1. Prolog fundamentals
Module 14.2 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

2. Topics Logic Programming Fundamentals Resolution Prolog Fundamentals
Prolog Syntax
The Prolog Database
Lists
Unification

3. Logic Programming Fundamentals
Horn clauses:
General form:
H  B1, B2, ... Bn
Meaning: if B1, B2, ... Bn are true, then H is true.
Deductive reasoning:
C  A,B
D  C
D  A,B

4. Two sample sessions >mother(X, Y):- parent(X,Y),female(X). Yes.
>parent(john, bill).
>parent(jane, bill).
>female(jane).
>?- mother(jane, bill).
>?- mother(john, bill).
>?- mother(X, bill).
X=''jane''.
>man(socrates).
Yes.
>mortal(X) :- man(X).
>?- mortal(socrates).
>?- mortal(X).
X=''socrates''.

5. Resolution
Process of deriving new statements, combining old ones, cancelling like terms, etc.
Variables may acquire values through unification. More later.
Example:
fun(X)  sunny(X)
sunny(Florida)
fun(Florida)

6. Prolog Fundamentals All Prolog programs built from terms: Programs
The data manipulated by programs
Three types of terms:
Constants: integers, real numbers, atoms.
Variables.
Compound terms.

7. Prolog Fundamentals Constants: Integers, e.g. 123; Reals, e.g.: 1.23
Atoms:
Lexically, a lowercase letter followed by any number of additional letters, digits or underscores, e.g. foobar, 'Hello'.
Atoms do look like variables in other languages, but foobar is not a variable; it has no binding, it is a unique value.

8. Prolog Fundamentals
Variables: begin with an upper-case letter, e.g. X, My_var.
Akin to “unknowns” in algebra.
Can be instantiated (take on a value) at run time.
A compound term, or structure, consists of an atom called a functor, and a list of arguments, e.g. sunny(florida), weird(prolog), related(jim, john).
No space allowed
A compound term may look like a function call, but it isn’t. It is structured data, or logical facts.

9. (partial) Prolog Syntax (using bnf)
<program> ::= <predicate> | <program><predicate>
<predicate> ::= <clause> | <predicate><clause>
<clause> ::= <base clause> | <nonbase clause>
<base clause> ::= <structure> .
<nonbase clause> ::= <structure> :- <structures> .
<structures> ::= <structure> | <structure> , <structures> <structure> ::= <name> | <name> ( <arguments> )
<arguments> ::= <argument> | <argument> , <arguments>
Even an arithmetic expression, usually written as 1+2, is just an abbreviation for +(1,2).

10. The Prolog Database
A Prolog system maintains a collection of facts and rules of inference, a database.
A Prolog program is just a “store” of facts for this database.
The simplest item in the database is a fact (term followed by a period.
?- sunny(florida).
Yes.
?- father(jim, ann).
?- father(jim, tom).
No.
?- sunny(X). Attempt to match X.
X = florida; Type a semi-colon, and
X = california; the system tries again.
No. This time it fails.

11. Lists Similar to Lisp. [a, b, c] is syntactic sugar.
Separate head from tail using '|'.
'.' similar to 'cons' in Lisp.
List notation
Term denoted []
[1]
.(1,[])
[1,2,3]
.(1,.(2,.(3,[])))
[1,parent(X,Y)]
.(1,.(parent(X,Y),[]))
[1|X]
.(1,X)
[1,2|X]
.(1,.(2,X)))
[1,2|[3,4]]
[1,2,3,4]

12. Pattern Matching: Unification
Examples:
[george, X] unifies with [george, tom]
[X, fred, [1, X]] unifies with [jane, fred, [1, Y]]
by Y = X = jane
[X, fred, [1, X]] does not unify with [jane, fred, [1, ralph]], because X cannot match both jane and ralph.

13. Unification A constant unifies only with itself.
Two structures unify iff they have
The same functor.
The same number of arguments.
The arguments unify recursively.
A variable X unifies with anything. The other thing could:
have a value. So, instantiate X.
be an uninstantiated variable. Link the two variables, so that
if either is instantiated later, they both share the value.

14. Example of Unification
Unify ([p, q, [c, X]], [Y, q, [X, c]]) =
Unify(p,Y) and Unify([q, [c, X]], [q, [X, c]]) =
(Y=p) and Unify(q,q)
and Unify( [[c, X]], [[X, c]]) =
(Y=p) and Unify( [c, X], [X, c]) and Unify(nil,nil) =
(Y=p) and Unify(c,X) and Unify([X],[c]) =
(Y=p) and (X=c) and Unify(X,c) and Unify(nil,nil) =
(Y=p) and (X=c) and Unify(valueof(X),c) =
(Y=p) and (X=c) and Unify(c,c) =
(Y=p) and (X=c).

15. summary Logic Programming Fundamentals Resolution Prolog Fundamentals
Prolog Syntax
The Prolog Database
Lists
Unification