Definition I.0: (partial and total correctness, termination)
The description of a desired calculation is given in the form of a functional specification F: D -> W.
(0) If ALG is an algorithm that performs the desired calculation, then ALG is said to be partially correct with respect to F if, for all permitted inputs x from the domain D of F, ALG outputs the corresponding function value of F(x)
from W as a response.
(0) An algorithm ALG is said to be terminating if and only if ALG
ends after a finite number of steps for all permitted inputs.
(0) If (0) and (0) hold, then ALG is said to be totally correct