Tracing my rules

Question

As said in another question, I apply a set of rules to a string (OK, technically written as a function F of several arguments so I can easily apply rules on the fly). Now I want to check whether the correct rule is applied correctly (which can get chaotic). Obviously Trace[expr] does the trick, but the output is not less chaotic, since many rules apply, but most are rejected since they match the pattern, but not an additional /; condition. Ideally MATHEMATICA would show me only rules that didn't fail, the number of the rule (I could introduce it by storing the rule number in the first argument of my function, and then do Trace[expr,F]) and the inbetween values. Some silly artificial working example:

(*rule set*)
F[n_,X___,1,1,Y___]:=F[1,X,2,Y];(*rule 1*)
F[n_,X___,2,3,Y___]:=F[2,X,3,Y]/;Y==4;(*rule 2*)
F[n_,X___,2,3,Y___]:=F[3,X,3,Y]/;Y!=4;(*rule 3*)
(*raw trace: Trace[expr])
{F[0,1,1,3,5],F[1,2,3,5],{{5==4,False},RuleCondition
[$ConditionHold[$ConditionHold[F[2,3,5]]],
False],Fail},{{5!=4,True},
RuleCondition[$ConditionHold[$ConditionHold
[F[3,3,5]]],True],
$ConditionHold[$ConditionHold[F[3,3,5]]]},F[3,3,5]}
(*processed evaluation trace: Trace[expr,F]*)
F[0,1,1,3,5] (*start*)
F[1,2,3,5] (*rule 1 applied successfully*)
F[3,3,5] (*rule 3 applied successfully*)

Note that although this approach already solves my problem, I would prefer a solution without numbering rules, as this must be pattern-matched too and my program is already snailish enough...

(*idea of time-saving output, no n_ in F rules*)
F[1,1,3,5], 
F[2,3,5] F[X___,1,1,Y___]->F[X,2,Y]
F[3,5] F[X___,2,3,Y___]->F[X,3,Y],Y!=4

The processing of Trace may be snailish since I just use that for spot-checking correctness.

P.S. Why does letting Y___=Nothing (say input F[0,2,3]) match Y==4 (as the output is F[2,3], not F[3,3])? Is an empty slot equal to anything?

Answer 1

Perhaps you can do:

Clear[F]
F[X___, 1, 1, Y___] := Echo[Unevaluated @ F[X, 2, Y], "rule 1:"]
F[X___, 2, 3, Y___] := Echo[Unevaluated @ F[X, 3, Y], "rule 2:"] /; Y==4
F[X___, 2, 3, Y___] := Echo[Unevaluated @ F[X, 3, Y], "rule 3:"] /; Y!=4

Then:

F[1, 1, 3, 5]

rule 1: F[2,3,5]

rule 3: F[3,5]

F[3, 5]