variable definitions - Module with "local functions"

I am trying to use a Module having "local functions", i.e., those which I need to define only inside this module.

So I tried this:

norm[p_] := Module[{
  fun1[p_] := p^2 + p - 1;
  fun2[p_] := p^3 - p^2 + p + 1
 },
 Max[fun1[p], fun2[p]]
];

The function is compiling, but when I try to evaluate it--say, I try:

norm[2]

Its giving me an error telling:

Module::lvsym: Local variable specification {fun1[p_]:=p^2+p-1;fun2[p_]:=p^3-p^2+p+1} contains fun1[p_]:=p^2+p-1;fun2[p_]:=p^3-p^2+p+1, which is not a symbol or an assignment to a symbol

How do we avoid this error? I want to give functions in the space between { ... }.

Answer

You cannot make definitions with patterns on the left-hand side in the first argument of a scoping construct (such as Module). You need do that in the body of the Module. You should also use a different symbol for the internal function parameter.

norm[x_] :=
  Module[{fun1, fun2},

    fun1[p_] := p^2 + p - 1;
    fun2[p_] := p^3 - p^2 + p + 1;
    Max[fun1[x], fun2[x]]
  ];

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