Oct 29, 2003
-------------

- More on PROLOG
	- in Prolog, all functions are predictes
		- i.e., return true or false
	- have to "fake" returns of other types with a padded argument
	- Writing simple functions using rules

Files used in this session
<functions.pl>
isempty([]).

ismember(X,[X|_]).
ismember(X,[_|Z]) :- ismember(X,Z).

isalist([]).
isalist([_|_]).

<factorial.pl>
factorial(0,1).
factorial(X,Y) :- X > 0, /* some outputs below didn't  have this line */
                  Z is X-1,
                  factorial(Z,M),
                  Y is M*X.

sum(0,0).
sum(X,Y) :- X > 0, /* some outputs below didn't have this line */
            Z is X-1,
            sum(Z,M),
            Y is M+X.

<lists.pl>
/* function to append lists */
/* first two are the inputs, last is the
appended list */

append([],X,X).
append(X,[],X).
append([X|Y],Z,[X|M]) :- append(Y,Z,M).

/* function to find the last element of
a list */

last(X,List) :- append(_,[X],List).

/* function to check if X is a member
of list List ; fill in the blanks yourself 
member(X,List) :- append(  ,  ,  ). */

Transcript of session:
----------------------
?- consult(functions).
% functions compiled 0.00 sec, 520 bytes

Yes
?- [functions].
% functions compiled 0.00 sec, 0 bytes

Yes
?- isempty(X).

X = [] ;

No
?- isempty([]).

Yes
?- isempty([jack, jill]).

No
?- make.
% /root/Languages/Prolog/functions.pl compiled 0.00 sec, 352 bytes

Yes
?- ismember(2,[1,2,3]).

Yes
?- ismember(nil,nil).

No
?- ismember(5,[1,2,3]).

No
?- ismember(X,[1,2,3,4]).

X = 1 ;

X = 2 ;

X = 3 ;

X = 4 ;

No
?- ismember(1,X).

X = [1|_G208] ;

X = [_G207, 1|_G211] ;

X = [_G207, _G210, 1|_G214] ;

X = [_G207, _G210, _G213, 1|_G217] ;

X = [_G207, _G210, _G213, _G216, 1|_G220] ;

X = [_G207, _G210, _G213, _G216, _G219, 1|_G223] ;

X = [_G207, _G210, _G213, _G216, _G219, _G222, 1|_G226] ;

X = [_G207, _G210, _G213, _G216, _G219, _G222, _G225, 1|_G229] ;

X = [_G207, _G210, _G213, _G216, _G219, _G222, _G225, _G228, 1|...] 
Action (h for help) ? abort
% Execution Aborted
?- ismember([book],[[book],[tommy],[jimmy, rang, the, bell]]).

Yes
?- make.
% /root/Languages/Prolog/functions.pl compiled 0.00 sec, 232 bytes

Yes
?- isalist([book,justin]).

Yes
?- isalist(justin).

No
?- isalist([[justin]]).

Yes
?- make.
% /root/Languages/Prolog/functions.pl compiled 0.00 sec, 8 bytes

Yes
?- isalist(X).

X = [] ;

X = [_G208] ;

No
?- isalist([justin,jimmy,johnny]).

No
?- [factorial].
% factorial compiled 0.00 sec, 692 bytes

Yes
?- factorial(1,X).

X = 1 ;

No
?- factorial(X,1).

X = 0 ;

X = 1 ;

No
?- factorial(10,X).

No
?- make.
% /root/Languages/Prolog/functions.pl compiled 0.00 sec, -8 bytes
% /root/Languages/Prolog/factorial.pl compiled 0.00 sec, 48 bytes

Yes
?- factorial(5,X).

X = 120 

Yes
?- factorial(10,X).

X = 3628800 

Yes
?- factorial(X,3628800).
ERROR: Arguments are not sufficiently instantiated
^  Exception: (9) _L167 is _G160-1 ? abort
% Execution Aborted
?- factorial(5,X).

X = 120 ;
ERROR: Out of local stack
?- make.
% /root/Languages/Prolog/factorial.pl compiled 0.00 sec, 40 bytes

Yes
?- factorial(5,X).

X = 120 ;

No
?- make.
% /root/Languages/Prolog/factorial.pl compiled 0.00 sec, 360 bytes

Yes
?- sum(4,T).

T = 10 ;

No
?- sum(T,68493).
ERROR: Arguments are not sufficiently instantiated
^  Exception: (8) _G157>0 ? abort
% Execution Aborted
?- [lists].
% lists compiled 0.00 sec, 620 bytes

Yes
?- append([1,2],[3,4],Z).

Z = [1, 2, 3, 4] ;

No
?- append(Z,[3,4],[1,2,3,4]).

Z = [1, 2] ;

No
?- append([1,2,X,5],[6,7],[1,2,4,5,6,7]).

X = 4 ;

No
?- append(X,Y,[3,4,5,6]).

X = []
Y = [3, 4, 5, 6] ;

X = [3, 4, 5, 6]
Y = [] ;

X = [3]
Y = [4, 5, 6] ;

X = [3, 4, 5, 6]
Y = [] ;

X = [3, 4]
Y = [5, 6] ;

X = [3, 4, 5, 6]
Y = [] ;

X = [3, 4, 5]
Y = [6] ;

X = [3, 4, 5, 6]
Y = [] ;

X = [3, 4, 5, 6]
Y = [] ;

X = [3, 4, 5, 6]
Y = [] ;

No
?- [lists].
% lists compiled 0.00 sec, 160 bytes

Yes
?- last(X,[3,4,5]).

X = 5 ;

No
?- last(3,X).

X = [3] 

Yes
?- last(3,X).

X = [3] ;

X = [_G219, 3] ;

X = [_G219, _G225, 3] ;

X = [_G219, _G225, _G231, 3] ;

X = [_G219, _G225, _G231, _G237, 3] ;

X = [_G219, _G225, _G231, _G237, _G243, 3] ;

X = [_G219, _G225, _G231, _G237, _G243, _G249, 3] ;

X = [_G219, _G225, _G231, _G237, _G243, _G249, _G255, 3] 

Yes