ICS 313: Programming Language Theory

1. ICS 313: Programming Language Theory Module 15: Prolog

2. Logic programming vs. Prolog • Logic programming involves use of inference across relations to perform computation. • Prolog is a particular instance of a logic programming language. • Other languages use logic-based programming (i.e. constraint-based languages). • Prolog is the most popular and successful example of a logic programming language

3. Logic programming as computing with relations • A relation is a table with a fixed number of columns and a possibly infinite set of rows. • A tuple (x1, x2, ..., xn) is in a relation if the tuple appears in some row of the relation. • Consider the following table of relations representing the append operation.

4. Append as a table: • Relations can be used as predicates: • Is tuple T in relation R? • Example: • ([a], [b], [a, b]) is in R • ([a], [b], []) is not in R

5. Relations vs. Functions • The functional version of append: • (x, y) -> z • The relational version of append: • Allows x, y, and/or z to be return value! • Example relational queries: • Does [a,b] appended with [c, d] yield [a,b,c,d]? • Answer: yes. • Is there a Z such that [w, x] appended with [y] yields Z? • Answer: yes, when Z = [w, x, y] • Is there a Q such that [x, y] appended with Q yields [x, y, z]? • Answer: yes, when Q = [z].

6. Logic Programming Concepts • Logic programming languages have in common: • Declaring primitive facts about a domain • Defining rules to express relationships between facts in the domain • Use of deduction to answer questions about domain

7. Logic Programming vs. Imperative • Conceptual differences between “pure” logic paradigm and imperative paradigm: • Little to no explicit control flow statements • No if-then-else or other conditionals • No while loops or other iteration • No global variables or other globally modifiable state • However, there is a lot of implicit control flow (Prolog allows “cheating” via the cut goal.)

8. Logic + Control • Kowalski (1979) coined the following famous expression: • Algorithm = Logic + Control • Prolog supplies the “control” part of an algorithm automatically. • User provides only “Logic” portion.

9. Defining facts • One way to express the fact that “John likes Mary” is: • likes (john, mary). • This defines two arguments, john and mary, and a predicate, likes • The period is needed to terminate a fact. • This fact is a constant value, not a function invocation! • The use of lower case indicates atomic values • likes (mary, john). is a different fact

10. Facts cont. • Facts can have arbitrary arity: • valuable (gold). • gives (john, book, mary). • food. • The current facts (and rules) constitutes the “database”.

11. Asking questions • Questions are simply facts prefaced by ?- • ?- likes (mary, john). • Informally: Does mary like john? • More formally: Can it be proven from the current facts in the database that the relation likes (mary, john) holds?

12. Questions cont. • Proving a fact involves matching: • Two facts match if their predicates are the same and if each of their corresponding arguments are the same from left to right. • Prolog searches the database in order that the facts were entered for matching facts • If Prolog can find a matching fact for the question, it responds yes, otherwise it will respond no. • “No” does not mean “it is false”.

13. Variables • Variables allow Prolog to return information from the database. • Variables are represented by names beginning with a capital letter • Variables become instantiated when bound to an object in the database

14. Variable Instantiation • ?- likes (john, X). X = wine

15. Implicit control flow: • Database is searched from top to bottom for a predicate matching likes • Each matching predicate is searched in order for a first argument matching john • Each matching predicate and first argument is searched for a second argument matching (the uninstantiated) X • X matches wine • X is instantiated to wine • Prolog marks the place where the match was made

16. Re-satisfying questions • When a question is satisfied by finding a match for the predicate and each argument, the values for all instantiated variables are printed out. • Typing a semi-colon instructs Prolog to attempt to re-satisfy the last match it found, starting from the place marker. • ?- likes (john, X). X = wine; X = mary; no

17. Conjunctions • Conjunctions allow specification of multiple conditions to be satisfied simultaneously • Conjunctions are represented by commas between predicates • Do john and mary like each other? ?- likes (john, mary), likes (mary, john). no • Is there anything that both John and Mary like? ?- likes (mary, X), likes (john, X). • First, is there anything that John likes? • Second, does Mary also like it?

18. Backtracking • Database is searched for match to first goal. • The first match is: likes (mary, food) • X is instantiated to food everywhere • Prolog marks place in database where this goal was satisfied • Database is searched (from top) for • likes (john, food) • No such fact exists, so goal fails.

19. Backtracking (cont). • Prolog attempts to re-satisfy previous goal • All instantiations to previous goal are undone • Search continues from the placemarker • Database searched again for match to first goal • The new match is: likes (mary, wine) • X is instantiated to wine • Prolog marks this place in database • Database searched (from top) for: likes (john, wine) • This matches a fact in the database • Prolog marks the place where the match occurred • Prolog returns: X = wine

20. Rules • Rules • express general statements about objects and their relationships to each other. • indicate when a fact depends on other facts. • “name” collections of terms (subroutine). • Rules consist of two parts: • Head: what fact the rule is intended to define. • Body: a conjunction of goals to be satisfied if the head is to be true.

21. Rules (cont.) • To satisfy/match a rule head, all of its body must be satisfied. • Example: • Mary likes anyone who likes wine • likes (mary, X) :- likes (X, wine).

22. Rule example • ?- likes (mary, Y). • Y = food ; • Y = wine ; • Y = mary ; • Y = john ; • no

23. end of module