/* 

  Production rules in Picat.

  From Nilsson & Matuszynski: "Logic, Programming and Prolog"
  Page 186f (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

  Also see logic_grammars1.pi for another (and better) approach
  to represent this (and other) grammar(s).

  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.

/*
[sentence]
[noun_phrase,verb_phrase]
[the,noun,verb_phrase]
[the,engine,verb_phrase]
[the,engine,runs]
[the,rabbit,verb_phrase]
[the,rabbit,runs]
[the,noun,runs]
[the,engine,runs]
[the,rabbit,runs]
[noun_phrase,runs]
[the,noun,runs]
[the,engine,runs]
[the,rabbit,runs]

*/
go ?=>
  derives([sentence],X),
  println(X),
  fail,
  
  nl.
go => true.


prod_rule(sentence,[noun_phrase,verb_phrase]).
prod_rule(noun_phrase,[the,noun]).
prod_rule(verb_phrase,[runs]).
prod_rule(noun,[engine]).
prod_rule(noun,[rabbit]).


derives_directly(X,Y) :-
  append(Left,[Lhs],Right,X),
  prod_rule(Lhs,Rhs),
  append(Left,Rhs,Right,Y).

derives(X,X).
derives(X,Z) :-
  derives_directly(X,Y),
  derives(Y,Z).

/*
append4(X,Y,Z,W) :-
  append(X,Y,Tmp),
  append(Tmp,Z,W).
*/

% "more efficient"
% But Picat has append/4 so I use that....
append4([],[],X,X).
append4([],[Head|Y],Z,[Head|W]) :- append4([],Y,Z,W).
append4([Head|X],Y,Z,[Head|W])  :- append4(X,Y,Z,W).