Prolog a declarative language

1. Prolog a declarative language • A program in a declarative programming language consists of assertions rather than assignments and control flow statements. • These declarations are actually statements or propositions in symbolic logic. • Program doesn’t state how a result is to be computed but what the result is.

2. Prolog program composition • Collections of statements • Kinds of statements • Facts • Rules • Statements are constructed from terms • A term is a constant, a variable, or a structure

3. Prolog program elements • Constants are • Atoms or integers • Atoms are • Symbolic values of Prolog • String of letters, digits, and underscores that begins with a lowercase letter OR • String of any printable ASCII characters delimited by apostrophes

4. Prolog program elements • Variables are • any string of letters, digits, and underscores that begins with an upper case letter • not bound to types by declarations • bound to values and types by instantiations • Instantiation occurs only in resolution process • not like variables in imperative languages

5. Prolog program elements • Structures • have the general form functor(parameter_list) • functor is any atom & it identifies the structure • parameter_list can be any list of atoms variables or other structures. • are the way to specify facts in Prolog • can be thought of as objects • are relations • are predicates

6. Prolog facts • Facts • state relations explicitly • man(paul). • rich(joan). • SWI-Prolog doesn’t like spaces between the name of the relation and the left parenthesis. PDProlog doesn’t care. • are propositions that are assumed to be true • are the statements from which new information can be inferred • are headless Horn clauses • have no intrinsic semantics

7. Prolog rules • Rules • are headed Horn clauses • right side is the antecedent or if part • left side is the consequent or then part • consequent must be a single term, • antecedent may be either a single term or a conjunction • rich(joan) :- has_money(joan). • rich(joan) :- has_health(joan),has_job(joan). • Conjunctions contain multiple terms separated by logical and • :- is read as if • , means and

8. Example parent(X,Y) :- mother(X,Y). parent(X,Y) :- father(X,Y). grandparent(X,Z) :- parent(X,Y), parent(Y,Z). sibling(X,Y) :- mother(M,X),mother(M,Y),father (F,X), father(F,Y).

9. Prolog as a theorem proving model • proposition • is the form of the theorem that we want to prove or disprove • is called a goal • is called a query • syntactic form is that of a headless Horn clause • man(fred). • returns yes OR returns no • yes means that system proved goal was true under given database of facts and relationships • no means either the goal was proved false OR system was simply unable to prove it.

10. Sidebar 1 • The process of determining useful values for variables is called unification. • The temporary assigning of values to variables to allow unification is called instantiation. • Resolution is an inference rule that allows inferred propositions to be computed from given propositions.

11. Sidebar 2 • Horn clauses come in two forms • Single atomic proposition on the left side OR • Empty left side • Left side is called the head • Horn clauses with left sides are called headed Horn clauses • Horn clauses with empty left sides are called headless Horn clauses.

12. Database: p(X) :- q(X), not (r(X)). r(X) :- w(X), not (s(X)). q(a). q(b). q(c). s(a). s(a). w(a). w(b). Queries p(a). p(b). p(c). Example

13. Database: bachelor(P) :- male(P), not (married(P)). male(henry). male(tom). married(tom). Queries: bachelor(henry). bachelor(tom). bachelor(Who). married(Who). not(married(Who)). Example

14. Prolog operators • relational operators \= = >= <= > < • Assignment operator is is peculiar - not like ordinary assignment operator

15. Behavior of Prolog “is” • takes an arithmetic expression as its right operand • takes a variable as its left operand • all variables in the arithmetic expression must already be instantiated • left-side variable cannot be previously instantiated • Discussion Examples: A is B / 17 + C X is X + 1

16. Prolog Arithmetic Example • speed(ford,100). • speed(chevy,105). • speed(dodge,95). • speed(volvo,80). • time(ford,20). • time(chevy,21). • time(dodge,24). • time(volvo,24). • distance (X,Y) :- speed(X,Speed), time(X,Time), Y is Speed * Time.

17. Short Prolog backtracking example /* facts */ likes(jake,chocolate). likes(jake,apricots). likes(darcie,licorice). likes(darcie,apricots). /* query or goal */ likes(jake,What), likes(darcie,What).

18. Miscellanea • parameters , arguments • arity – number of parameters/arguments in a parameter list • anonymous variable – used when don’t care mother (X, _). likes (_, What). • logical operators , means and ;means or \+ means not in SWI - Prolog not means not inPD Prolog

19. Miscellania • retract( ). - can be used to delete a single fact or relation • forget( ). – can be used to remove a file you have consulted • halt. – exits gracefully from SWI-Prolog • differences between • listing. • dir p. • dir.

20. Prolog lists • Lists • are written in square brackets with commas between the list’s element [condor,whooping_crane, dusky_seaside_sparrow] • can be used as the argument of a relation rarebird([condor,whooping_crane, dusky_seaside_sparrow]). • can be queried • can take advantage of anonymous variables • have a head and a tail • can be processed recursively

21. List Example Database: rarebird([condor,whooping_crane, dusky_seaside_sparrow]). Queries: rarebird(condor). rarebird(What).

22. List Example - continued Database: rarebird([condor,whooping_crane, dusky_seaside_sparrow]). noteworthy(Bird) :- rarebird([Bird, __,__]). noteworthy(Bird) :- rarebird([__,Bird, __]). noteworthy(Bird) :- rarebird([__,__, Bird]). Queries: rarebird(condor). rarebird(What). noteworthy(condor). noteworthy(Who).

23. List Example - continued Database: rarebird([condor,whooping_crane, dusky_seaside_sparrow]). noteworthy(Bird) :- rarebird([Bird, __,__]). noteworthy(Bird) :- rarebird([__,Bird, __]). noteworthy(Bird) :- rarebird([__,__, Bird]). rarebird(Bird) :- noteworthy(Bird). Queries: rarebird(condor). rarebird(What). noteworthy(condor). noteworthy(Who).

24. Head | Tail examples • Database rarebird([condor,whooping_crane, dusky_seaside_sparrow]). • Query rarebird([H | T]).

25. P638.pro append ([], List, List). append([Head | List_1], List_2, [Head | List_3]) :- append (List_1, List_2, List_3).

26. P6382.pro list_op_2( [],[]). list_op_2( [Head | Tail], List) :- list_op_2 (Tail, Result), append (Result, [Head], List).

27. P639.pro member (Element, [Element | _ ] ). member (Element, [_ | List]) :- member (Element, List

29. Matching a goal to a fact • Start with facts and rules and attempt to find a sequence of matches that lead to the goal. • Called bottom-up resolution • Also called forward chaining • Start with the goal and attempt to find a sequence of matching propositions that lead to a set of original facts in the database. • Called top-down resolution • Also called backward chaining • Prolog implementations use backward chaining.

30. How is solution found? • A depth-first search finds a complete sequence of proposition - a proof- for the first subgoal before working on the others. • A breadth-first search works on all subgoals of a given goal in parallel. • Prolog’s designers chose depth-first approach • uses fewer resources

31. Backtracking • When a goal with multiple subgoals is being processed and the system fails to show the truth of one of the subgoals, the system abandons the subgoal it could not prove. • It then reconsiders the previous subgoal,if there is one, and attempts to find an alternative solution to it. • A new solution is found by beginning the search where the previous search for that subgoal stopped. • Multiple solutions to a subgoal result from different instantiations of its variables.