/* 

  Logic grammar in Picat.

  From Nilsson & Matuszynski: "Logic, Programming and Prolog"
  Page 187f (Chapter 10: Logic and Grammar)

  This defines the grammar (page 184) 
     <sentence>    -> <noun-phrase>, <verb-phrase>
     <noun-phrase> -> the <noun>
     <verb-phrase> -> runs
     <noun>        -> engine
     <noun>        -> rabbit

  Compare with production_rules1.pi for another (and slower) representation 
  of this grammar.

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

*/

% import v3_utils.
% import util.
% import cp.


main => go.

go ?=>
  sentence([the,rabbit,runs]),
  sentence([the,X,runs]),
  println(x=X),
  fail,
  nl.
go => true.


% Since we use difference lists, we must take
% care of that in the call of sentence2/1.
%
% Picat> sentence2(X)
% X = [the,engine,runs|_f408] - _f408 ?;
% X = [the,rabbit,runs|_f408] - _f408
% yes
% 
% Picat> sentence2([the,engine,runs])
% no
% 
% Picat> sentence2($X-[])                
% X = [the,engine,runs] ?;
% X = [the,rabbit,runs]
% yes
% 
% Picat> sentence2($[the,rabbit,runs,quickly]-[quickly])
% yes
% 
% Picat> sentence2($[the,rabbit,runs,quickly]-[X])      
% X = quickly
% yes
%
go2 ?=>
  sentence2($X-[]),
  println(X),
  fail,
  nl.
go2 => true.

%
% Picat> sentence3($X-[])                   
% X = [the,engine,runs] ?;
% X = [the,rabbit,runs]
% yes
%
go3 ?=>
  sentence3($X-[]),
  println(X),
  fail,
  nl.
go3 => true.


/*
% Original
% This is rather inefficient.
% and loops after sentences has been generated
sentence(Z) :-
  append(X,Y,Z),
  noun_phrase(X),
  verb_phrase(Y).
*/
% Fixed (comment at page 188)
sentence(Z) :-
  noun_phrase(X),
  verb_phrase(Y),
  append(X,Y,Z).


noun_phrase([the|X]) :- noun(X).

verb_phrase([runs]).

noun([engine]).
noun([rabbit]).


% Using difference lists: more efficient
% Example 10.5 (page 188f)
sentence2(X0-X2) :-
  noun_phrase2($X0-X1),
  verb_phrase2($X1-X2).

noun_phrase2(X0-X2) :-
  diff(X0,X1,[the]),noun2($X1-X2).

verb_phrase2(X0-X1) :-
  diff(X0,X1,[runs]).

noun2(X0-X1) :- diff(X0,X1,[engine]).
noun2(X0-X1) :- diff(X0,X1,[rabbit]).

diff([X|Y],Y,[X]).


% A simpler variant using difference list
% Example 10.6 (page 190)
sentence3(X0-X2) :- noun_phrase3($X0-X1), verb_phrase3($X1-X2).
noun_phrase3([the|X1]-X2) :- noun3($X1-X2).
verb_phrase3([runs|X1]-X1).
noun3([engine|X1]-X1).
noun3([rabbit|X1]-X1).