This example concerns the planning of a simple project. Tasks are only dependent on the completion of other tasks. Further analysis reveals the ``critical path'' - those tasks in which a delay would be critical to the completion of the project on time.

The tasks A through G comprise the planned project. Each task requires a certain amount of time to complete and is dependent on the completion of other tasks according to the following diagram:

:- import(const_domain).

program :- Jobs = [A,B,C,D,E,F,G],
           Durations = [Da,Db,Dc,Dd,De,Df,Dg],
           Durations = [ 4, 2, 4, 3, 4, 4, 3],

           A ?>= 0 + Da,     D ?>= B + Dd,     F ?>= D + Df,
           B ?>= A + Db,     D ?>= C + Dd,     G ?>= F + Dg,
           C ?>= A + Dc,     E ?>= C + De,     G ?>= E + Dg,

           label(Jobs),  print(Jobs).

[user] ?- program.
[4,6,8,11,12,15,18]
yes

In the IF/Prolog program, inter-dependencies between the jobs (A...G) are represented as arithmetic constraints, for example D ?>= B + Dd can be read as Job D is completed after the start and duration of Job B.

The constraints themselves (?>=/2) do not activate to determine a solution to the variables they contain, until they are passed to one of the solver predicates which then solves the complete problem. The label/1 predicate finds values for all variables in the list Jobs.

In the above, label/1 is quickly able to determine that a value for variable A exists as its start time and duration are fixed. Then, through ``constraint propagation'', values are calculated for the remaining variables.