# File Test.ML

    (*  Title:    HOL/Prolog/Test.ML
        ID:       $Id: Test.ML,v 1.5 2005/09/07 19:07:09 wenzelm Exp $
        Author:   David von Oheimb (based on a lecture on Lambda Prolog by Nadathur)
    *)

    val prog_Test = prog_HOHH@[append, reverse, mappred, mapfun, age, eq, bag_appl];
    fun pgoal s = (case Goal s of _ => by (prolog_tac prog_Test));
    val p = ptac prog_Test 1;

    pgoal "append ?x ?y [a,b,c,d]";
    back();
    back();
    back();
    back();

    pgoal "append [a,b] y ?L";
    pgoal "!y. append [a,b] y (?L y)";

    pgoal "reverse [] ?L";

    pgoal "reverse [23] ?L";
    pgoal "reverse [23,24,?x] ?L";
    pgoal "reverse ?L [23,24,?x]";

    pgoal "mappred age ?x [23,24]";
    back();

    pgoal "mappred (%x y. ? z. age z y) ?x [23,24]";

    pgoal "mappred ?P [bob,sue] [24,23]";

    pgoal "mapfun f [bob,bob,sue] [?x,?y,?z]";

    pgoal "mapfun (%x. h x 25) [bob,sue] ?L";

    pgoal "mapfun ?F [24,25] [h bob 24,h bob 25]";

    pgoal "mapfun ?F [24] [h 24 24]";
    back();
    back();
    back();

    (*
    goal (the_context ()) "f a = ?g a a & ?g = x";
    by (rtac conjI 1);
    by (rtac refl 1);
    back();
    back();
    *)

    pgoal "True";

    pgoal "age ?x 24 & age ?y 23";
    back();

    pgoal "age ?x 24 | age ?x 23";
    back();
    back();

    pgoal "? x y. age x y";

    pgoal "!x y. append [] x x";

    pgoal "age sue 24 .. age bob 23 => age ?x ?y";
    back();
    back();
    back();
    back();

    (*set trace_DEPTH_FIRST;*)
    pgoal "age bob 25 :- age bob 24 => age bob 25";
    (*reset trace_DEPTH_FIRST;*)

    pgoal "(!x. age x 25 :- age x 23) => age ?x 25 & age ?y 25";
    back();
    back();
    back();

    pgoal "!x. ? y. eq x y";

    pgoal "? P. P & eq P ?x";
    (*
    back();
    back();
    back();
    back();
    back();
    back();
    back();
    back();
    *)

    pgoal "? P. eq P (True & True) & P";

    pgoal "? P. eq P op | & P k True";

    pgoal "? P. eq P (Q => True) & P";

    (* P flexible: *)
    pgoal "(!P k l. P k l :- eq P Q) => Q a b";
    (*
    loops:
    pgoal "(!P k l. P k l :- eq P (%x y. x | y)) => a | b";
    *)

    (* implication and disjunction in atom: *)
    goal (the_context ()) "? Q. (!p q. R(q :- p) => R(Q p q)) & Q (t | s) (s | t)";
    by (fast_tac HOL_cs 1);

    (* disjunction in atom: *)
    goal (the_context ()) "(!P. g P :- (P => b | a)) => g(a | b)";
    by (step_tac HOL_cs 1);
    by (step_tac HOL_cs 1);
    by (step_tac HOL_cs 1);
    by (fast_tac HOL_cs 2);
    by (fast_tac HOL_cs 1);
    (*
    hangs:
    goal (the_context ()) "(!P. g P :- (P => b | a)) => g(a | b)";
    by (fast_tac HOL_cs 1);
    *)

    pgoal "!Emp Stk.(\
    \                       empty    (Emp::'b) .. \
    \         (!(X::nat) S. add    X (S::'b)         (Stk X S)) .. \
    \         (!(X::nat) S. remove X ((Stk X S)::'b) S))\
    \ => bag_appl 23 24 ?X ?Y";

    pgoal "!Qu. ( \
    \          (!L.            empty    (Qu L L)) .. \
    \          (!(X::nat) L K. add    X (Qu L (X#K)) (Qu L K)) ..\
    \          (!(X::nat) L K. remove X (Qu (X#L) K) (Qu L K)))\
    \ => bag_appl 23 24 ?X ?Y";

    pgoal "D & (!y. E) :- (!x. True & True) :- True => D";

    pgoal "P x .. P y => P ?X";
    back();
    (*
    back();
    -> problem with DEPTH_SOLVE:
    Exception- THM ("dest_state", 1, ["P x & P y --> P y"]) raised
    Exception raised at run-time
    *)