Meanwhile I have changed my faulty testprogram from my first post (sorry about that). It now prints exp within the functions and not after the call.
Now everything works as expected by using Replace. No matter if the functions are defined with or without Module. My mistake was, that I used the same name "a" for function parameters and the global expression exp=a*x.
It's still a bit strange and I do not fully understand it. But it works.
If[True,
ClearAll["Global`*"];
exp = a*x; Print["#1: Global exp: ", exp, "\n\tok"];
a = 3; Print["#2: a=3 substituted: ", exp, "\n\tok"];
a =.; Print["#3: a reset: ", exp, "\n\tok"];
f14[aparm_] :=
Print["#14: a=", aparm,
" substituted within a function by Replace: ", exp /. a -> aparm,
"\n\tok"];
f14[3];
f14[myA];
f16[aparm_] :=
Module[{},
Print["#16: a=", aparm,
" substituted within a function-Module by Replace: ",
exp /. a -> aparm, "\n\tok"];
];
f16[3];
f16[myA];
]
#1: Global exp: a x
ok
#2: a=3 substituted: 3 x
ok
#3: a reset: a x
ok
#14: a=3 substituted within a function by Replace: 3 x
ok
#14: a=myA substituted within a function by Replace: myA x
ok
#16: a=3 substituted within a function-Module by Replace: 3 x
ok
#16: a=myA substituted within a function-Module by Replace: myA x
ok
