1/*  Copyright 1986-2020 David H. D. Warren and Fernando C. N. Pereira
    2
    3    Permission is hereby granted, free of charge, to any person obtaining a
    4    copy of this software and associated documentation files (the
    5    "Software"), to deal in the Software without restriction, including
    6    without limitation the rights to use, copy, modify, merge, publish,
    7    distribute, sublicense, and/or sell copies of the Software, and to
    8    permit persons to whom the Software is furnished to do so, subject to
    9    the following conditions:
   10
   11    The above copyright notice and this permission notice shall be included
   12    in all copies or substantial portions of the Software.
   13
   14    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
   15    OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
   16    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
   17    IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
   18    CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
   19    TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
   20    SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
   21*/
   22
   23/* Simplifying and executing the logical form of a NL query. */
   24
   25:-public write_tree/1, answer/1.   26
   27:-mode write_tree(+).   28:-mode wt(+,+).   29:-mode header(+).   30:-mode decomp(+,-,-).   31:-mode complex(+).   32:-mode othervars(+,-,-).   33
   34write_tree(T):-
   35   numbervars(T,0,_),
   36   wt(T,0),
   37   fail.
   38write_tree(_).
   39
   40wt((P:-Q),L) :- !, L1 is L+3,
   41   write(P), tab(1), write((:-)), nl,
   42   tab(L1), wt(Q,L1).
   43wt((P,Q),L) :- !, L1 is L-2,
   44   wt(P,L), nl,
   45   tab(L1), put("&"), tab(1), wt(Q,L).
   46wt({P},L) :- complex(P), !, L1 is L+2,
   47   put("{"), tab(1), wt(P,L1), tab(1), put("}").
   48wt(E,L) :- decomp(E,H,P), !, L1 is L+2,
   49   header(H), nl,
   50   tab(L1), wt(P,L1).
   51wt(E,_) :- write(E).
   52
   53header([]).
   54header([X|H]) :- write(X), tab(1), header(H).
   55
   56decomp(setof(X,P,S),[S,=,setof,X],P).
   57decomp(\+(P),[\+],P) :- complex(P).
   58decomp(numberof(X,P,N),[N,=,numberof,X],P).
   59decomp(X^P,[exists,X|XX],P1) :- othervars(P,XX,P1).
   60
   61othervars(X^P,[X|XX],P1) :- !, othervars(P,XX,P1).
   62othervars(P,[],P).
   63
   64complex((_,_)).
   65complex({_}).
   66complex(setof(_,_,_)).
   67complex(numberof(_,_,_)).
   68complex(_^_).
   69complex(\+P) :- complex(P).
   70
   71% Query execution.
   72
   73:-mode respond(?).   74:-mode holds(+,?).   75:-mode answer(+).   76:-mode yesno(+).         :-mode replies(+).   77:-mode reply(+).   78:-mode seto(?,+,-).   79:-mode satisfy(+).   80:-mode pickargs(+,+,+).   81:-mode pick(+,?).   82
   83respond([]) :- display('Nothing satisfies your question.'), nl.
   84respond([A|L]) :- reply(A), replies(L).
   85
   86answer((answer([]):-E)) :- !, holds(E,B), yesno(B).
   87answer((answer([X]):-E)) :- !, seto(X,E,S), respond(S).
   88answer((answer(X):-E)) :- seto(X,E,S), respond(S).
   89
   90seto(X,E,S) :-
   91%	portray_clause(({X} :- E)),
   92	phrase(satisfy(E,G),Vars),
   93%	portray_clause(({X} :- G)),
   94	(   setof(X,Vars^G,S)
   95	->  true
   96	;   S = []
   97	).
   98
   99holds(E,True) :-
  100	phrase(satisfy(E, G), _),
  101	(   G
  102	->  True = true
  103	;   True = false
  104	).
  105
  106yesno(true) :- display('Yes.').
  107yesno(false) :- display('No.').
  108
  109replies([]) :- display('.').
  110replies([A]) :- display(' and '), reply(A), display('.').
  111replies([A|X]) :- display(', '), reply(A), replies(X).
  112
  113reply(N--U) :- !, write(N), display(' '), write(U).
  114reply(X) :- write(X).

 satisfy(+Term, -Goal)//

Originally, Term was meta-interpreted. If we do not want every ^/2-term to act as an existential quantification, this no longer works. Hence, we now compile the term into a goal and compute the existentially quantified variables.

  123satisfy((P0,Q0), (P,Q)) --> !, satisfy(P0, P), satisfy(Q0, Q).
  124satisfy({P0}, (P->true)) --> !, satisfy(P0, P).
  125satisfy(X^P0, P) --> !, satisfy(P0, P), [X].
  126satisfy(\+P0, \+P) --> !, satisfy(P0, P).
  127satisfy(numberof(X,P0,N), (setof(X,Vars^P,S),length(S,N))) --> !,
  128	{ phrase(satisfy(P0,P),Vars) },
  129	[S], Vars.			% S is an internal variable!
  130satisfy(setof(X,P0,S), setof(X,Vars^P,S)) --> !,
  131	{ phrase(satisfy(P0,P),Vars) },
  132	Vars.
  133satisfy(+P0, \+ exceptionto(P)) --> !,
  134	satisfy(P0, P).
  135satisfy(X<Y, X<Y) --> !.
  136satisfy(X=<Y, X=<Y) --> !.
  137satisfy(X>=Y, X>=Y) --> !.
  138satisfy(X>Y, X>Y) --> !.
  139satisfy(P, database(P)) --> [].
  140
  141exceptionto(P) :-
  142   functor(P,F,N), functor(P1,F,N),
  143   pickargs(N,P,P1),
  144   exception(P1).
  145
  146exception(P) :- database(P), !, fail.
  147exception(_P).
  148
  149pickargs(0,_,_) :- !.
  150pickargs(N,P,P1) :- N1 is N-1,
  151   arg(N,P,S),
  152   pick(S,X),
  153   arg(N,P1,X),
  154   pickargs(N1,P,P1).
  155
  156pick([X|_],X).
  157pick([_|S],X) :- !, pick(S,X).
  158pick([],_) :- !, fail.
  159pick(X,X)