% Figure 20.9  A qualitative model of bath tub.

:- op( 900, fy, not).
:-  op( 220, xfy, ..).

% not Goal): negation as failure; 
%   Note: This is often available as a built-in predicate,
%   often written as prefix operator "\+", e.g. \+ likes(mary,snakes)

not Goal  :-
  Goal, !, fail
  ; 
  true.

% A bath tub model 

landmarks( amount, [ zero, full, inf]).
landmarks( level, [ zero, top, inf]).
landmarks( flow, [ minf, zero, inflow, inf]).

correspond( amount:zero, level:zero).
correspond( amount:full, level:top).

legalstate( [ Level, Amount, Outflow, Netflow])  :-
  mplus( Amount, Level),
  mplus( Level, Outflow),
  Inflow = flow:inflow/std,           % Constant in-flow
  sum( Outflow, Netflow, Inflow),     % Netflow = Inflow - Outflow
  deriv( Amount, Netflow),
  not overflowing( Level).            % Water not over the top

overflowing( level:top..inf/_).       % Over the top

initial( [ level: zero/inc,
           amount: zero/inc, 
           flow: zero/inc,
           flow: inflow/dec ] ).