In the class about Re-Completeness it is said that Atm is Re-Complete. here is a copy paste of the begining of the proof:
"Suppose L is in Re, and let ML be a TM accepting it. Then fL(w) = <ML, w> is a mapping reduction from L to Atm."
My question is why is f computable? To generate it's input, f must build the coding of ML. How would she do this? It is obvoius that ML exists, but my question regards to the process of computing it.