[Jtsummers]

p is a predicate, which is a function mapping elements of some type to true/false (booleans). A total function is a function which is defined for all possible inputs. So a total predicate is a function that maps all possible inputs to either true or false.

[pvillano]

For real numbers, f(x)=x² is a total function, but g(x)=√x is not, because g is undefined for x<0