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replacement rules from a pattern and a matching expression


(This seems to be a very basic necessity in a language having pattern-matching capabilities such as Mathematica, yet I struggled for many hours to find a common solution to this problem.)


Suppose there is a pattern with some of its sub-elements named, and there is an expression that matches it. How do I generate a list of replacement rules that maps sub-element names into their values in the matching expression? E.g.,



patt=f_[_, s_, x___];
expr=ab[c, d, e, f];
mkMatchRules[expr,patt]
>> {f -> ab, s -> d, x -> Sequence[e, f]}

I have written a solution to this,


collectAllPattVars[patt_] := Union[Map[Part[#, 1] &,
  Cases[patt, _Pattern, {0, Infinity}, Heads -> True]]];
mkMatchRules[expr_, patt_] := Module[
  {pattVars = collectAllPattVars[patt], mkRhs},

  mkRhs = Block[{$}, ReleaseHold[Hold[patt :> $] /. $ -> With[{$ = Map[List, pattVars]}, $]]]; 
  If[MatchQ[expr, patt],
     MapThread[Rule[#1, If[Length[#2] == 1, #2[[1]], Sequence @@ #2]] &, 
               {pattVars, Replace[expr, mkRhs]}],
     $Failed]];

which produces the result in the example above However, I hope somebody knows a more elegant way to do this.




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