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Christian Ohlsson
2026-03-05 13:42:07 +01:00
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Free_In_and_Rename_Var/lab2.pl Normal file
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/*****************************/
/* Christian Ohlsson */
/* Logik för dataloger */
/* Karlstad 990228 */
/* Laboration 2 i Logik */
/*****************************/
/* Functions included */
/* free_in */
/* rename_var */
/*****************************/
:- op(200, fx, -).
:- op(400, xfy, #).
:- op(400, xfy, &).
:- op(700, xfy, ->).
:- op(700, xfy, <->).
exist(X, [H|T]) :- X = H, !, fail.
exist(X, [H|T]) :- Z =.. T, free_in(X, Z).
all(X, [H|T]) :- X = H, !, fail.
all(X, [H|T]) :- Z =.. T, free_in(X, Z).
operators(X, [H|T]) :- free_in(X, H), Z =.. T, free_in(X, Z).
falsum(X) :- true.
/* Del 1 - free_in */
/* free_in(+variabel, +TermOrFormula */
free_in(X, Y) :- Y =.. [H|T], T = [].
free_in(X, Y) :- Y =.. [H|T], member(H, [&, #, ->, <->]), operators(X, T).
free_in(X, Y) :- Y =.. [H|T], member(H, [all, exist]), call(H, X, T).
free_in(X, Y) :- Y =.. [H|T], member(H, [-]), falsum(X).
free_in(X, Y) :- Y =.. [H|T], member(H, [as, pr, fu, qu, rt]).
/* Del 2 - rename_var */
/* rename_var(+Element, +TermOrFormula, +Nyttelement, -NyTermOrFormula) */
ersatt(E1, E2, [], []).
ersatt(E1, E2, [E1|R], [E2|S]) :- ersatt(E1, E2, R, S).
ersatt(E1, E2, [X|R], [X|S]) :- ersatt(E1, E2, R, S).
rv(E1, E2, [H|T], New) :- T = [], atom(H), ersatt(E1, E2, [H], New).
rv(E1, E2, [H|T], New) :- T = [], rename_var(E1, H, E2, Next), append([Next], [], New).
rv(E1, E2, [H|T], New) :- rv(E1, E2, T, N1), rv(E1, E2, [H], N2), append(N2,N1, New).
rename_var(E1, Old, E2, New) :- Old =.. [H|T], T = [], ersatt(E1, E2, [H], Z), New =.. Z.
rename_var(E1, Old, E2, New) :- Old =.. [H|T], rv(E1, E2, T, Next), New =.. [H|Next].

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Prenex_Normal_Form/lab3.pl Normal file
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/*****************************/
/* Christian Ohlsson */
/* Logik för dataloger */
/* Karlstad 990228 */
/* Laboration 3 i Logik */
/*****************************/
/* Functions included */
/* prenex */
/* implout */
/* negin */
/* kvant */
/* free_in */
/* rename_var */
/*****************************/
:- op(200,fx,~).
:- op(400,xfy,#).
:- op(400,xfy,&).
:- op(700,xfy,->).
:- op(700,xfy,<->).
prenex(Formel,PNF):-
implout(Formel,Svar1),
negin(Svar1,Svar2),
kvant(Svar2,PNF,[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10],L).
/* ***************************** IMPLOUT **************************** */
implout((P<->Q),((P1&Q1)#(~P1&~Q1))) :- !,implout(P,P1),implout(Q,Q1).
implout((P->Q),(~P1#Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout(all(X,P),all(X,P1)) :- !,implout(P,P1).
implout(exist(X,P),exist(X,P1)) :- !,implout(P,P1).
implout((P&Q),(P1&Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout((P#Q),(P1#Q1)) :- !,implout(P,P1),implout(Q,Q1).
implout((~P),(~P1)) :- !,implout(P,P1).
implout(P,P).
/* ***************************** NEGIN **************************** */
negin((~P),P1) :- !,neg(P,P1).
negin(all(X,P),all(X,P1)) :- !,negin(P,P1).
negin(exist(X,P),exist(X,P1)) :- !,negin(P,P1).
negin((P&Q),(P1&Q1)) :- !,negin(P,P1),negin(Q,Q1).
negin((P#Q),(P1#Q1)) :- !,negin(P,P1),negin(Q,Q1).
negin(P,P).
neg((~P),P1) :- !,negin(P,P1).
neg(all(X,P),exist(X,P1)) :- !,neg(P,P1).
neg(exist(X,P),all(X,P1)) :- !,neg(P,P1).
neg((P&Q),(P1#Q1)) :- !,neg(P,P1),neg(Q,Q1).
neg((P#Q),(P1&Q1)) :- !,neg(P,P1),neg(Q,Q1).
neg(P,(~P)).
/* ***************************** RENAME-VAR **************************** */
r_v(X,exist(X,P),exist(F,P1),[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,exist(Y,P),exist(Y,P1),[F|R]):- X\==Y, r_v(X,P,P1,[F|R]).
r_v(X,all(X,P),all(F,P1),[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,all(Y,P),all(Y,P1),[F|R]):- X\==Y, r_v(X,P,P1,[F|R]).
r_v(X,Y#Z,Y1#Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y&Z,Y1&Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y->Z,Y1->Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y<->Z,Y1<->Z1,[F|R]):- r_v(X,Y,Y1,[F|R]),r_v(X,Z,Z1,[F|R]).
r_v(X,Y,Y2,[F|R]):- Y=..[T,S],r_v(X,S,Y1,[F|R]), Y2=..[T,Y1].
r_v(X,[T|S],[F|S1],[F|R]):- X==T, r_v(X,S,S1,[F|R]).
r_v(X,[T|S],[S2|S1],[F|R]):- X\==T, r_v(X,S,S1,[F|R]),r_v(X,T,S2,[F|R]).
r_v(X,~P,~P1,[F|R]):- r_v(X,P,P1,[F|R]).
r_v(X,X,F,[F|R]).
r_v(X,U,U,[F|R]):- X\==U.
/* ***************************** FREE ****************************** */
free_in(X,exist(Y,P)):- X\==Y, free_in(X,P).
free_in(X,all(Y,P)):- X\==Y, free_in(X,P).
free_in(X,Y#Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y&Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y->Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y<->Z):-free_in(X,Y);free_in(X,Z).
free_in(X,Y):- Y=..[F,R],free_in(X,R).
free_in(X,[F|R]):-free_in(X,F);free_in(X,R).
free_in(X,~Z):-free_in(X,Z).
free_in(X,X).
/* ********************************************************************* */
/* ***************************** ALL & ***************************** */
kvant(all(X,Y)&Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Y1&Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Y1&Z2)),SY,L2,L3)).
/* ***************************** & ALL **************************** */
kvant(Z&all(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Z2&Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Z2&Y1)),SY,L2,L3)).
/* ***************************** ALL # **************************** */
kvant(all(X,Y)#Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Y1#Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Y1#Z2)),SY,L2,L3)).
/* ***************************** # ALL **************************** */
kvant(Z#all(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(all(X,(Z2#Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(all(X,(Z2#Y1)),SY,L2,L3)).
/* *************************** EXIST & ************************** */
kvant(exist(X,Y)&Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Y1&Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Y1&Z2)),SY,L2,L3)).
/* *************************** & EXIST ************************** */
kvant(Z&exist(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Z2&Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Z2&Y1)),SY,L2,L3)).
/* *************************** EXIST # ************************** */
kvant(exist(X,Y)#Z,SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Y1#Z2)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Y1#Z2)),SY,L2,L3)).
/* *************************** # EXIST ************************** */
kvant(Z#exist(X,Y),SY,[F|R],L3):-
(free_in(X,Z),
r_v(X,Z,Z1,[F]),
kvant(Y,Y1,R,R1),
kvant(Z1,Z2,R1,L2),
kvant(exist(X,(Z2#Y1)),SY,L2,L3));
(kvant(Y,Y1,R,R1),
kvant(Z,Z2,R1,L2),
kvant(exist(X,(Z2#Y1)),SY,L2,L3)).
/* *************************** & ************************** */
kvant(P&Q,PQ,L,L3):-
kvant(P,P1,L,L1),
kvant(Q,Q1,L1,L2),
((P1\==P);(Q1\==Q)),
kvant(P1&Q1,PQ,L2,L3).
/* *************************** # ************************** */
kvant(P#Q,PQ,L,L3):-
kvant(P,P1,L,L1),
kvant(Q,Q1,L1,L2),
((P1\==P);(Q1\==Q)),
kvant(P1#Q1,PQ,L2,L3).
/* *************************** EXIST ************************** */
kvant(all(X,F),all(X,F1),L1,L2):-
kvant(F,F1,L1,L2).
/* *************************** ALL ************************** */
kvant(exist(X,F),exist(X,F1),L1,L2):-
kvant(F,F1,L1,L2).
/* *************************** BASFALL ************************** */
kvant(X,X,L,L).

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/*****************************/
/* Christian Ohlsson */
/* Logik för dataloger */
/* Karlstad 990228 */
/* Lab 1 i Logik */
/*****************************/
/* Functions included: */
/* smaller_than_all */
/* exchange_all */
/* exchange_nth */
/* subset */
/* member */
/*****************************/
/* sum */
/* product */
/* fac */
/*****************************/
/* diff */
/* ismother */
/* isfather */
/* isson */
/* sisterof */
/* grandpaof */
/* sibling */
/*****************************/
/******************************************************
smaller_than_all (M, [array of numbers]).
Kollar om M är mindre än alla tal i arrayen
och om så är fallet svarar kompilatorn med Yes
*/
smaller_than_all(M,[]).
smaller_than_all(M,[Y|L]) :- M < Y, smaller_than_all(M, L).
/******************************************************
exchange_all(E1,E2,[indata-array],[utdata-array])
Byter ut alla E1 mot E2 i indata-arrayen
och lagrar detta i utdata-arrayen
*/
exchange_all(E1,E2,[],[]).
exchange_all(E1,E2,[Y|L], [F|R]):-E1 = Y, F is E2,exchange_all(E1,E2,L,R).
exchange_all(E1,E2,[Y|L], [Y|R]):-exchange_all(E1,E2,L,R).
/******************************************************
exchange_nth(E1,E2,[indata-array],[utdata-array])
Byter ut elementet på plats E1 mot E2
*/
exchange_nth(E1,E2,[],[]).
exchange_nth(E1,E2,[Y|L],[F|R]):-E1 = 1,F is E2, exchange_nth(0,E2,L,R).
exchange_nth(E1,E2,[Y|L], [Y|R]):-W is E1-1,exchange_nth(W,E2,L,R).
/******************************************************
subset([array1], [array2])
Kollar om alla element i array1 finns med
i array2 och returnerar då Yes.
*/
subset([], L).
subset([Y|L], R):- member(Y, R),subset(L,R).
member(X,[X|_]).
member(X,[_|Y]):-member(X,Y).
/******************************************************
sum
Tar emot tre värden och svarar
Yes om det tredje värdet är summan av
de två tidigare.
product
Tar emot tre värden och svarar
Yes om det tredje värdet är produkten
av de två tidigare.
fac
Tar emot två värden och svarar
Yes om det andra värdet är faculteten
av det första.
*/
sum(N, N1, S) :- S is N + N1.
product(N1, N2, S) :- S is N1 * N2.
fac(1,1).
fac(N, S) :- M is N-1, fac(M, Z), S is N * Z.
/******************************************************
Familjen
*/
/* Män */
male(martin).
male(olle).
male(pelle).
male(peter).
male(stefan).
male(tadek).
male(sven).
/* Kvinnor */
female(anna).
female(claudia).
female(edyta).
female(terry).
female(berit).
female(halina).
/* parents(X, Y, Z) = Z, Y föräldrar till X */
parents(anna, berit, stefan).
parents(martin, berit, stefan).
parents(edyta, halina, tadek).
parents(peter, halina, tadek).
/* father(X, Y) = X är far till Y */
father(stefan, anna).
father(sven, tadek).
father(stefan, martin).
father(tadek, edyta).
father(tadek, peter).
/* mother(X, Y) = X är mor till Y */
mother(berit, anna).
mother(berit, martin).
mother(halina, edyta).
mother(halina, peter).
/* parent(X, Y) = X är förälder till Y */
parent(berit, anna).
parent(berit, martin).
parent(stefan, anna).
parent(stefan, martin).
parent(halina, edyta).
parent(halina, peter).
parent(tadek, edyta).
parent(tadek, peter).
/* diff(X, Y) = X är inte densamma som Y */
diff(X, Y) :- X \= Y.
/* ismother(X) = X är en mor */
ismother(X) :- parents(_, X, _), female(X).
/* isfather(X) = X är en far */
isfather(X) :- parents(_, _, X), male(X).
/* isson(X) = X är en son */
isson(X) :- parents(X, _, _), male(X).
/* sisterof(X, Y) = X är syster till Y */
sisterof(X, Y) :- female(X), parents(X,_,_), parents(Y,_,_), diff(X, Y).
/* grandpaof(X, Y) = X är grandpa till Y */
grandpaof(X, Y) :- male(X), father(X, FF), parents(Y, _, FF).
/* sibling(X, Y) = X och Y är syskon */
sibling(X, Y) :- parents(X, _, F), parents(Y, _, F), diff(X, Y).