, 
         If[x == {}, 1^-10 #[[2]] + 10^10, First[x] + 1^-10 #[[2]]]]@
        Pick[weights[[2]], weights[[1]], #[[1]]] &]
   ];

So now compare

sort[{"Red", "Green", "Blue", "Yellow"}, weights]
(*{"Blue", "Green", "Red", "Yellow"}*)
sort3[{"Red", "Green", "Blue", "Yellow"}, weights]
(*{"Red", "Green", "Blue", "Yellow"}*)

sort[{"Red", "Green", "bub", "Blue", "ash", "Yellow"}, weights]
(*{"Blue", "Green", "Red", "Yellow", "ash", "bub"}*)
sort3[{"Red", "Green", "bub", "Blue", "ash", "Yellow"}, weights]
(*{"Red", "Green", "Blue", "Yellow", "bub", "ash"}*)

Now the sorting function accounts for position in the original phrase.