1 COMP313A Programming Languages Logic Programming (3)

2 Lecture Outline Some Prolog Unification

3 Some more prolog Recursive rules example predecessor relation predecessor(X,Z) :- parent(X,Z). predecessor(X,Z) :- parent(X,Y), parent(Y,Z) And so on… predecessor(X,Z) :- parent(X,Y), predecessor(Y,Z).

4 Some more prolog parent(pam,bob). parent(tom,bob). parent(tom,liz). parent(bob, ann). parent(bob, pat). parent(pat, jim). ? predecessor(pam,bob). ? predecessor(pam, ann). ? predecessor(pam, liz). ? predecessor(pam, X).

5 A prolog program comprises clauses - facts, rules and queries PROGRAM big(bear).%clause 1 big(elephant).%clause 2 small(cat).%clause 3 brown(bear).%clause 4 black(cat).%clause 5 grey(elephant).%clause 6 dark(Z) :- black(Z).%clause 7 dark(Z) :- brown(Z).%clause 8 ?dark(X), big(X).

6 Data Objects Atoms versus numbers versus Variables Atoms –strings of letters, digits, and the underscore character beginning with a lower case letter –some strings of special characters –can enclose strings of characters in single quotes e.g. ‘Fred’ Numbers –integers and floats

7 Data Objects Atoms versus Variables Variables are strings of characters, digits and underscores that begin with an uppercase letter or an underscore Can use the anonymous underscore hasachild(X) :- parent(X,Y) hasachild(X) :- parent(X,_) ? parent(X, _)

8 Data Objects Structured objects objects that have several components location(X, Y, Orientation). location(156, 786, 25). location(156, 786, Orientation). location is the functor

9 Structures date(X,Y,Z). date(20, june, 2005). date(Day, june, 2005). date(Day, Month, Year) :- Day > 0, Day <= 31,…….

10 data objects simple objects structures constantsvariables atomsnumbers These are all terms

11 Operations on lists Membership The member relation member(X,L) ? member(d, [a, b, h, d]). ? ? member(d, [a,b,[d h], e]). ? ?member([d, h], [a, [d,h], e f]). ?

12 Membership X is a member of L if –X is the head of L, or –X is a member of the tail of L. member(X, [X|Tail]). member(X, [Head | Tail]) :- member(X,Tail). Note two separate clauses

13 Membership X is a member of L if –X is the head of L, or –X is a member of the tail of L, or –X is a member of a sublist of L member(X, [X|Tail]). member(X, [Head | Tail]) :- member(X,Tail). plus one more clause……

14 Concatenation The concatenation relation – conc(L1, L2, L3) ? conc([a,b], [c,d], [a,b,c,d]) yes ? conc([a,b], [c,d], [a, b, [c,d]]) no ?conc([a,b], [c,d], X). X = [a,b,c,d]

15 Concatentation conc(L1, L2, Result) If L1 is the empty list –then L2 and Result must be equal If L1 is nonempty –then have [X|L1tail] –recursively X becomes the head of Result and we use conc to find the tail of result [X|TailResult] –Eventually will have exhausted L1 and TailResult will be L2.

16 Concatentation conc([], L, L). conc([X | L1], L2, [X | L3]) :- conc(L1, L2, L3).

17 Unification Matching clauses with variables Have to find the appropriate substitutions for variables so that the clauses match Process is called unification –Process by which variables are instantiated

18 GCD example gcd(u,0,u)  not zero(v), gcd(v, u mod v, w) gcd(u,v,w)  not zero(v), gcd(v, u mod v, w) Using resolution the goal  gcd(15, 10, x)  gcd(15, 10, x)

19 Unification in Prolog A constant unifies only with itself ? me = me. Yes ?me = you. No  Gcd(5, 0, 5)  Gcd(5, 10, w)  Gcd(5, 0, w)

20 Unification in Prolog… A variable that is uninstantiated unifies with anything and becomes instantiated with that thing ? me = X. X = me ? f(a,X) = f(Y, b). X = b Y = a ? f(X) = f(Y)  not zero(v), gcd(v, u mod v, w), gcd(15, 10, x). gcd(u,v,w)  not zero(v), gcd(v, u mod v, w), gcd(15, 10, x). gcd(15, 10, x)  not zero(10), gcd(10, 15 mod 10, x), gcd(15, 10, x).

21 Unification in Prolog A structured term (predicate or function applied to arguments requires –Same predicate/function name –Same number of arguments –Arguments can be unified recursively ? f(X) = g(X) ? f(X) = f(a,b) ? f(a, g(X)) = f(Y, b) ? f(a, g(X)) = f(Y, g(b))

22 Unification examples Unify the following : p(X,Y) and p(a, Z) p(X,X) and p(a,b) ancestor(X,Y) and ancestor(bill, W) p(X,a,Y) and p(Z,Z,b) p(Marcus, g(X,Y)) and f(x, g(Caesar, Marcus)) g(X, X) and g(f(X), f(X))