I have the following code:
c[theta_, xi_] = theta*xi + theta^xi^2; xbar[theta_, xi_] = theta/xi + xi^2 + theta^3; f[x_, y_, theta_, xi_] = x*y*c[theta, xi]*theta*xi + xbar[theta, xi]; That is, I would like to define $f$ as a function $x,y,theta,xi$ using two predefined functions $c$ and $xbar$. But mathematica gives tag times is protected. How to deal with it? Many thanks!
You need to make sure there are no active definitions on the constituent parameters. You can do this with ClearAll as E.Doroskevic proposes, though I imagine you will not want to clear all Global` definitions.
You can Block the Symbols in use as described in Scoping in assigning a derivative. To make this convenient I propose using the function localSet which I wrote for How to make a function like Set, but with a Block construct for the pattern names.
xi = "fail!"; y = "bad!"; localSet[c[theta_, xi_], theta*xi + theta^xi^2] localSet[xbar[theta_, xi_], theta/xi + xi^2 + theta^3] localSet[f[x_, y_, theta_, xi_], x*y*c[theta, xi]*theta*xi + xbar[theta, xi]] ?f Global`f
f[x_, y_, theta_, xi_] = theta^3 + theta/xi + xi^2 + theta x xi (theta^xi^2 + theta xi) y
Observe that the definition is correct despite the definitions on xi and y.
Try:
ClearAll["Global`*"] c[theta_, xi_] = theta*xi + theta^xi^2; xbar[theta_, xi_] = theta/xi + xi^2 + theta^3; f[x_, y_, theta_, xi_] = x*y*c[theta, xi]*theta*xi + xbar[theta, xi]; 
Remove[c, xbar, f]before the function definitions. $\endgroup$