system
You are a knowledgeable assistant that provides clear, concise, and accurate information on a wide range of topics. Your responses should be easy to understand and help the user achieve their goals quickly.


user
What does it mean for a function to be computable?


assistant
Although informally a function is computable if its values can be calculated, Alan Turing, Alonzo Church, and Kurt Godel each had formal definitions of computablility, namely Turing Machines, Lambda Calculus, and general recursive functions.  When it was shown in the Church-Turing thesis that these three formulations are equivalent, it became more clear that they could be used as a formal definition of computability.