/* 

  circuits (and taxes) in Picat.

  From Nilsson & Matuszynski: "Logic, Programming and Prolog"
  Page 242ff (Chapter 14: Constraint Logic Programming)

  Note: As stated the program res/* don't output evaluated results,
        and this is the same in some other Prologs I tested.
        It seems that the book use clp(R) which is a little
        more clever about handling "under constrained" equations.

  res2/* use constraint programming and give some results.
  

  E.g.: 
   - res($serial(r(10),r(20)),X1)
     X1 is 10 + 20, instead of 30 as stated in the book.

     res2($serial(r(10),r(20)),X1)
     give X1 = 30

   - res($serial(r(X2),r(Y2)),30)
     As stated it just give false. It should yield "X = 30-Y"

     res2($serial(r(X2),r(Y2)),30)
     Lists [0,30],[1,29], etc      



  This model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import v3_utils.
import cp.
% import smt.
% import sat.
% import mip.


main => go.

% This don't work as expected.
% See go2/0 instead
go ?=>
  % page 242
  res($serial(r(10),r(20)),X1),
  println(x1=X1), % X1 = 10 + 20

  % This evaluates to false
  res($serial(r(X2),r(Y2)),30),
  println([x2=X2,y2=Y2]),
  
  nl.
go => true.


%
% Output:
% x1 = 30
% [x2 = 0,y2 = 30]
% [x3 = 6,y3 = 30]
% [x4 = 10,y4 = 10]
% 
go2 ?=>
  % page 242
  X1 :: 0..100,
  res2($serial(r(10),r(20)),X1),
  solve([X1]),
  println(x1=X1),

  % page 243
  % expected: X = 30 - Y
  [X2,Y2] :: 0..100,
  res2($serial(r(X2),r(Y2)),30),
  solve([X2,Y2]),
  println([x2=X2,y2=Y2]),

  % page 244
  % expected: 5*X + 5*Y = X*Y
  [X3,Y3] :: 0..100,
  res2($parallel(serial(r(X3),cell(5)),r(Y3)),5),
  solve([X3,Y3]),
  println([x3=X3,y3=Y3]),

  % page 244
  % exptected: X = 10, Y = 10
  [X4,Y4] :: 0..100,
  res2($parallel(serial(r(X4),cell(5)),r(Y4)),5),X4 = 10,
  solve([X4,Y4]),
  println([x4=X4,y4=Y4]),
  
  % fail,
  nl.
go2 => true.

% Tax example page 244
% I had to rewrite this as well.
% 
% Output:
% x1 = 80000
% x2 = 130000
% [x3 = 30004,y3 = 1]
% 
go3 ?=>
  % expected: X = 80000
  tax2(160000,X1),
  println(x1=X1), % we don't need solve here

  % expected: X = 130000
  tax2(X2,25000),
  solve([X2]),
  println(x2=X2),

  % expected: X = 30000 + 4*Y, 20000 > Y
  [X3,Y3] :: 1..1000000,
  tax2(X3,Y3), Y3 #< 20000,
  solve([X3,Y3]),
  println([x3=X3,y3=Y3]),

  nl.
go3 => true.

%
% page 242
% Original
% Note: there are some typos in the book.
%
res(r(X),X).
res(cell(_X),0).
res(serial(X,Xs),R+Rs) :-
  res(X,R),res(Xs,Rs).
res(parallel(X,Xs),R*Rs/(R+Rs)) :-
  res(X,R),res(Xs,Rs).

% Adjusted version
res2(r(X),X).
res2(cell(_X),0).
res2(serial(X,Xs),RRs) :-
  RRs #= $R+Rs,
  res2(X,R),res2(Xs,Rs).

res2(parallel(X,Xs),RR) :-
  res2(X,R),res2(Xs,Rs),
  RR #= $R*Rs/(R+Rs).


%
% Another example, page 244
% About tax calculations.
%
tax(X,0.5*X) :-
  X > 150000.
tax(X,0.25*(X-30000)) :-
  X =< 150000.

tax2(X,Res) :-
  Res #= $X/2, % Picat don't like 
  X #> 150000.
tax2(X,Res) :-
  Res #= $(X-30000)/4,
  X #<= 150000.