How to compare FullDefinition of two function to check if they are actually equal?

Question

I usually use WReach's define tool to define new functions.

For example, running

define[f[x_]:=x]
FullDefinition[f]

we got a bunch of definitions.

f[x_]:=x
 
def$:f[___]:=(Message[define::badargs,f,def$];Abort[])


 
Attributes[def$]={Temporary}
 
Attributes[define]={HoldAll}
 
define[body_,attribute_Symbol]:=define[body,{attribute}]
 
define[body:_Set|_SetDelayed,attributes_List:{}]:=define[CompoundExpression[body],attributes]
 
define[body:CompoundExpression[(Set|SetDelayed)[name_Symbol[___],_]..],attributes_List:{}]:=(ClearAll[name];SetAttributes[name,DeleteCases[attributes,Open]];If[!MemberQ[attributes,Open],def:name[___]:=(Message[define::badargs,name,def];Abort[])];body;)
 
def:define[___]:=(Message[define::malformed,def];Abort[])


 
define/:define::badargs=There is no definition for '``' applicable to ``.
 
define/:define::malformed=Malformed definition: ``

Now I define another function

define[g[x_]:=x]

We know function g is actually equivalent to f except with a different name. Is there a way to have a function

compareFullDefinition[f,g]

that check this actual equivalence and will give True for this case?

Answer 1

We get Information for both functions and change the information into a list. Now we replace the the name of the first function by the name of the second function. Unfortunately the names appear not only as symbols, but also in strings. Therefore we need to throw out these strings. After having prepared the lists, we can finally compare them:

CompareFullDefinition[f_, g_] := Module[{t1, t2},
  t1 = Normal[Information[f][[1]]] /. {f -> g, 
     HoldPattern[Rule["Usage", _]] -> Nothing, 
     HoldPattern["FullName" -> _] -> Nothing};
  t2 = Normal[Information[g][[1]]] /. {f -> g, 
     HoldPattern[Rule["Usage", _]] -> Nothing, 
     HoldPattern["FullName" -> _] -> Nothing};
  t1 === t2
  ]

CompareFullDefinition[f, g]
(*True*)