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1 COMP313A Programming Languages Logic Programming (3)

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2 Lecture Outline Some Prolog Unification

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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).

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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).

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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).

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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

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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, _)

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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

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

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

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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]). ?

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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

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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……

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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]

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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.

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

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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

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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)

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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)

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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).

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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))

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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))

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© Johan Bos Logic Programming About the course –Taught in English –Tuesday: mostly theory –Thursday: practical work [lab] Teaching material –Learn Prolog.

© Johan Bos Logic Programming About the course –Taught in English –Tuesday: mostly theory –Thursday: practical work [lab] Teaching material –Learn Prolog.

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