469 lines
12 KiB
Prolog
469 lines
12 KiB
Prolog
/*************************************************************************
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* *
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* YAP Prolog *
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* *
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* Yap Prolog was developed at NCCUP - Universidade do Porto *
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* *
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* Copyright L.Damas, V.S.Costa and Universidade do Porto 1985-1997 *
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* *
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**************************************************************************
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* *
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* File: arith.yap *
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* Last rev: *
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* mods: *
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* comments: arithmetical optimization *
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* *
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*************************************************************************/
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% the default mode is on
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expand_exprs(Old,New) :-
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(get_value('$c_arith',true) ->
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Old = on ;
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Old = off ),
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'$set_arith_expan'(New).
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'$set_arith_expan'(on) :- set_value('$c_arith',true).
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'$set_arith_expan'(off) :- set_value('$c_arith',[]).
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compile_expressions :- set_value('$c_arith',true).
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do_not_compile_expressions :- set_value('$c_arith',[]).
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'$c_built_in'(IN, M, OUT) :-
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get_value('$c_arith',true), !,
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'$do_c_built_in'(IN, M, OUT).
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'$c_built_in'(IN, _, IN).
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'$do_c_built_in'(G, M, OUT) :- var(G), !,
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'$do_c_built_metacall'(G, M, OUT).
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'$do_c_built_in'(Mod:G, _, OUT) :- !,
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'$do_c_built_metacall'(G, Mod, OUT).
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'$do_c_built_in'(\+ G, _, OUT) :-
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nonvar(G),
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G = (A = B),
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!,
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OUT = (A \= B).
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'$do_c_built_in'(call(G), _, OUT) :-
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nonvar(G),
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G = (Mod:G1), !,
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'$do_c_built_metacall'(G1, Mod, OUT).
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'$do_c_built_in'(call(G), Mod, OUT) :-
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var(G), !,
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'$do_c_built_metacall'(G, Mod, OUT).
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'$do_c_built_in'(depth_bound_call(G,D), M, OUT) :- !,
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'$do_c_built_in'(G, M, NG),
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% make sure we don't have something like (A,B) -> $depth_next(D), A, B.
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( '$composed_built_in'(NG) ->
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OUT = depth_bound_call(NG,D)
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;
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OUT = ('$set_depth_limit_for_next_call'(D),NG)
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).
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'$do_c_built_in'(once(G), M, (yap_hacks:current_choice_point(CP),NG,'$$cut_by'(CP))) :- !,
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'$do_c_built_in'(G,M,NG0),
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'$clean_cuts'(NG0, NG).
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'$do_c_built_in'(forall(Cond,Action), M, \+((NCond, \+(NAction)))) :- !,
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'$do_c_built_in'(Cond,M,ICond),
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'$do_c_built_in'(Action,M,IAction),
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'$clean_cuts'(ICond, NCond),
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'$clean_cuts'(IAction, NAction).
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'$do_c_built_in'(ignore(Goal), M, (NGoal -> true ; true)) :- !,
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'$do_c_built_in'(Goal,M,IGoal),
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'$clean_cuts'(IGoal, NGoal).
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'$do_c_built_in'(if(G,A,B), M, (yap_hacks:current_choicepoint(DCP),NG,yap_hacks:cut_at(DCP),NA; NB)) :- !,
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'$do_c_built_in'(G,M,NG0),
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'$clean_cuts'(NG0, NG),
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'$do_c_built_in'(A,M,NA),
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'$do_c_built_in'(B,M,NB).
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'$do_c_built_in'((G*->A;B), M, (yap_hacks:current_choicepoint(DCP),NG,yap_hacks:cut_at(DCP),NA; NB)) :- !,
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'$do_c_built_in'(G,M,NG0),
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'$clean_cuts'(NG0, NG),
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'$do_c_built_in'(A,M,NA),
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'$do_c_built_in'(B,M,NB).
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'$do_c_built_in'((G*->A), M, (NG,NA)) :- !,
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'$do_c_built_in'(G,M,NG0),
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'$clean_cuts'(NG0, NG),
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'$do_c_built_in'(A,M,NA).
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'$do_c_built_in'('C'(A,B,C), _, (A=[B|C])) :- !.
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'$do_c_built_in'(trace, _M, '$do_trace') :- !.
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'$do_c_built_in'(X is Y, M, P) :-
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primitive(X), !,
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'$do_c_built_in'(X =:= Y, M, P).
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'$do_c_built_in'(X is Y, M, (P,A=X)) :-
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nonvar(X), !,
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'$do_c_built_in'(A is Y, M, P).
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'$do_c_built_in'(X is Y, _, P) :-
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nonvar(Y), % Don't rewrite variables
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!,
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(
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number(Y) ->
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P = ( X = Y); % This case reduces to an unification
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'$expand_expr'(Y, P0, X0),
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'$drop_is'(X0, X, P0, P)
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).
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'$do_c_built_in'(Comp0, _, R) :- % now, do it for comparisons
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'$compop'(Comp0, Op, E, F),
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!,
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'$compop'(Comp, Op, U, V),
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'$expand_expr'(E, P, U),
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'$expand_expr'(F, Q, V),
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'$do_and'(P, Q, R0),
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'$do_and'(R0, Comp, R).
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'$do_c_built_in'(P, _, P).
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'$do_c_built_metacall'(G1, Mod, '$execute_wo_mod'(G1,Mod)) :-
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var(Mod), !.
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'$do_c_built_metacall'(G1, Mod, '$execute_in_mod'(G1,Mod)) :-
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var(G1), atom(Mod), !.
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'$do_c_built_metacall'(Mod:G1, _, OUT) :- !,
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'$do_c_built_metacall'(G1, Mod, OUT).
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'$do_c_built_metacall'(G1, Mod, '$execute_in_mod'(G1,Mod)) :-
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atom(Mod), !.
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'$do_c_built_metacall'(G1, Mod, call(Mod:G1)).
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'$do_and'(true, P, P) :- !.
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'$do_and'(P, true, P) :- !.
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'$do_and'(P, Q, (P,Q)).
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% V is the result of the simplification,
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% X the result of the initial expression
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% and the last argument is how we are writing this result
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'$drop_is'(V, V1, P0, G) :- var(V), !, % usual case
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V = V1, P0 = G.
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'$drop_is'(V, X, P0, P) :- % atoms
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'$do_and'(P1, X is V, P).
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% Table of arithmetic comparisons
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'$compop'(X < Y, < , X, Y).
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'$compop'(X > Y, > , X, Y).
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'$compop'(X=< Y,=< , X, Y).
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'$compop'(X >=Y, >=, X, Y).
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'$compop'(X=:=Y,=:=, X, Y).
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'$compop'(X=\=Y,=\=, X, Y).
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'$composed_built_in'(V) :- var(V), !,
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fail.
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'$composed_built_in'((yap_hacks:current_choice_point(_),NG,'$$cut_by'(_))) :- !,
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'$composed_built_in'(NG).
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'$composed_built_in'((_,_)).
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'$composed_built_in'((_;_)).
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'$composed_built_in'((_|_)).
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'$composed_built_in'((_->_)).
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'$composed_built_in'(_:G) :-
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'$composed_built_in'(G).
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'$composed_built_in'(\+G) :-
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'$composed_built_in'(G).
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'$composed_built_in'(not(G)) :-
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'$composed_built_in'(G).
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% expanding an expression:
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% first argument is the expression not expanded,
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% second argument the expanded expression
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% third argument unifies with the result from the expression
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'$expand_expr'(V, true, V) :-
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var(V), !.
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'$expand_expr'([T], E, V) :- !,
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'$expand_expr'(T, E, V).
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'$expand_expr'(A, true, A) :-
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atomic(A), !.
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'$expand_expr'(T, E, V) :-
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T =.. [O, A], !,
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'$expand_expr'(A, Q, X),
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'$expand_expr'(O, X, V, Q, E).
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'$expand_expr'(T, E, V) :-
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T =.. [O, A, B], !,
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'$expand_expr'(A, Q, X),
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'$expand_expr'(B, R, Y),
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'$expand_expr'(O, X, Y, V, Q, S),
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'$do_and'(R, S, E).
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% expanding an expression of the form:
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% O is Op(X),
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% after having expanded into Q
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% and giving as result P (the last argument)
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'$expand_expr'(Op, X, O, Q, Q) :-
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number(X), !,
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is( O, Op, X).
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'$expand_expr'(Op, X, O, Q, P) :-
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'$unary_op_as_integer'(Op,IOp),
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'$do_and'(Q, is( O, IOp, X), P).
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% expanding an expression of the form:
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% O is Op(X,Y),
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% after having expanded into Q
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% and giving as result P (the last argument)
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% included is some optimization for:
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% incrementing and decrementing,
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% the elementar arithmetic operations [+,-,*,//]
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'$expand_expr'(Op, X, Y, O, Q, Q) :-
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number(X), number(Y), !,
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is( O, Op, X, Y).
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'$expand_expr'(+, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$plus'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(-, X, Y, O, Q, P) :-
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var(X), number(Y),
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Z is -Y, !,
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'$expand_expr'(+, Z, X, O, Q, P).
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'$expand_expr'(-, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$minus'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(*, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$times'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(//, X, Y, O, Q, P) :-
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nonvar(Y), Y == 0, !,
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'$binary_op_as_integer'(//,IOp),
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'$do_and'(Q, is(O,IOp,X,Y), P).
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'$expand_expr'(//, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$div'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(/\, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$and'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(\/, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$or'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(<<, X, Y, O, Q, P) :-
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var(X), number(Y), Y < 0,
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Z is -Y, !,
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'$expand_expr'(>>, X, Z, O, Q, P).
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'$expand_expr'(<<, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$sll'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(>>, X, Y, O, Q, P) :-
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var(X), number(Y), Y < 0,
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Z is -Y, !,
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'$expand_expr'(<<, X, Z, O, Q, P).
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'$expand_expr'(>>, X, Y, O, Q, P) :- !,
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'$preprocess_args_for_non_commutative'(X, Y, X1, Y1, E),
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'$do_and'(E, '$slr'(X1,Y1,O), F),
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'$do_and'(Q, F, P).
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'$expand_expr'(Op, X, Y, O, Q, P) :-
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'$binary_op_as_integer'(Op,IOp),
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'$do_and'(Q, is(O,IOp,X,Y), P).
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'$preprocess_args_for_commutative'(X, Y, X, Y, true) :-
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var(X), var(Y), !.
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'$preprocess_args_for_commutative'(X, Y, X, Y, true) :-
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var(X), integer(Y), \+ '$bignum'(Y), !.
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'$preprocess_args_for_commutative'(X, Y, X, Z, Z = Y) :-
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var(X), !.
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'$preprocess_args_for_commutative'(X, Y, Y, X, true) :-
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integer(X), \+ '$bignum'(X), var(Y), !.
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'$preprocess_args_for_commutative'(X, Y, Z, X, Z = Y) :-
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integer(X), \+ '$bignum'(X), !.
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'$preprocess_args_for_commutative'(X, Y, Z, W, E) :-
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'$do_and'(Z = X, Y = W, E).
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'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
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var(X), var(Y), !.
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'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
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var(X), integer(Y), \+ '$bignum'(Y), !.
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'$preprocess_args_for_non_commutative'(X, Y, X, Z, Z = Y) :-
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var(X), !.
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'$preprocess_args_for_non_commutative'(X, Y, X, Y, true) :-
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integer(X), \+ '$bignum'(X), var(Y), !.
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'$preprocess_args_for_non_commutative'(X, Y, X, Z, Z = Y) :-
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integer(X), \+ '$bignum'(X), !.
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'$preprocess_args_for_non_commutative'(X, Y, Z, W, E) :-
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'$do_and'(Z = X, Y = W, E).
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/* Arithmetics */
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between(I,M,J) :-
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(
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var(I)
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->
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'$do_error'(instantiation_error,between(I,M,J))
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;
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integer(I)
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->
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(
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var(M)
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->
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'$do_error'(instantiation_error,between(I,M,J))
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;
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integer(M)
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->
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(
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var(J)
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->
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I =< M, '$between'(I,M,J)
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;
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integer(J)
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->
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J >= I, J =< M
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;
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'$do_error'(type_error(integer, J),between(I,M,J))
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)
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;
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M == inf ->
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(
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var(J)
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->
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'$between_inf'(I,J)
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;
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integer(J)
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->
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J >= I
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;
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'$do_error'(type_error(integer, J),between(I,M,J))
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)
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;
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M == infinity ->
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(
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var(J)
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->
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'$between_inf'(I,J)
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;
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integer(J)
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->
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J >= I
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;
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'$do_error'(type_error(integer, J),between(I,M,J))
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)
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;
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'$do_error'(type_error(integer, M),between(I,M,J))
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)
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;
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'$do_error'(type_error(integer, I),between(I,M,J))
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).
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'$between'(I,M,I) :- (I == M -> ! ; true ).
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'$between'(I0,I,J) :- I0 < I,
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'$plus'(I0, 1, I1),
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'$between'(I1,I,J).
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'$between_inf'(I,I).
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'$between_inf'(I,J) :-
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'$plus'(I, 1, I1),
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'$between_inf'(I1,J).
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% M and N nonnegative integers, N is the successor of M
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succ(M,N) :-
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(
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var(M)
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->
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(
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integer(N),
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N > 0
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->
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'$plus'(N,-1,M)
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;
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'$succ_error'(M,N)
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)
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;
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integer(M),
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M >= 0
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->
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(
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var(N)
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->
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'$plus'(M,1,N)
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;
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integer(N),
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N > 0
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->
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'$plus'(M,1,N)
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;
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'$succ_error'(M,N)
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)
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;
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'$succ_error'(M,N)
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).
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'$succ_error'(M,N) :-
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var(M),
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var(N), !,
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'$do_error'(instantiation_error,succ(M,N)).
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'$succ_error'(M,N) :-
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nonvar(M),
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\+ integer(M),
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'$do_error'(type_error(integer, M),succ(M,N)).
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'$succ_error'(M,N) :-
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nonvar(M),
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M < 0,
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'$do_error'(domain_error(not_less_than_zero, M),succ(M,N)).
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'$succ_error'(M,N) :-
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nonvar(N),
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\+ integer(N),
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'$do_error'(type_error(integer, N),succ(M,N)).
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'$succ_error'(M,N) :-
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nonvar(N),
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N < 0,
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'$do_error'(domain_error(not_less_than_zero, N),succ(M,N)).
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plus(X, Y, Z) :-
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(
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var(X)
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->
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(
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integer(Y), integer(Z)
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->
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'$minus'(Z,Y,X)
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;
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'$plus_error'(X,Y,Z)
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)
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;
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integer(X)
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->
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(
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var(Y)
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->
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(
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integer(Z)
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->
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'$minus'(Z,X,Y)
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;
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'$plus_error'(X,Y,Z)
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)
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;
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integer(Y)
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->
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(
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integer(Z)
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->
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'$minus'(Z,Y,X)
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;
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var(Z)
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->
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'$plus'(X,Y,Z)
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;
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'$plus_error'(X,Y,Z)
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)
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;
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'$plus_error'(X,Y,Z)
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)
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;
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'$plus_error'(X,Y,Z)
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).
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'$plus_error'(X,Y,Z) :-
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nonvar(X),
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\+ integer(X),
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'$do_error'(type_error(integer, X),plus(X,Y,Z)).
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'$plus_error'(X,Y,Z) :-
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|
nonvar(Y),
|
|
\+ integer(Y),
|
|
'$do_error'(type_error(integer, Y),plus(X,Y,Z)).
|
|
'$plus_error'(X,Y,Z) :-
|
|
nonvar(Z),
|
|
\+ integer(Z),
|
|
'$do_error'(type_error(integer, Z),plus(X,Y,Z)).
|
|
'$plus_error'(X,Y,Z) :-
|
|
'$do_error'(instantiation_error,plus(X,Y,Z)).
|
|
|
|
|
|
|