% File 'additive'
 
:- include 'arithmetic'.

:- variables
  V_A,V_A1,V_A2,V_A3,V_A4            :: action;
  V_I,V_I1                           :: additiveInteger;
  V_NNI                              :: nnAdditiveInteger.

% parsing propositions involving 'increments' and 'decrements'

:- op(1010,xfx,increments).
:- op(1010,xfx,decrements).
:- op(1015,xfx,by).

% definitions of 'increments' and 'decrements'

:- macros 
  #1 increments #2 by #3 if #4 
    -> caused contribution(#1,#2) = #3 if #1 & #4 ;

  #1 increments #2 by #3
    -> #1 increments #2 by #3 if true;

  #1 decrements #2 by #3 if #4
    -> caused contribution(#1,#2) = -(#3) if #1 & #4 ;

  #1 decrements #2 by #3 
    -> #1 decrements #2 by #3 if true .

% total order on actions induced by @<

:- macros 
  next(#1,#2) -> (#1 @< #2 & 
                     -([\/V_A2 | (#1 @< V_A2 & V_A2 @< #2)]));
  first(#1) -> -([\/V_A3 | (V_A3 @< #1)]);
  last(#1) ->  -([\/V_A4 | (#1 @< V_A4)]).