Prog prng: a yourf course for nners - ULisboa · Prog prng: a yourf course for nners Day 1 a z Depar t of onal s r d vy, r uc¨ ken, r ny [email protected] sb. de .u ni- sb. de /k ri

Prolog programming: a do-it-yourselfcourse for beginners

Day 1

Kristina StriegnitzDepartment of Computational Linguistics

Saarland University, Saarbrucken, [email protected]

http://www.coli.uni-sb.de/˜kris

Day 1: Facts, Rules, and Queries – p.1

[email protected]

http://www.coli.uni-sb.de/~kris

kb1: A knowledge base of facts

wizard(harry).wizard(ron).wizard(hermione).

muggle(uncle_vernon).muggle(aunt_petunia).

chases(crookshanks, scabbars).


kb1: queries we can askwizard(harry).

wizard(ron).

wizard(hermione).

muggle(uncle vernon).

muggle(aunt petunia).

chases(crookshanks,scabbars).

?- wizard(harry).

yes

?- chases(crookshanks,scabbars).

yes

?- muggle(harry).

no

?- muggle(dumbledore).

no

?- wizard(dumbledore).

no

?- witch(hermione).

ERROR: Undefined procedure: witch/1


kb1: more queries we can askwizard(harry).

wizard(ron).

wizard(hermione).




?- muggle(X).

X = uncle vernon ;

X = aunt petunia ;

no

?- chases(X,Y).

X = crookshanks

Y = scabbars ;

no

?- chases(X,X).

no


A bit of syntax: atoms and variablesAtoms:

• All terms that consist of letters, numbers, and the underscore andstart with a non-capital letter are atoms: harry, uncle vernon,ritaSkeeter, nimbus2000, . . . .

• All terms that are enclosed in single quotes are atoms:’Professor Dumbledore’, ’(@ *+ ’, . . . .

• Certain special symbols are also atoms: +, ,, . . . .

Variables:

• All terms that consist of letters, numbers, and the underscore andstart with a capital letter or an underscore are variables: X,Hermione, ron, . . . .

• is an anonymous variable: two occurrences of are differentvariables. Day 1: Facts, Rules, and Queries – p.10

A bit of syntax: complex terms

Complex terms:

• Complex terms are of the form: functor (argument, ..., argument).

• Functors have to be atoms.

• Arguments can be any kind of Prolog term, e.g., complex terms.likes(ron,hermione), likes(harry,X),f(a,b,g(h(a)),c), . . . .


A bit of syntax: facts and queries

• Facts are complext terms which are followed by a full stop.wizard(hermione).



• Queries are also complext terms which are followed by a full stop.?- wizard(hermione).

Query

Prompt provided by the Prolog interpreter.


kb2: a knowledge base of facts and rules

eating(dudley).

happy(aunt petunia) :- happy(dudley).

happy(uncle vernon) :- happy(dudley), unhappy(harry).

happy(dudley) :- kicking(dudley,harry).

happy(dudley) :- eating(dudley).



eating(dudley).





if ... then ...: If happy(dudley) is true, then happy(aunt petunia)

is true.



eating(dudley).


happy(uncle vernon) :- happy(dudley) , unhappy(harry).



and: If happy(dudley) is true and unhappy(harry) is true, thenhappy(uncle vernon) is true.



eating(dudley).





or: If kicking(dudley,harry) is true or if eating(dudley) is true,then happy(dudley) is true.


Querying kb2eating(dudley).


happy(uncle vernon) :- happy(dudley),

unhappy(harry).



?- happy(dudley).

yes

?- happy(aunt petunia).

yes

?- happy(uncle vernon).

no

?- happy(X).

X = aunt petunia ;

X = dudley ;

no


A bit of syntax: rules

• Rules are of the form Head :- Body.

• Like facts and queries, they have to be followed by a full stop.

• Head is a complex term.

• Body is complex term or a sequence of complex terms separatedby commas.happy(aunt petunia) :- happy(dudley).

happy(uncle vernon) :- happy(dudley),

unhappy(harry).


kb3: facts and rules containing variables

This knowledge base defi nes 3 predi-

cates: father/2, mother/2, and

wizard/1.

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).

For all X, Y, Z, if father(Y,X)

is true and wizard(Y) is true

and mother(Z,X) is true

and wizard(Z) is true, then

wizard(X) is true. I.e., for all X,

if X’s father and mother are wizards,

then X is a wizard.


Querying kb3 father(albert,james).


mother(ruth,james).

mother(lili,harry).

wizard(lili).

wizard(ruth).

wizard(albert).

wizard(X) :- father(Y,X),

wizard(Y),

mother(Z,X),

wizard(Z).

?- wizard(james).yes

?- wizard(harry).yes

?- wizard(X).X = lili ;X = ruth ;X = albert ;X = james ;X = harry ;no

?- wizard(X), mother(Y,X), wizard(Y).X = jamesY = ruth ;X = harryY = lili ;no


Prolog terms (overview)

atoms: Start with non-capital letters or are enclosed in single quotes.harry, nimbus2000, ’Professor Dumbledore’,aunt petunia

numbers 3, 6, 2957, 8.34, ...

variables Start with a capital letter or an underscore.Harry, harry

complex terms An atom (the functor) is followed by a commaseparated sequence of Prolog terms enclosed in parenthesis (thearguments).like(harry, X), np(det(the),n(potion))


Ancestors

Paul Helen Albert Ruth

JamesLiliPetuniaVernon

Dudley Harry

parent of(paul,petunia).

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).

Task: Define a predicate ancestor of(X,Y) which is true if Xis 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 wehave 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 an-cestors of (i.e., of all the descendants of their children).


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 wehave 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 an-cestors of (i.e., of all the descendants of their children).

recursion


Example 1

KB: wizard(harry).

wizard(ron).

wizard(hermione).




Query: ?- wizard(hermione).

yes

Easy: wizard(hermione) is a fact in the knowledge base.


Example 2

KB: wizard(harry).wizard(ron).

wizard(hermione).




Query: ?- wizard(X).

X = harry ;

X = ron ;

X = hermione ;

no

• The query wizard(X) matches the fact wizard(harry). Thisinstantiates the variable X with harry.

• It also matches the facts wizard(ron) and wizard(hermione).


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 getsinstantiated with the other term.Ex.: X = wizard(harry)Ex.: X = Y

• Two complex terms match if they have the same functor and thesame number of arguments and if all pairs of parallel argumentsmatch.Ex.: like(harry,hargrid) = like(harry,X)Ex.: like(harry,hargrid) = like(harry,X,Y)Ex.: like(harry,hargrid) \= like(X,X)


\=

Back to Example 2KB: wizard(harry).

wizard(ron).

wizard(hermione).




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.


Example 3

KB: eating(dudley).


happy(uncle vernon) :- happy(dudley),unhappy(harry).



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.


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).

eating(h)eating(d),unhappy(h)

happy(X)

eating(d)happy(d) happy(d),unhappy(h)

kicking(d,h) kicking(d,h),unhappy(h)

unhappy(d)

kicking(d,h)

X=ap

X=d

X=ap X=uv X=d X=d


d

Example 5

father(albert,james).


mother(ruth,james).

mother(lili,harry).

wizard(lili).

wizard(ruth).

wizard(albert).

wizard(X) :-

father(Y,X),

wizard(Y),

mother(Z,X),

wizard(Z).

wizard(I3)

wizard(albert),

mother(I3,james),

wizard(I3)

wizard(james),

mother(I3,harry),

father(I2,I1),

wizard(I2),

mother(I3,I1),

wizard(I3)

wizard(I3)

mother(I3,james),

wizard(ruth)

I4=albert

I5=ruth

wizard(X)

wizard(I3)

mother(I3,harry),

father(I4,james),

wizard(I4),

mother(I5,james),

wizard(I5)

wizard(I3)

mother(I3,harry),

wizard(lili)

I3=ruth

I3=lili

X=lili

I2=albert I2=james

X=I1

I1=james I1=harry

X=ruthX=albert


Ancestors (cont.)

parent of(paul,petunia).

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).

ancestor of(X,Y) :-

parent of(X,Y).

ancestor of(X,Y) :-

parent of(X,Z),

ancestor of(Z,Y).

ancestor_of(albert,harry)

parent_of(albert,I1)

ancestor_of(I1,harry)

ancestor_of(james,harry)

parent_of(james,harry)

I1=james

parent_of(albert,harry)


Lists

• Intuitively: sequences or enumerations of things

• In Prolog: a special kind of data structure, i.e., special kinds ofProlog terms

Day 3: Lists – p.6

Another way of writing lists in Prolog

• .(a,Tail) = [a|Tail]

• .(a,.(b,Tail)) = [a,b|Tail]

• .(a,.(b,.(c,[]))) = [a,b,c]


Working with lists (1)

trans a b/2: a predicate for “translating” a list of as into a list of bs.

trans a b(X,Y) should be true if X, the ‘input’, is a list of as and Y, the‘output’, is a list of bs which has just as many bs as the input has as.

trans a b([],[]).If the input is empty, then the output is empty as well.

trans a b([a|InputTail], [b|OutputTail]) :-trans a b(InputTail, OutputTail).

Otherwise the first a in the input list has to correspond to a b in theoutput list. The tail of the output list has to be the “translation” ofthe input list.


Working with lists (2)

element of/2: a predicate for testing whether a list contains a givenProlog term.

element of(X,Y): should be true if X is an element of Y.

element of(X, [X|Tail]).

If the first element of the list is the one that we are looking for, weare done.

element of(X, [ |Tail]) :- element of(X,Tail).

Otherwise, check whether the term we are looking for is in the tailof the list.

In SWI-Prolog element of/2 is predefined under the name member.


Working with lists (3)concatenate/3: a predicate for concatenating two lists.

concatenate(X,Y,Z) should be true if Z is the concatenation of Xand Y; for example, concatenating [a] with [b,c] yields [a,b,c].

concatenate([],L,L).Concatenating the empty list with any other list L yields L.

concatenate([Head|Tail],L,[Head|NewTail]) :-concatenate(Tail,L,NewTail).

Otherwise, the first element of the output list has to be the same asthe first element of the first input list. And the tail of the output listis the concatenation of the tail of the first input list with the secondinput list.


Concatenating lists

concatenate(.(Head,Tail),L,.(Head,NewTail)) :-concatenate(Tail,L,NewTail).

H Tail L

Tail L

Input 1 Input 2

concatenate

H

In SWI-Prolog element of/2 is predefined under the name member.


Prolog predicates can be used in many ways

?- trans a b([a,a,a],L).

L = [b,b,b] ;

no

?- trans a b([a,a,a],[b]).

no

?- trans a b(L,[b,b]).

L=[a,a] ;

no

?- member(a,[a,b,c]).

yes

?- member(X,[a,b,c]).

X = a ;

X = b ;

X = c ;

no

?- member(a,L).

L = [a| G280] ;

L = [ G279, a| G283] ;

L = [ G279, G282, a| G286] ;

L = [ G279, G282, G285, a| G289]

Yes


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Prog prng: a yourf course for nners - ULisboa · Prog prng: a yourf course for nners Day 1 a z Depar t of onal s r d vy, r uc¨ ken, r ny [email protected] sb. de .u ni- sb. de /k ri