Prolog

1. Prolog Harry R. Erwin, PhD COMM2M University of Sunderland

2. Primary Resources • Kluzniak and Szpakowicz, Prolog for Programmers, Academic Press, 1985. • Pratt and Zelkowitz, Programming Languages, Prentice-Hall, 3rd edition, 1996. • Sebesta, Concepts of Programming Languages, Addison-Wesley, 3rd edition, 1996. • swi-prolog is available in M4 and on the upper terraces. • There are three versions of Prolog, including swi-prolog, available from sourceforge.org.

3. Prolog Introduction • A major language in the logic programming category. • Not a general-purpose language, instead it is a tool for solving problems in predicate calculus. • Is applied to two different areas: • Database queries • Mathematical proofs

4. What is Prolog • Prolog is a ‘descriptive’ rather than an imperative programming language. • The programmer need only specify ‘what’, not how. • It does have procedural elements. • Non-standardized. 8(

5. History of Prolog • Invented by Alain Coulmerauer and Philippe Roussel, 1970-73. • They needed a language for making deductions from text. • First working implementation in 1972 using Algol. • Specified by 1973. • Several fairly similar versions exist.

6. Predicate Calculus and Prolog • Proposition—logical statement that may or may not be true. Consists of objects and relationships. • Objects are simple terms, either constants or variables. A variable can represent different objects at different times. • Atomic propositions consist of simple compound terms, composed of a functor and an ordered list of parameters. • Propositions can be stated as truths (facts) or of unknown validity (queries).

7. Compound Propositions • Compound propositions have two or more atomic propositions, connected by logical operators. • Negation (¬) ¬a is “not a” • Conjunction () a b is “a and b” • Disjunction () ab is “a or b” • Equivalence () ab is “a is equivalent to b” • Implication () ab is “a implies b” • Implication () ab is “a is implied by b”

8. Variables • Variables appear in propositions but only in conjunction with quantifiers. • Existential  •  X.P means “There exists a value of X such that P is true” • Universal  •  X.P means “For all X, P is true.”

9. Clausal Forms • All propositions can be restricted to ‘clausal’ form. This has the following general syntax: B1B2 …  BnA1A2…Am • I.e., this means if all of the As are true, at least one B is true. • Existential quantifiers are not needed. • Universal quantifiers are implicit in the use of variables. • Only conjunction and disjunction are required.

10. Resolution • An inference rule that generalizes the transitive relation: AB and BC implies AC • It works as follows: ‘and’ the left sides of both. Then ‘and’ the right side of both. Delete the terms present in both expressions. Toss in a ‘’ between the left and right sides. • The presence of variables in the propositions requires values for those variables that allow this. This process is called ‘unification’ and involves a (long) search process with backtracking. (Backtracking can be blocked in Prolog.)

11. Horn Clauses • A restricted kind of clausal form, invented by A. Horn. • The types of propositions used in unification. • Either have a single atomic proposition on the left side, or none at all. The left side is called the ‘head’, and those with a left side are called headed Horn clauses. likes(bob,mary)likes(bob,redhead)redhead(mary) • Headless Horn clauses are used to state facts. father(bob,jake) • Most (but not all) propositions can be stated as Horn clauses.

12. How Prolog Works • Prolog usually runs under an interpreter. • The function consult reads new rules and facts into a database. • consult(user) allows the user to enter facts, usually terminated by ctrl-D. • writeit :- write(’Hello world’), nl. • ‘writeit.’ then prints ‘Hello world’.

13. Overview • Programs consist of: • Facts • Concrete relationships between facts • A set of rules • The user enters a query, a set of terms that all must be made true. The facts and rules are then consulted to determine the resulting values of the variables. This magic is called ‘unification’. • Programming in Prolog is like programming in Lisp or ML.

14. Prolog Terms • A constant, a variable, or a structure • Constants are either atoms or integers. • Atoms are strings of letters, digits, and underscores beginning with a lowercase letter or a string of printable ASCII characters delimited by apostrophes. • Variables are strings of letters, digits, and underscores beginning with an uppercase letter. These are unbound.

15. Variables • When you bind a value (and thus a type) to a variable is called instantiation. This occurs during resolution. • Instantiations last only long enough to prove or disprove one proposition.

16. Structures • Represent atomic propositions of the predicate calculus. • Have the format: • functor(parameter list) • The functor is an atom. • The parameter list is a list of atoms, variables, or other structures. • Used to specify facts.

17. Assertions (headless Horn clauses) female(shelley). male(bill). female(mary). male(jake). father(bill, jake). father(bill, shelley). mother(mary, jake). mother(mary, shelley).

18. Logical Propositions • Based on headed Horn clauses (‘rules’). • Can involve conjunctions (indicated by ‘,’) • In Prolog, AND is implied. female(shelley), child(shelley). • Horn clauses are expressed as: • consequence :- antecedent. ancestor(mary, shelley) :- mother(mary, shelley). • Consequences are single terms; antecedents can be conjunctions.

19. Goals or Queries • Appear identical to headless Horn clauses. man(fred). • The system responds ‘yes’ or ‘no’. Yes means the system can prove it. • Conjunctive propositions and propositions with variables are also legal goals. When variables are present, Prolog identifies the instantiations that make the goal true. • Interactive Prolog has two modes: one for entering facts and rules, and the other for queries.

20. Data in Prolog • Constant names are: • A sequence of digits, possibly prefixed with ‘-’. These are called integers. • A string of letters, digits, and underscores, beginning with a lower case letter, called identifiers. • Symbols consisting of a non-empty sequence of ‘+ - * / < = > . : ? $ & @ # \ ’ • Any one of ‘, ; !’ • [] (pronounced “nil”) • Quoted strings: e.g, ‘string’

21. Arithmetic • Operates on integers (some systems handle reals, too.) • Notation can be confusing. Consider: • X is 2 + 3, X = 5 • X = 2 + 3, X = 5 • The Prolog operator ‘is’ means assign the equivalent value, while the operator = means assign the pattern. Clause 1 succeeds while clause 2 fails.

22. Comparisons • Prolog compares integers arithmetically • It compares all other constants as strings

23. Input/Output • Interprets all symbols as sequences of characters forming their names.

24. Compound Objects • The type name is an integral part of all occurrences of the object’s description. • Define an object with its type, followed by a list of its components: • rectangle( 19, 24) • timeofday( 19, 24) • The type’s name is called a ‘functor’ and the components are called ‘arguments’. • The type attributes are its name and number of arguments.

25. Functor Names • Rules are the same for all numbers of arguments. • Integers can only be constants, not functors • [] is only a constant.

26. Object Descriptions • Descriptions of constants and compound objects are ‘terms’. Sometimes the objects are also called ‘terms’. • The arguments of a term are any terms. • The outermost functor is the main or principal functor • Parentheses can be omitted using Polish notation • A binary functor can be placed between its arguments: • a & b is equivalent to &(a, b)

27. Precedence • Various standard functors (prefix, infix, and postfix) are given priorities to eliminate ambiguity if parentheses are omitted. • These standard functors are called operators. • Operator names may not be quoted. • Some functors (‘-’) are multiple types.

28. List Structures (similar to Lisp) • Empty list is denoted ‘[]’ • Constructing functor is ./2 (. with two arguments, hence infix) • a cons b cons c cons emptylist becomes • a.b.c.[] • Don’t put whitespace immediately after ‘.’ That has a syntactic meaning to Prolog • Written [a, b, c, …] • [A|B] means A is the list head and B the tail.

29. Strings • Characters are constants of the same name. Quoting a character is equivalent to writing the character without the quotes. • Strings are lists of characters. Write them in double quotes. • “string” is the same as s.t.r.i.n.g.[]

30. Variables • Not the same as variables in normal programming languages. • A term denoting a variable is called a variable or variable name. • Has an unknown structure. If it ever becomes defined, the variable becomes ‘instantiated’, and ceases to be a variable. • In terms of logic, a free or unbound variable has become ‘bound’ to a term. If there are no variables in the binding, it becomes ‘ground’. • If want to refer to an arbitrary unnamed variable, you can refer to it as ‘_’.

31. Term • A set of objects • Definition of a type • Objects can satisfy explicit properties • painting(Painter, ‘Saskia’) • All ‘Saskia’s of an unknown artist • painting(rembrandt, Picture) • All pictures by Rembrandt

32. Prolog Operations • Mostly user-defined procedures • Standard or built-in operations are rarely used. • Every operation is written as a procedure call. • foo(bar(baz,quux), quuux(quuuux, qVux)) • foo is a ‘predicate symbol’ or ‘predicate’.

33. Procedure Calls • Arguments may be both input and output. • carcdr(Head.Tail, Head, Tail). • The ‘stop’ or ‘.’ terminates the specification. In this case, it defines the procedure. • Call the procedure as follows: • carcdr(1.2.3.[], H, T) • This sets H to 1 and T to 2.3.[] • The actual parameters of procedure calls are the current instantiations of terms written in the call.

34. cons • cons(Object, Another, Object.Another) • Note that this is also the ‘definition’ of carcdr. Which arguments are input or output depends on the arguments, not the definition! The meaning is defined by context.

35. Prolog-10 (Edinburgh) Systems • Versions of Prolog based on Prolog-10 function in two modes: • Command mode, where the system reads and executes directives terminated by ‘.’ • Queries—one or more procedure calls separated by commas. Used to ask questions of the system. • Commands—queries prefixed by “:-”. Do not print. • Definition mode, used to define procedures. • Enter consult/1 or reconsult/1. The argument is a file name with the procedure definitions, terminated by ‘.’

36. Comments • Start with % and extend to the end of the line. • The expression ‘.%’ does not terminate a clause and start a comment, so don’t do it.

37. consult(filename) reconsult(filename) fail see(filename) write(term) tell(filename) told nl atom(X) var(X) integer(X) trace notrace Some Standard Functions

38. How do Procedure Calls Work? • ‘unification’ is the magic word. • We’ll work an example.

39. Prolog Deficiencies • Efficiency reflects the ordering of pattern matching during resolution. This can be very slow. • Infinite loops are easy to write. f(X, Y) :- f(Z, Y), g(X, Z). (solution--reorder!) • It assumes a closed world. If it isn’t in the database, it’s false. • Negation is very hard to handle.

40. Conclusions • Prolog is a computer system for doing mathematical logic. If, like me, you’ve studied this field, you’ll find a lot of ideas familiar. (You also may develop a case of schizophrenia like Goedel, Price, or Nash. YMMV 8) • It allows you to describe logical relationships and deduce the implications. • Treat it more like a powerful reasoning tool than a traditional programming language.