programming: Prolog a do-it-yourself course for beginners
Day 2
Kristina Striegnitz Department of Computational Linguistics Saarland University, Saarbrucken, Germany
[e-mail] http://www.coli.uni-sb.de/~kris
Day 2: Matching and Proof Search p.1
Day 2: Matching and Proof Search
Today:
recursive predicate definitions how Prolog answers queries
Reader: Lectures 2 and 3 of Learn Prolog Now!
Day 2: Matching and Proof Search p.2
Ancestors
parent of(paul,petunia).
Paul Helen Albert Ruth
parent of(helen,petunia). parent of(paul,lili). parent of(helen,lili). parent of(albert,james). parent of(ruth,james). parent of(petunia,dudley). parent of(vernon,dudley). parent of(lili,harry). parent of(james,harry).
Vernon
Petunia
Lili
James Harry
Dudley
Task: Define a predicate ancestor of(X,Y) which is true if X is an ancestor of Y.
Day 2: Matching and Proof Search p.3
Ancestors (cont.)
grandparent of(X,Y) :- parent of(X,Z), parent of(Z,Y). greatgrandparent of(X,Y) :- parent of(X,Z), parent of(Z,A), parent of(A,Y). greatgreatgrandparent of(X,Y) :- parent of(X,Z), parent of(Z,A), parent of(A,B), parent of(B,Y).
Doesn't work for ancestor of; don't know "how many parents we
have to go back".
ancestor of(X,Y) :- parent of(X,Y).
People are ancestors of their children,
ancestor of(X,Y) :- parent of(X,Z), ancestor of(Z,Y).
and they are ancestors of anybody that their children may be ancestors of (i.e., of all the descendants of their children).
Day 2: Matching and Proof Search p.4
Ancestors (cont.)
grandparent of(X,Y) :- parent of(X,Z), parent of(Z,Y). greatgrandparent of(X,Y) :- parent of(X,Z), parent of(Z,A), parent of(A,Y). greatgreatgrandparent of(X,Y) :- parent of(X,Z), parent of(Z,A),
recursion parent of(A,B), parent of(B,Y).
Doesn't work for ancestor of; don't know "how many parents we
have to go back".
ancestor of(X,Y) :- parent of(X,Y).
People are ancestors of their children,
ancestor of(X,Y) :- parent of(X,Z), ancestor of(Z,Y).
and they are ancestors of anybody that their children may be ancestors of (i.e., of all the descendants of their children).
Day 2: Matching and Proof Search p.5
Example 1
KB:
wizard(harry). wizard(ron). wizard(hermione). muggle(uncle vernon). muggle(aunt petunia). chases(crookshanks,scabbars).
Query:
?- wizard(hermione). yes
Easy: wizard(hermione) is a fact in the knowledge base.
Day 2: Matching and Proof Search p.6
Example 2
KB: wizard(harry).
wizard(ron). wizard(hermione). muggle(uncle vernon). muggle(aunt petunia). chases(crookshanks,scabbars).
Query: ?- wizard(X).
X = harry ; X = ron ; X = hermione ; no
The query wizard(X) matches the fact wizard(harry). This instantiates the variable X with harry.
It also matches the facts wizard(ron) and wizard(hermione).
Day 2: Matching and Proof Search p.7
Matching
Two atoms match if they are the same atom. Ex.: harry = harry, but harry \= 'Harry'.
A variable matches any other Prolog term. The variable gets instantiated with the other term. Ex.: X = wizard(harry) Ex.: = X Y
Two complex terms match if they have the same functor and the same number of arguments and if all pairs of parallel arguments match. Ex.: like(harry,hargrid) = like(harry,X) Ex.: like(harry,hargrid) = like(harry,X,Y) Ex.: like(harry,hargrid) \= like(X,X)
Day 2: Matching and Proof Search p.8
Back to Example 2
KB: wizard(harry).
wizard(ron). wizard(hermione). muggle(uncle vernon). muggle(aunt petunia). chases(crookshanks,scabbars).
Query: ?- wizard(X).
X = harry ; X = ron ; X = hermione ; no
Prolog checks for facts that match the query. (There are three.) Prolog starts from the top of the knowledge base and, therefore, finds wizard(harry) first.
Typing ; forces Prolog to check whether there are other possibilities.
Day 2: Matching and Proof Search p.9
Example 3
KB:
eating(dudley). happy(aunt petunia) :- happy(dudley). happy(uncle vernon) :- happy(dudley),unhappy(harry). happy(dudley) :- kicking(dudley,harry). happy(dudley) :- eating(dudley).
Query:
?- happy(aunt petunia). yes
Check for a fact or a rule's head that match the query. If you find a fact, you're done. If you find a rule, prove all goals specified in the body of the rule.
Day 2: Matching and Proof Search p.10
Example 4
KB:
eating(dudley). happy(aunt petunia):-happy(dudley). happy(uncle vernon):-happy(dudley),unhappy(harry). happy(dudley):-kicking(dudley,harry). happy(dudley):-eating(dudley).
Query:
?- happy(X).
happy(X) X=ap happy(d) X=uv X=d X=d kicking(d,h) eating(d)
happy(d),unhappy(h)
kicking(d,h)
eating(h)
kicking(d,h),unhappy(h) eating(d),unhappy(h) X=d
X=ap
unhappy(d)
Day 2: Matching and Proof Search p.11
Example 5
father(albert,james). father(james,harry). mother(ruth,james). mother(lili,harry). wizard(lili). wizard(ruth). wizard(albert). wizard(X) :father(Y,X), wizard(Y), mother(Z,X), wizard(Z).
...