Prolog Harry R. Erwin, PhD COMM2M University of Sunderland

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

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

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(

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

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).

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”

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.”

Clausal Forms All propositions can be restricted to ‘clausal’ form. This has the following general syntax: B 1  B 2  …  B n  A 1  A 2  …  A m 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.

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.)

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.

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’.

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.

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.

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.

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.

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

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.

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.

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’

Arithmetic Operates on integers (some systems handle reals, too.) Notation can be confusing. Consider: 1. X is 2 + 3, X = 5 2. 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.

Comparisons Prolog compares integers arithmetically It compares all other constants as strings

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

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.

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

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)

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.

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.

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.[]

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 ‘_’.

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

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’.

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.

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.

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 ‘.’

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.

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

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

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.

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.