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The following are the sequence of steps that can be followed to systematically develop the axiomatic specifications of a function:  

  1. Establish the range of input values over which the function should behave correctly. Also find out other constraints on the input parameters and write it in the form of a predicate.  
  2. Specify a predicate defining the conditions which must hold on the output of the function if it behaved properly.  
  3. Establish the changes made to the function’s input parameters after execution of the function. Pure mathematical functions do not change their input and therefore this type of assertion is not necessary for pure functions.  
  4. Combine all of the above into pre and post conditions of the function.

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