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provador_cabral.pl
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:- dynamic clause/1.
:- op( 100, fy, ~ ).
:- op( 110, xfy, & ).
:- op( 120, xfy, v ).
:- op( 130, xfy, => ).
translate( F & G ) :- !,
translate( F ),
translate( G ).
translate(Formula) :-
transform( Formula, NewFormula), !,
translate( NewFormula).
translate(Formula) :-
to_list( Formula, ListFormula),
msort(ListFormula, SortedFormula),
list_to_set( SortedFormula, Clauses ),
simplify_clause( Clauses, SimplifiedClauses ),
assert( clause( SimplifiedClauses) ).
% Simplifing
transform(X v X, X) :- !.
% Eliminating double negations
transform( ~(~X), X) :- !.
% Eliminating implications
transform( X => Y, ~X v Y) :- !.
% de Morgan
transform( ~( X & Y), ~X v ~Y) :- !.
transform( ~( X v Y), ~X & ~Y) :- !.
% Distribution
transform( X & Y v Z, (X v Z) & ( Y v Z)) :- !.
transform( X v Y & Z, ( X v Y) & ( X v Z)) :- !.
% transforming sub-expressions:
transform( X v Y, X1 v Y) :-
transform( X, X1), !.
transform( X v Y, X v Y1):-
transform( Y, Y1), !.
transform( ~X, ~X1) :-
transform( X, X1).
% Transforming formula to List
to_list(X v Y, List) :- to_list(X, ListX), to_list(Y, ListY), append(ListX, ListY, List).
to_list(X, [X]).
%Simplifing clauses
simplify_clause([X|Clause], NewClause) :-
=(X, ~Y),
member(Y, Clause),
delete([X|Clause], ~Y, NewList),
delete(NewList, Y, ClauseDelete),
simplify_clause(ClauseDelete, NewClause).
simplify_clause([X|Clause], NewClause) :-
member(~X, Clause),
delete([X|Clause], ~X, NewList),
delete(NewList, X, ClauseDelete),
simplify_clause(ClauseDelete, NewClause).
simplify_clause([X|Clause], NewClause) :- verify_all([X|Clause], [X|Clause], NewClause).
simplify_clause([], []).
verify_all([Head|Clause], List, NewList) :- not(member(~Head, List)), verify_all(Clause, List, NewList).
verify_all([Head|Clause], List, Result) :-
member(~Head, List),
delete(List, ~Head, NewList),
delete(NewList, Head, DeletedList),
verify_all(Clause, DeletedList, Result).
verify_all([], List, List).
%calculating resolver
resolve(C1, C2, Result) :-
union(C1, C2, C3),
simplify_clause(C3, Result),
not(empty(Result)),
assert(clause(Result)).
resolve(C1, C2, Result) :-
union(C1, C2, C3),
simplify_clause(C3, Result),
empty(Result),
assert(clause([])),
print_proof,
writeln("Formula Insatisfativel"),
abort.
% strategy for resolution depth first search
depth_resolution([[HeadTerm|Terms]|Clauses], [HeadCopyClause|CopyClauses]) :-
=(HeadTerm, ~Y),
member(Y, HeadCopyClause),
resolve([HeadTerm|Terms], HeadCopyClause, CreatedClause),
depth_resolution([CreatedClause|Clauses], [HeadCopyClause|CopyClauses]).
depth_resolution([[HeadTerm|Terms]|Clauses], [HeadCopyClause|CopyClauses]) :-
member(~HeadTerm, HeadCopyClause),
resolve([HeadTerm|Terms], HeadCopyClause, CreatedClause),
depth_resolution([CreatedClause|Clauses], [HeadCopyClause|CopyClauses]).
depth_resolution([[HeadTerm|Terms]|Clauses], [_|CopyClauses]) :-
depth_resolution([[HeadTerm|Terms]|Clauses], CopyClauses).
depth_resolution([[_|Terms]|Clauses], [HeadCopyClause|CopyClauses]) :-
head(Terms, NewTerm),
not(empty(NewTerm)),
tail(Terms, NewTerms),
depth_resolution([[NewTerm|NewTerms]|Clauses], [HeadCopyClause|CopyClauses]).
depth_resolution([_|Clauses], [HeadCopyClause|CopyClauses]) :-
head(Clauses, NewClause),
not(empty(NewClause)),
tail(Clauses, NewClauses),
depth_resolution([NewClause|NewClauses], [HeadCopyClause|CopyClauses]).
depth_resolution(_, _) :- writeln("Formula Satisfativel").
% print proof
print_proof :-
writeln("========PROVA========"),
foreach(clause(Clause), print_clause(Clause)),
writeln("======RESULTADO======").
print_clause(Clause) :- writeln(Clause).
%resolution
solve(Formula) :-
retractall(clause(_)),
translate(~Formula),
setof(Clause, clause(Clause), Clauses),
depth_resolution(Clauses, Clauses).
/*TODO -> Do the enumeration of each clause and put in the database and on proof*/
%utility predicates
head([Head|_], Head).
head([], []).
tail([_|Tail], Tail).
tail([], []).
empty([]).
empty(_) :- false.