/* 

  Deriv benchmark in Picat.

  Prolog code from
  http://www.jekejeke.ch/idatab/doclet/prod/en/docs/05_run/15_stdy/06_bench/09_programs/03_deriv/01_deriv.p.html

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

*/


% import util.
% import cp.


main => go.

% Prolog code
/**
 * Prolog code for the symbolic derivation benchmark.
 *
 * This is the benchmark of page 222 of:
 * Warren, D.H.D. (1983): Applied Logic – Its Use and
 * Implementation as a Programming Tool,
 * Technical Note 290, SRI International, 1983
 *
 * Copyright 2010, XLOG Technologies GmbH, Switzerland
 * Jekejeke Prolog 0.8.3 (a fast and small prolog interpreter)
 */

/*
d(U + V, X, DU + DV) =>
      d(U, X, DU),
      d(V, X, DV).
d(U - V, X, DU - DV) =>
      d(U, X, DU),
      d(V, X, DV).
d(U * V, X, DU * V + U * DV) =>
      d(U, X, DU),
      d(V, X, DV).
d(U / V, X, (DU * V - U * DV) / ^(V, 2)) =>
      d(U, X, DU),
      d(V, X, DV).
d(^(U, N), X, DU * N * ^(U, N1)) =>
      N1 = N - 1,
      d(U, X, DU).
d(-U, X, -DU) =>
      d(U, X, DU).
d(exp(U), X, exp(U) * DU) =>
      d(U, X, DU).
d(log(U), X, DU / U) =>
      d(U, X, DU).
d(X, X, 1) => true.

d(_, _, Zero) => Zero = 0.

*/

%
% From http://www.picat.org/download/exs.pi
%
% Note: This adds some extra parenthesis compared to the Prolog version, 
%       e.g. x^2 -> (x^2)
%
d(U+V,X,D) => 
    D = $DU+DV,
    d(U,X,DU),
    d(V,X,DV).
d(U-V,X,D) =>
    D = $DU-DV,
    d(U,X,DU),
    d(V,X,DV).
d(U*V,X,D) =>
    D = $DU*V+U*DV,
    d(U,X,DU),
    d(V,X,DV).
d(U/V,X,D) =>
    D = $(DU*V-U*DV)/(^(V,2)),
    d(U,X,DU),
    d(V,X,DV).
d(^(U,N),X,D) =>
    D = $DU*N*(^(U,N1)),
    integer(N),
    N1=N-1,
    d(U,X,DU).
d(-U,X,D) =>
    D = $-DU,
    d(U,X,DU).
d(exp(U),X,D) =>
    D = $exp(U)*DU,
    d(U,X,DU).
d(log(U),X,D) =>
    D = $DU/U,
    d(U,X,DU).
d(X,X,D) => D=1.
d(_,_,D) => D=0.


% Answer should be:
%    (1+0)*((x^2+2)*(x^3+3))+(x+1)*((1*2*x^1+0)*(x^3+3)+(x^2+2)*(1*3*x^2+0))
ops8(E) => 
   Exp = $((x+1) * ((^(x,2)+2)*(^(x,3)+3))),
   d(Exp,x,E).


% Answer should be:
%    (((((((((1*x-x*1)/x^2*x-x/x*1)/x^2*x-x/x/x*1)/x^2*x-x/x/x/x*1)/x^2*x-x/x/x/x/x*1)/x^2*x-x/x/x/x/x/x*1)/x^2*x-x/x/x/x/x/x/x*1)/x^2*x-x/x/x/x/x/x/x/x*1)/x^2*x-x/x/x/x/x/x/x/x/x*1)/x^2
divide10(E) => 
   Exp= $((((((((x/x)/x)/x)/x)/x)/x)/x)/x)/x,
   d(Exp,x,E).


% Answer should be:
%    1/x/log(x)/log(log(x))/log(log(log(x)))/log(log(log(log(x))))/log(log(log(log(log(x)))))/log(log(log(log(log(log(x))))))/log(log(l
log10(E) => 
  Exp = $(log(log(log(log(log(log(log(log(log(log(x))))))))))),
  d(Exp, x, E).

% Answer should be:
%   ((((((((1*x+x*1)*x+x*x*1)*x+x*x*x*1)*x+x*x*x*x*1)*x+x*x*x*x*x*1)*x+x*x*x*x*x*x*1)*x+x*x*x*x*x*x*x*1)*x+x*x*x*x*x*x*x*x*1)*x+x*x*x*x*x*x*x*x*x*1
times10(E) => 
  Exp = $(((((((((x * x) * x) * x) * x) * x) * x) * x) * x) * x),
  d(Exp, x, E).

deriv =>
   ops8(E1), 
   println(ops8=E1),
   divide10(E2),
   println(divide10=E2),
   log10(E3),
   println(log10=E3),
   times10(E4),
   println(time10=E4).
      
deriv2 =>
   ops8(_E1), 
   divide10(_E2),
   log10(_E3),
   times10(_E4).
      


go => deriv.
go2 => deriv2.