1. Artificial Intelligence
Lecture 5

2. more Prolog test vs. find built-in predicates user-defined operators
list operations: member, append, nth0, reverse, …
not, default vs. logical negation
comparison operators, arithmetic
user-defined operators
position, precedence, associativity

3. Test vs. find Prolog programs define relations:
query w/ constants: "test" whether relation holds between the constants
query w/ variables: "find" values for which the relation holds
?- member(X, [a, b, c]).
X = a ;
X = b ;
X = c ; No
?- member(a, X).
X = [a|_G260] ;
X = [_G259,a|_G262]
Yes
?- member(X, Y).
X = _G209
Y = [_G209|_G270] ;
Y = [_G275,_G209|_G278]
with a variable as first argument, the query is used to "find" members of the given list
with a variable as the second argument, the query is used to "find" lists that have the given item as member
with both variables, the query is used to "find" general schemas for list membership

4. Append predicate
another useful predefined predicate for list manipulation
append(L1,L2,L3): L3 is the result of
placing the items in L1 at the front of L2
can be used in reverse to partition a list
?- append([a,b], [c,d], L).
L = [a,b,c,d]
Yes
?- append(L1, L2, [a,b,c,d]).
L1 = []
L2 = [a,b,c,d] ;
L1 = [a]
L2 = [b,c,d] ;
L1 = [a,b]
L2 = [c,d] ;
L1 = [a,b,c]
L2 = [d] ;
L1 = [a,b,c,d]
L2 = [] ; No

5. Other list predicates ?- is_list([]). Yes
is_list(Term): succeeds if Term is a list
length(List,Len): Len is the number of items in List
nth0(Index,List,Item): Item is the item at index Index of List(starting at 0)
nth1(Index,List,Item): Item is the item at index Index of List(starting at 1)
reverse(List,RevList): RevList is List with the items in reverse order
delete(List,Item,NewList): NewList is the result of deleting every occurrence of Item from List
select(Item,List,Remain): Remain is the List with an occurrence of Item removed
?- is_list([]).
Yes
?- L = [a,b,c,d],
length(L, Len), nth1(Len, L, X).
L = [a,b,c,d]
Len = 4
X = d
?- reverse([a,b,a,c], Rev),
delete(Rev, a, Del).
Rev = [c,a,b,a]
Del = [c,b]
?- select(a, [a,b,a,c], R).
R = [b,a,c] ;
R = [a,b,c] ; No

6. not predicate anything Prolog can't prove true it assumes to be false!
?- not(is_list([])). No
?- member(d, [a,b,c]).
?- not(member(d, [a,b,c])).
Yes
?- member(X, [a,b,c]).
X = a
?- not(member(X, [a,b,c])).
?- X = d, not(member(X, [a,b,c])).
X = d
?- not(member(X, [a,b,c])), X = d.
not defines the (default) negation of conditional statements
when applied to relations with no variables, it is equivalent to logical negation ()
in reality, it returns the opposite of whatever its argument would return
if X would succeed as a query, then not(X) fails
if X would fail as a query,
then not(X) succeeds
anything Prolog can't prove true it assumes to be false!

7. Programming exercises
suppose we want to define a relation to test if a list is palindromic
palindrome(List): succeeds if List is a list whose elements are the same backwards & forwards

8. Programming exercises
palindrome([]).
palindrome(List) :- reverse(List, Rev), List = Rev.
suppose we want to define relation to see if a list has duplicates
has_dupes(List): succeeds if List has at least one duplicate element
has_dupes([H|T]) :- member(H, T).
has_dupes([_|T]) :- has_dupes(T).
suppose we want the opposite relation, that a list has no dupes
no_dupes(List): succeeds if List has no duplicate elements
no_dupes(List) :- not( has_dupes(List) ).

9. Built-in comparison operators
?- foo = foo.
Yes
?- X = foo.
X = foo
?- [H|T] = [a,b,c].
H = a
T = [b,c]
?- foo \= bar.
?- X \= foo. No
?- 4+2 = 6.
X = Y does more than test equality, it matches X with Y, instantiating variables
if necessary
X \= Y determines whether X & Y are not unifiable
for ground terms, this means inequality
can think of as: not(X = Y)
again, doesn't make a lot of sense for variables
Note: arithmetic operators (+, -, *, /) are not evaluated
 +(4, 2)
can force evaluation using 'is'
?- X = ?- X is
X = X = 6
Yes Yes

10. Programming exercise
suppose we want to define relation to see how many times an item occurs in a list
num_occur(Item,List,N): Item occurs N times in List
num_occur(_,[],0).
num_occur(H, [H|T], N) :-
num_occur(H, T, TailN), N is TailN+1.
num_occur(H, [_|T], N) :-
num_occur(H, T, TailN), N is TailN.
is the first answer supplied by this relation correct?
are subsequent answers obtained via backtracking correct?

11. User-defined operators
it is sometimes convenient to write functors/predicates as operators
predefined: +(2, 3) 
user defined? likes(dave, cubs)  dave likes cubs
operators have the following characteristics
position of appearance
prefix e.g., -3
infix e.g.,
postfix e.g., 5!
precedence
2 + 3 * 4  2 + (3 * 4)
associativity
8 –  8 – (5 – 2)

12. op new operators may be defined as follows
:- op(Prec, PosAssoc, Name).
Name is a constant
Prec is an integer in range 0 – 1200 (lower number binds tighter)
PosAssoc is a constant of the form
xf, yf (postfix)
fx, fy (prefix)
xfx, xfy, yfx, yfy (infix)
the location of f denotes the operator position
x means only operators of lower precedence may appear here
y allows operators of lower or equal precedence
Example: :- op(300, xfx, likes).

13. Operator example
%%% likes.pro
likes(dave, cubs).
likes(kelly, and(java,
and(scheme,prolog))).
%%% likes.pro
:- op(300, xfx, likes).
:- op(250, xfy, and).
dave likes cubs.
kelly likes java and scheme and prolog.
?- likes(dave, X).
X = cubs
Yes
?- likes(Who, What).
Who = dave
What = cubs ;
Who = kelly
What = and(java, and(scheme,prolog)) ; No
?- dave likes X.
X = cubs
Yes
?- Who likes What.
Who = dave
What = cubs ;
Who = kelly
What = java and scheme and prolog ; No
by defining functors/predicates as operators, can make code more English-like

14. IQ Test choose the most likely answer by analogy
Question 1:
IQ Test choose the most likely answer by analogy
Question 3:
Question 2:

15. Next week… AI as search Be prepared for a quiz on
problem states, state spaces
uninformed search strategies
depth first search
breadth first search
iterative deepening
Be prepared for a quiz on
this week’s lecture (moderately thorough)
the reading (superficial)

16. Questions & Answers
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